Notation.

1. Materials: general.

A musical notation requires, in essence, two things: an assemblage of ‘signs’ and a convention as to how those signs relate to one another. A written musical notation requires further a spatial arrangement of the signs on the writing surface that makes a ‘system’ of the assemblage; it is this system that forms an analogue with the system of musical sound, thus enabling the signs to ‘signify’ individual elements of it.

Only rarely has music fashioned its own sign systems. It has generally been content to take over systems in use for other purposes (such as the representation of arithmetical values, of speech inflection or of the sounds of natural language). In so doing it has often discarded part of the system and modified the shapes of the signs to suit its purpose. Such signs, the ‘materials’ of notation, can be broadly classified into two categories: the phonic and the graphic. Phonic signs include letters, syllable-signs and word-signs (signs that convey both the meaning of the word and its sound in speech – known as ‘logo-syllabic signs’). Certain systems of numerals also come into this category: systems that assign names to at least the lower range of numbers. Graphic signs include geometric shapes, lines, dots, curves, grids and the like.

Phonic signs are by their nature already representational of sounds outside music. They can be ‘spoken’ as well as written, which increases their communicative power. But they have an all-important additional quality: either they have meaning (like word signs and numbers) or they belong to some system of ordering (like letters and in some cases syllables). These are the properties that were implied above in speaking of the adoption for other purposes of systems already in use.

2. Letters of the alphabet.

For the requirements of an alphabetical notation, it is not in fact the phonic – or perhaps ‘phonemic’, since each letter at least in principle signifies a single sound of language – quality of a letter that is important but rather its position within a conventional order: an alphabet. The ordering of letters in an alphabet offers a ready-made base for notation, as it can be directly related to the intrinsic acoustical order of musical sound. It thus becomes an analogue of musical order: an item in the musical order is specified by reference to its place on the analogous system.

As stated above (§I, 2), the earliest-known alphabetic writing dates to the middle of the 2nd millennium bce. The first known to have an established order of letters is the Hebrew alphabet, traceable back at least to the 6th century bce. This order corresponds to the acrostics in the Bible (Lamentations, Proverbs, Psalms). Until the 17th century alphabetic writing existed in only a small area of the world: the Middle East, the Mediterranean countries, Eastern and Western Europe, South Asia and Korea. The earliest alphabets – Hebrew, Phoenician, Aramaic and North Semitic – all developed between 1000 and 500 bce. From these developed the Greek, Latin, Cyrillic and early Indian alphabets. As to order of letters, the Greek alphabet is close to the Hebrew, the Latin close to the Greek.

One of the advantages of an alphabet for music notation is that it consists of single rather than compound signs – signs that are distinctive and at the same time compact. Another is that it contains a convenient number of signs (alphabets range from about 20 to 50 letters, most having between 20 and 30) to represent a chromatic double octave or a diatonic triple octave; fewer can be selected to represent a single octave in a repeating scheme or the frets on a stopped-string instrument. Moreover, the letters of alphabets are generally assigned names (the fourth letter of the Hebrew alphabet being called daleth, the Greek delta, the Latin and modern Western European de and so forth), so that the notation can be spoken as well as written.

The alphabet was used for pitch notation in ancient Greece, and then around the 10th century in western Europe before being formalized in shape and absorbed into staff notation as clefs (C, F, G) and accidentals (‘b’, ‘h’). The alphabetic system is implicit still in staff notation, since in most European countries the placing of notes on the staff is translated into spoken letter-names (except in France, where they are translated into fixed solmization syllables; see Pitch nomenclature). The Western system is a repeating one, since the letters refer only to pitch classes, not to specific pitches; therefore the 19th-century German philosopher and scientist Hermann von Helmholtz developed a scheme of dashes to indicate pitch register (the dashes deriving from Greek notation but the letters coming from the Latin alphabet): A, B, C–B, C–B, c–b, c' (middle C)–b', c''–b'', c'''–b''' etc. The alphabet has also been used to denote keys, finger positions or frets in many Western tablature systems.

There are many examples of verbal abbreviation in Western notations: the letter p, for example, is used as an instruction to play softly (piano) and, in a rather elaborate formalized fashion (as an alternative to ‘Ped.’), below the staves, to indicate application of the sustaining pedal of the piano. ‘Significative letters’ were used in conjunction with some early Western neumatic notations to indicate duration (c to stand for cito or celeriter, ‘quickly’, i.e. ‘short’ value) and direction of movement (l to stand for levare, s for sursum, both meaning ‘upward’).

In all these non-alphabetic uses of letters, the notation can be described as ‘secondary’: that is, the letters signify words that in turn signify musical elements, rather than signifying musical elements directly. However, such is the force of tradition that formalized letters often cease to be recognizable: by this means a pedal mark has become a graphic sign that refers directly to the pianist’s foot movement. The same is true even for alphabetic uses of letters: the treble and bass clefs are now scarcely recognizable as formalized letters ‘G’ and ‘F’, and have become instead graphic signs for the two fixed pitches g' and f with a range of special technical connotations associated.

3. Syllables.

As with letters, syllable notations fall into two categories: those that operate by reference to an established order of syllables, and thus relate directly to a musical order (‘primary’ notations), and those that use syllabic abbreviations of words, and operate by reference to meaning or name (‘secondary’ notations). Cutting across this categorization is the orthographic one: that some of these syllable systems are expressible as single symbols (ideograms or ‘characters’) while others have to be spelt out in letters.

A classic case of the first (‘primary’) category is the set of Japanese syllables i, ro, ha, ni, ho, he, to. These are the initial seven syllables of an established order of some 48 Japanese characters closely analogous to the order of an alphabet – that is, it is a conventional order rather than an intrinsic one. In Western music terminology in Japan, these first seven function exactly like the Western letters A, B, C, D, E, F, G, with repetition for each octave in the same way. Thus a C major scale is represented as ha–ni–ho–he–to–i–ro–ha, each having a single character to represent it in written form. (A more extensive set from this series was used in 17th-century shamisen tablature to represent successive finger positions from the open bass string to the highest position on the treble string.) A simpler example is the set of syllables for the Balinese five-note slendro scale, a set that rotates through five vowel sounds: ding–dong–dèng–dung–dang. It is almost an alphabetical system using only vowels, save for the fact that Balinese literary script uses characters rather than letters and therefore has no alphabet. The characters for these five notes are shown in fig.3 (see also Indonesia, §II, 1(ii)(b), Table 1).

Similar to this is the set of Chinese syllables for the pentatonic scale: gong–shang–jue–zhi–yu (see fig.4a, with the parallel set of Korean syllables using the same Chinese characters, fig.4b).

The Chinese gongche notation is a more complex system of the same type. It consists of ten characters, or ideograms, each representing a syllable that stands for a note on a largely diatonic scale extending over a 9th. Fig.5 shows these syllables and their characters, with he arbitrarily set to the pitch c. Octave positions are sometimes shown by the addition of an affix or small mark. A chromatic scale could be produced from this by the use of the prefixes gao- (‘high’) to raise a note, or xia- (‘low’) to lower it, by a semitone; but after the 11th century gao- ceased to be used. Korean musicians in the 15th century adopted the ten basic characters, applying their own pronunciation: hap, sa, il, sang, ku, ch’ŏk, kong, pŏm, yuk and o. The Korean notation is called kongch’ŏkpo and it does not use affixes or marks, allowing sa to denote d or d, and similarly with il, kong and pŏm. It is noteworthy that four of the characters in gongche notation are numerals (si is four, yi is one, liu is six and wu is five); thus the notation is partly numerical.

The South Asian system of syllabic solmization is usually written down in Devanagiri script in North India, or Tamil or Telugu script in the South (fig.6). Although notation is generally considered to be of little importance in what are predominantly oral traditions, it is widely used as an aid to memory or as a learning tool. This is particularly true of Karnatak music, which relies to a much greater extent on a body of compositions than does Hindustani music. The syllables themselves may describe the duration of a pitch through the use of a short or long vowel: usually a short vowel stands for a pitch of one mātrā (‘beat’) or less and a long vowel for two beats or more. Symbols modifying the pitches vary from system to system but common devices include a short vertical line above the syllable denoting a sharpened pitch, or a short horizontal line below the syllable showing a flattened pitch. The syllables are arranged on a framework which shows the rhythmic cycle (tāla), one line of notation being equal to one cycle of the tāla (see fig.7).

Rather different, but not unlike the Indian solmization syllables, are the Western medieval ut, re, mi, fa, sol, la. They are indeed syllables in written form, being the initial syllables of the first six lines of a seven-line hymn to St John, the text of which is attested from about 800 and would have been well known in the 11th century when Guido of Arezzo created a solmization system from them. The syllables were by chance distinctive, and operated by reference to a textual order. But their referential character was much strengthened by the fact that the first six lines of the hymn’s melody began successively on the degrees of the scale c–a, and they thus operated by reference also to an established external musical order – though whether the melody existed before the solmization system, or whether it was designed as a supporting aid, is not known. The derivation is shown in ex.1. Out of this succession of notes was created the ‘natural hexachord’, which was flanked by a ‘soft hexachord’ of the same succession transposed a 5th lower and a ‘hard hexachord’ transposed a 5th higher, the three forming together the underlying musical system known as musica recta. This total system was transposable to other relative pitch levels, and isolated hexachords of ‘alien’ pitch levels could be introduced, each hexachord having the identical set of syllables (see Solmization, §I, 1; Hexachord; Musica ficta; and Guido of Arezzo).

Javanese titilaras kepatihan (‘cipher notation’) whose seven syllables, ji, ro, lu, pat, ma, nem and pi, are abbreviations for the numbers 1 to 7: siji, loro, telu, papat, lima, nĕm and pitu.

In addition to their referential power and their capacity (as abbreviations) to refer to the meanings of words, syllables have a further quality: onomatopoeia. The degree of openness or closedness of the vowel sound, the presence or absence of initial and terminal consonants, and the character of any such consonants (dental, labial, nasal etc.) is frequently used to reflect tone-colour, attack or rhythmic value. A simple case is ‘scat singing’ in jazz, where doo is used for a stressed and sustained note, bee for a short unstressed note and bop for a staccato note, stressed but often off the beat. Thus the pattern bop bop bee-doo-bee-doo-bee-doo-bee can be sung to the rhythmic pattern shown in ex.2 by a scat singer almost as if it were a rhythmic solmization; it can also be used as a verbal communication of the rhythmic pattern and is thus halfway to being a notation of a rudimentary and imprecise kind.

Onomatopoeic syllables are used by Ewe drummers in Ghana. Two strokes of the butts of the hands in succession at the centre of the drumhead are represented by the syllables ga-da, the softer sounds of the hands brushing across the centre of the drum by ka-tsa, and the use of splayed fingers to produce a combination of round drum tone and sharpness of attack by ga-tsya. But the relationship between drum sounds and syllables goes beyond representation: it is an identity – the drums are themselves thought of as producing the syllables, and when syllables are spoken to the drums they are spoken at the same pitches as the drums. Oral drum notations are widespread in South Asia and are described at length elsewhere in the dictionary (see India, §III, 6(iii)(a)–(b); Mrdangam §1; and Tabla, §3).

4. Syllables and vowel acoustics.

Whereas the syllabic systems discussed above (§II, 3) represent specific pitch classes, scale degrees or performance techniques, other syllable systems, less formalized but highly regular, tend to use vowels and consonants in accordance with their acoustic phonetic features to reflect iconically relative pitch, duration, resonance, loudness and so on. The relations between such syllables and musical features are thus far from arbitrary.

Vowels, in particular, are often used in accordance with what phoneticians call their intrinsic pitch, intensity and duration (see Hughes, 1989). For example, the vowels i, e, a, o, u in their approximate Spanish or Japanese pronunciations are often perceived as constituting a descending pitch sequence (reflecting their ‘second formant’ pitches). Many cultures exploit this intrinsic pitch ordering of vowels in teaching instrumental music. Thus the fixed melodic repertory of the Japanese nōkan flute is taught by singing mnemonics such as ohyarai houhouhi, in which successive vowel pairs reveal melodic direction with over 90% accuracy: the sequences ohya, rai, uho and uhi all represent melodic ascents, with uhi signifying the largest leap because its two vowels are at opposite ends of the pitch spectrum; iho and hou represent melodic descents (see Japan, §VI). In several such systems in Japan (where scholars call them shōga) and Korea (yukpo or kum), exceptions to this relationship between vowels and melodic direction often result from the competing acoustics of intrinsic duration and intensity, whereby a is favoured for comparatively long, loud or metrically important notes, while i and u are used for weak or short notes, with e and o in between.

Consonants also play a role. In the sequence teren for Japanese shamisen lute, t indicates a normal, resonant down-pluck; r signifies a gentler sound (never the initial note of a phrase), either an up-pluck or a left-hand pizzicato; and n shows that the second sound is longer than the first. In many drum mnemonics throughout the world, a final k – a stopped sound – represents a damped stroke, while a final nasal or vowel shows that the sound is left to resonate and decay naturally.

Such systems could be called ‘acoustic-iconic systems’. Their oral origins are reflected in the lack of any indigenous explanations for their patterning; their iconic symbolic power (teachers emphasize their importance) lies precisely in their acoustic naturalness. Today, however, such systems are often written down. In many Japanese and Korean written notation systems (which tend to be different for each instrument), each line of tablature or pitch notation is accompanied by a line of acoustic-iconic syllables (see below fig.16b). The fact that this may happen even when this line adds no information to the tablature, as in shamisen bunka-fu notation, confirms the traditional importance of such syllables in transmission.

5. Words.

Words have assumed a place in Western staff notation only during the last 350 years or so. They have done so with the rise of the score and of the desire of composers to specify the instrumental forces for their music; and this has happened simultaneously with the desire also to specify tempo, mood, character and detailed matters of tone production and attack (see Tempo and expression marks). Thus, for tempo, words such as largo and allegro were introduced, and a set of modifiers was applied to them to express shades of meaning: molto, assai, non troppo, -etto and so on. Such words, together with others expressing mood and character – such as andante, scherzo and scherzando, dolente – generally appear at the beginnings of sections or whole movements (even serving as titles). It is no coincidence that their introduction occurred in that part of the Baroque period during which the doctrine of the Affections (Affektenlehre) was the predominant aesthetic, and that a great expansion of the range of terms, and of the languages from which they were drawn, took place during the Romantic era. Other words, such as rallentando, ritenuto and stringendo for tempo, and pizzicato, leggiero and flautando for attack and tone production, control temporary changes and localized features, and thus appear in the course of the musical notation.

The most striking aspect of the Western use of words is its consistently auxiliary nature. Words are almost never on the staff, but above or below it, or in the margin. They were not integral to the system when Western staff notation was being formulated during the late Middle Ages, when even the part-names tenor and contratenor were not always supplied and when a name was almost never given to the top voice. They have since become indispensable to staff notation, but have retained their auxiliary position, so that a music copyist will enter the note symbols representing pitch and rhythm before finding the most convenient places in which to add the verbal elements of the notation so that they can easily be read. This situation is not merely the result of historical circumstance. There is the more pragmatic ground that Western words are written alphabetically and thus have two disadvantages for notational use: they occupy a lot of space, and (more important) they take time to read and understand.

These disadvantages are not present in most East Asian writing systems, where characters represent syllables or words. The classical Chinese language is in essence made up of monosyllabic words that do not change or acquire prefixes or suffixes under different grammatical conditions as they do in most Western languages; the most that they do is become incorporated into compounds of monosyllables (e.g. nü-ren means ‘female’ + ‘person’, thus ‘woman’). So when, in the Chinese fixed-pitch system of the 12 lü, the names of individual pitches are written down, each pitch is represented by a pair of ideograms. Moreover, when the note names huangzhong (‘yellow bell’, pitch c), linzhong (‘forest bell’, g), yingzhong (‘answering bell’, b) and jiazhong (‘pressed bell’, d) are written down, the second ideogram is always the same. In fact, when the names of all the chromatic pitches are written down their first ideograms are distinctive (i.e. they do not require the second ideogram to distinguish them from others): ‘yellow bell’ (c), ‘greatest tube’ (c), ‘great frame’ (d), ‘pressed bell’ (d), ‘old purified’ (e), ‘mean tube’ (e or f), ‘luxuriant vegetation’ (f), ‘forest bell’ (g), ‘equalizing rule’ (g), ‘southern tube’ (a), ‘not determined’ (a) and ‘answering bell’ (b). Thus in notation the names are abbreviated to their first words, as shown in fig.8; see also China, §II, 4, Table 2

Words are often used as ‘labels’ or memory aids for standard melodic formulae. The so-called neumatic notation of Japanese karifu relies on words beneath the graphic symbols to indicate a large amount of the melodic inflection. The same is true of Tibetan Buddhist notation, whose neumes have written above them verbal instructions as to vocal production, directional movement and ornamentation. In oral traditions, groups of words and whole phrases are used as mnemonics for standard patterns. Ex.3 shows an African instance: the sentence ‘b’o tan ma tun ro’ko Baba ma j’iyan tan’ (‘else I must go back for more, Father, don’t finish the yam’) is broken up into syllables in the piece of music for a pair of hourglass drums and a small kettledrum, from the Yoruba in Nigeria.

6. Numbers.

Numbers would perhaps seem to be the most readily adaptable of all materials for notational purposes. They provide a reference system that can control any or all parameters of musical sound, as the pioneers of integral serialism demonstrated. In particular, pitch can be controlled by assigning numbers to the notes of a scale, to the keys of a keyboard, to the finger positions or frets of a string instrument, or to the holes or valves of a wind instrument (or the fingers of its players), and pitches can be represented in this way individually or relative to each other by the measurement of interval in a melody or chord. Duration lends itself most naturally to numerical representation because the hierarchy of beats in musical metre involves subdivision of a large time unit or multiplication and addition of small units and is thus intrinsically arithmetical. Any other parameter, such as loudness, attack or tone-colour, can in theory be measured as a scale of values and then be represented by those values as numbers (e.g. 1 for extremely soft, 5 for moderate and 10 for extremely loud, with the intervening numbers for gradations between these), but such systems have tended to be restricted to the coding of music for computers.

In practice, the measurement of pitch by numbers (other than for scientific purposes) has been very rare, and is a predominantly modern phenomenon. Perhaps the most important was the Galin-Paris-Chevé method from the mid-19th century. The numbers 1–7 represented pitches, with a dot below for lower octave and above for upper. The numbers were purely visual: they were spoken as ut, re and so on. This system was adopted in modified form in China, Japan and other countries. The abbreviated number system of the Javanese kepatihan notation has already been discussed as a syllabic notation (§3 above). Notational systems for the Japanese koto use the numbers 1–13 in Japanese characters (though the characters for 11–13 are not true numbers). But these are secondary systems in the sense that the numbers refer to the 13 strings on the instrument rather than directly to the pitches that they produce: the pitches will depend upon the scale to which the instrument has been tuned. Fig.9 shows the 13 characters and their Arabic numeral equivalents, together with the notes that they represent in the most common tuning (hirajōshi); because of the pentatonic scale in use the number of any note is five away from that of its octave. A similar system exists for the 25-string Chinese se, using the Chinese numbers 1–25. An even more extended number notation for pitch (not fixed-pitch) is the pitch representation of the Ford-Columbia computer input language for music. There, the numbers 1–49 designate leger lines and staff lines and their intervening spaces: thus 1 is the tenth leger line below the staff, 2 the space above that, and so on. The entire set of numbers is dependent on the clef governing the staff. One type of modern Japanese shamisen notation uses three kinds of numeral: Arabic numerals form a direct pitch notation using 1–7 for an ascending scale in the central octave and the same numbers with a dot to the left and the right respectively to represent the notes of the lower and higher octaves: Roman numerals I–III to the right of these numbers show the three strings of the instrument; and Japanese characters for the numbers 1–3 indicate which finger is to be used.

Probably the earliest, and at the same time the most complex, number notation is the jianzi pu for the Chinese Qin. Like the notation for the Japanese Koto, its numbers refer directly to the means of production and only indirectly to the sound produced. The strings of the qin can be stopped at studs which serve as frets, or at points between them. Numbers are used to indicate all three of these: 1–7 for strings, 1–13 for the studs (hui, in ascending order), and 1–10 as a guide to the distance between two studs (fen). The three (often only two, because there is not always a fen number) are gathered together into a complex note symbol, with the string number in the lower half and the other two in the upper half, together with other symbols to indicate the stopping finger, the plucking finger and certain technical details. Fig.10a shows the Chinese numerals, and Fig.10b shows a single note symbol made up of five elements, of which three are numbers and the remaining two special symbols.

Western notations use Arabic numerals in keyboard tablatures and Italian lute tablature of the Renaissance. They are also used in staff notation to indicate metre and to show unusual rhythmic groupings. Thus time signatures have a denominator that represents a level of note value (on a scale from semibreve = 1 to minim = 2, crotchet = 4, quaver = 8, semiquaver = 16 etc.: these numbers are used in American and German parlance to describe the levels of value, with semiquaver being ‘16th-note’ and ‘Sechzehntel’) and a numerator that indicates the number of units of that level in a bar. A triplet in a duple metrical context is indicated by a number 3 within a slur mark, and in Chopin’s music, for example, this is extended to groupings of 11, 21 and so on.

7. Graphic signs.

The act of writing a succession of notational syllables is graphic because it traces a path across the writing surface. That path is the analogue of the passage of music through time. The direction of the path tends to follow the prevailing direction of writing for the language of the country concerned. The Chinese, Korean and (to some extent) Japanese languages have been written from top to bottom, in columns beginning at the right-hand side of the page: consequently most Chinese and Korean notations have been written in columns in the same way, and so have Japanese instrumental notations. On the other hand, Japanese neumes (karifu, meyasu) are written horizontally from right to left. Tibetan, Javanese, Balinese, Greek and Latin are all written horizontally from left to right. Consequently Tibetan neumes and Javanese and Balinese ideographic notations all read in that direction, as do Western neumes, alphabetical and staff notations, and tablatures.

This path across the writing surface may be more precisely defined by the spacing out of notational symbols so that each space represents a beat of the prevailing metre. Thus in Chinese gongche notation the ideograms representing pitches are equidistant down their columns; and when there is a gap in the column of ideograms the previous pitch is assumed to continue to sound for a second beat. Alternatively, beats may be marked by a graphic symbol. One such is a dot – as in Japanese gagaku notation, which uses small dots for the basic beat and large dots for every fourth or eighth beat – defining two levels of metre (such dots often indicate the sound of percussion). Another such symbol is a line drawn at right angles to the path – as in Korean ‘mensural’ chŏnggan notation (which encloses its symbols in a grid with thin and thick horizontal lines to show their places within two levels of metre), in modern Japanese Ikuta-school koto notation (which uses short and long horizontal lines to show the same), or in the bar-lines of Western staff notation. Such graphic marks have the economic advantage that the spaces allocated for beats need not be equal in size: metrical units containing several symbols can be given more space than units with few or none.

So far, the path discussed has been one-dimensional. But it is also possible to define a broad path across the writing surface and to treat the width of the path as a second dimension. This dimension can be made the analogue of some other parameter of music: in particular, of a technical aspect of an instrument – the string or course of a zither or lute, for example, or the keys of a metallophone – or of pitch (as in diastematic neumatic notations) or volume (as in some electronic scores).

A system of notation recently discovered in Mongolia and used in Nomyu Khan monasteries in the 18th and 19th centuries is thought to describe melodic pitches arranged according to the tuning of the half-tube zither (yatga). This notation takes the form of lines tracing the broad tonal contours of the melody rather than a series of discrete notes and should probably be regarded as signifying the ten strings of the yatga running horizontally across the surface of the page (fig.11). Much more research is needed into this system, however, before definite conclusions can be drawn about what precisely it represents.

A simple way of using the second dimension for pitch in vocal music without need for new signs is to ‘height’ the syllables of text themselves, as in dasian notation; however, this does not work for music with any degree of melisma.

Western staff notation is another form of the same procedure. The dots, however, are made void or full and supplied with stems and flags or beams to represent grouped durations in such a way that the horizontal dimension between two bar-lines can be treated flexibly. In other words, the exact proportional use of space to time is obviated by the application of duration symbols to the dots. Such duration symbols are themselves graphic signs; moreover, their beaming into groups conveys other information such as accentuation, phrasing, differences of dynamic level and the application of syllables.

Such graphic signs as these last belong to a reference system – in this case a system representing duration and comprising only five elements: a stem, a flag, a dot and two kinds of note head; if the void head can be regarded as an ‘absent’ head then they constitute four signs, each of which operates in a binary way (see fig.12) as present (+) or absent (−) in appropriate positions. Similar graphic reference systems are the signs of Japanese goin-hakase notation and its later modifications, karifu and meyasu, and also the ‘teardrop’ notation, gomafu, and its later development bokufu. In the first three of these, a notched-stick shape is rotated through eight positions that correspond to eight pitches of a pentatonic scale, thus spanning a 10th (fig.13). They are linked together to form a graphic trace extending leftwards from the text syllable. The trace is not however an exact representation of pitch since the notation relies on the names of standard melodic formulae written beneath. In gomafu and bokufu marks are put to the left or right of syllables to indicate such standard formulae.

A comparable system is that of so-called dasian notation from the 9th century. The materials for this constitute a spatial matrix with pitch as the vertical axis and time as the horizontal, and the Greek prosōdia daseia in two transformations: first modified into four distinct forms to designate the four pitches of the tetrachord; and then with each form reversed, inverted, and reversed and inverted to represent the higher pair of tetrachords, with the first two also shown facing downwards giving 18 signs in all (fig.14; see also Organum, §2).

A rather special case of a notation that is graphic and operates on binary principles is Braille notation for the blind. The basic material is a display of six dots arranged in a matrix two (across) by three (down). These dots are raised from the surface of the paper by embossing, so that they can be felt. Each dot is either present (embossed) or absent. The pattern of the upper four dots designates pitch and the pattern of the lowest two designates duration. There are special patterns for octave register, accidentals and other notational devices.

Other graphic signs do not belong to such a system. They represent movement and shape in music, and thus display elements in relation to each other. They cannot specify individual musical elements, as can referential notations. Notations that rely on graphic relationship have only relative pitch significance, even when they have taken over an existing sign system, such as the accentual signs of the 5th-century Syriac writers (nine principal signs denoting main and subsidiary pauses, interrogative accents and so on, and made up of dots in different placings and groupings), or those of the 9th-century Tibetan scribes, or the classical Greek prosodic accent signs from which Byzantine ekphonetic notation evolved, or the signs of the Roman grammarians from which Western neumes are sometimes alleged to have developed (see Ekphonetic notation). That is because, without the imposition of a grid system, distance is difficult for the eye to judge, for both reader and writer. The line of text to which a melody was to be sung could be used as a pitch demarcation, with dots above and beneath syllables signifying higher and lower pitches, as in some Vedic chant books.

Neumes are stylized contour shapes. Their rises and falls and level lines represent rises and falls and level passages in a melodic line. Neumes thus differ from ekphonetic notations (though the dividing-line is sometimes difficult to draw) in that they are not concerned with inflection of voice between high, medium and low, but with groups of sung pitches rising and falling over a quite narrow range: a neume may represent a pattern of intervals whether it lies high or low in the voice’s compass. Each neume is thus self-contained; the pitch relationships between a neume and its neighbours are not necessarily graphically shown, though in the ‘heighted’ neumes that appear in Western European sources from about the 10th century some attempt is made to show this.

The neumes of Tibetan Buddhist notation are made up of curves and undulations of varying amplitudes that represent directional movement of the voice, together with crosses or circles representing the sound of drums or cymbals (see Tibetan music, §II, 4).

8. Hybrid systems.

Many notations are hybrid in that they use more than one type of material. Japanese karifu, for example, has already been discussed above (§§5 and 7): the notation is generally called ‘neumatic’, but is equally a verbal notation in that Japanese characters under the graphic neume shapes give essential information about melodic turns of phrase (see fig.15). Tibetan Buddhist chant notation has also been discussed in these two contexts, since verbal instructions as to vocal production and other aspects of performance appear above the line of neumes. The jianzipu notation for the Chinese qin has also been shown to contain special symbols as well as numbers. In the following discussion, three notations will serve to illustrate the interaction of materials.

Occasionally two materials interact in a tautologous way – that is, they call for the same musical result but by different visual means. But most interactions are in some way complementary.

A notation that combines tautologous and complementary uses of different materials is the notation for the kŏmun’go or Korean zither. The notation is known as hapchabo and dates from the 15th century. It is an adaptation of Chinese jianzipu, but whereas the Chinese notation uses numbers for the designation of both string and stopping-point, the Korean notation assigns names to its six strings (see fig.16a) and uses the string name in conjunction with a number for the stopping-point. Added to the left of this name and number is a graphic symbol indicating the left-hand stopping finger, and where necessary symbols for direction of stroke, ornaments and so on. The central part of the notation is thus a complementary hybrid of word, number and graphic signs. This compound symbol is placed in the middle of three columns. In the right-hand column appears the central scale degree kung from the Korean oŭmyakpo ‘five-note abbreviated notation’, and in the left-hand column appear a group of Korean letters that signify one of the Korean solmization syllables from series such as tŏng, tung, tang, tong and ting, or rŏ, ru, ra, ro and ri (see fig.16b). All these notational elements, with double tautology as to pitch, point to B stopped with the left thumb and plucked with an outward stroke (fig.16c).

The most fully hybrid of all notations is the staff notation of the West. It uses all the types of material discussed above. Fig.17, the beginning of the Prelude from Liszt’s first book of Etudes d’exécution transcendante, contains examples of letter notation in (1) the clefs, which are formalized letters G and F; (2) the accidentals, which are formalizations of ‘b’ () and ‘h’ (, ); and (3) the dynamic marking f, which is an abbreviated verbal notation. It also contains syllabic notations, both of them abbreviations for words: (1) the pedal application Ped., so formalized as almost to be a pure graphic symbol; and (2) the technical instruction rinforz., for rinforzando. It also contains two examples of full verbal notation: (1) the general designation ‘Presto’ for the tempo and character of the Prelude as a whole; and (2) the localized technical instruction energico. It has several examples of numerical notation: (1) the tempo specification, which supplements the tempo aspect of the verbal instruction ‘Presto’; (2) the indication of octave transposition; (3) the fingering in bar 2, which is a technical notation; and (4) the indication ‘19’ for rhythmic grouping. But its main constituents are graphic notations: (1) the staves, bar-lines and brace; (2) the note symbols and rests; (3) the time signature ‘’, which derives from the medieval half-circle designating duple division of breve and semibreve (and thus is not in origin a verbal abbreviation of ‘common time’, though it has acquired this status in more recent times); (4) the phrase mark, which is partly a graphic duplication of pitch and partly an indication of phrase articulation that duplicates the beaming of note symbols; (5) the pause sign; (6) the pedal release sign; (7) the staccatissimo signs; and finally two suggestively graphic signs, (8) the spread-chord indication in bar 1, and (9) the decrescendo and crescendo signs.

From this it can be seen that staff notation is a complex multiple hybrid system with very low redundancy, partly technical and tablature-like, partly representational.

2. Polyphony and secular monophony to c1260.

BIBLIOGRAPHY

H. Riemann: Studien zur Geschichte der Notenschrift (Leipzig, 1878/R)

H. Riemann: Geschichte der Musiktheorie im IX.–XIX. Jahrhundert (Leipzig, 1898, 2/1921/R; Eng. trans., 1967/R)

C.F.A. Williams: The Story of Notation (London and New York, 1903/R)

J. Wolf: Handbuch der Notationskunde (Leipzig, 1913–19/R)

J. Wolf: Musikalische Schrifttafeln (Leipzig, 1922–3, 2/1927)

W. Apel: The Notation of Polyphonic Music, 900–1600 (Cambridge, MA, 1942, rev. 5/1961; Ger. trans., rev., 1970)

C. Sachs: The Rise of Music in the Ancient World (London, 1944)

A. Machabey: La notation musicale (Paris, 1952, 3/1971)

R.C. Pian: Sonq Dynasty Musical Sources and their Interpretation (Cambridge, MA, 1967)

W. Tappolet: Notenschrift und Musizieren: das Problem ihrer Beziehung vom Frühmittelalter bis ins 20. Jahrhundert (Berlin, 1967)

L.U. Abraham: Einführung in die Notenschrift (Cologne, 1969)

W. Kaufmann: Musical Notations of the Orient (Bloomington, IN, 1972)

M. Hood: The Ethnomusicologist (Kent, OH, 1982)

A. Marett: ‘Tōgaku: Where Have the Tang Melodies Gone?’, EM, xxix (1985), 409–31

D. Hughes: ‘The Historical Uses of Nonsense: Vowel-Pitch Solfège from Scotland to Japan’, Ethnomusicology and the Historical Dimension, ed. M.L. Philipp (Ludwigsburg, 1989)

T. Ellingson: ‘Notation’, Ethnomusicology: an Introduction, ed. H. Myers (London, 1992), 153–64

R. Widdess: ‘The Oral in Writing: Early Indian Notations’, EMc, xxiv (1996), 391–405

Notation

III. History of Western notation.

1. Plainchant.

3. Polyphonic mensural notation, c1260–1500.

4. Mensural notation from 1500.

5. Alphabetical, numerical and solmization notations.

6. Non-mensural and specialist notations.

(ii) Principal characteristics.

1. Plainchant.

(i) Introduction.

(iii) Origins and earliest examples.

(iv) Early notations, 9th–11th centuries.

(v) Pitch-specific notations, 11th–12th centuries.

(vi) Pitch-specific notations, 13th–16th centuries.

(vii) Printed notations.

Notation, §III, 1: History of Western notation: Plainchant

(i) Introduction.

The earliest forms of plainchant notation, probably dating from the 9th century onwards, relied on signs generally known as ‘neumes’. Such neumatic notation is clearly of great historical importance, for it stands at the beginning of the development that led to the notational forms in use today. Yet the time, place and circumstances in which neumes were first used are all disputed. Ever since medieval plainchant was revived in the 19th century the rhythmic interpretation of the melodies has been controversial, and the debate continues still. To a lesser extent the precise significance of certain signs (e.g. the oriscus, quilisma and liquescent neumes) and the possible use of chromatic notes in a basically diatonic system are also the subject of argument. All these areas of uncertainty stem from the fact that the notation represents only a few aspects of what was sung. So not only must modern scholars and performers interpret the signs committed to parchment by medieval scribes, they also have to elucidate the conditions that determined what should be represented in musical notation (and also what need not be notated).

The foundations for the systematic investigation of chant notations were laid principally by the monks of Solesmes, as part of the restoration of medieval chant for modern liturgical use. The facsimiles published in the Solesmes series Paléographie musicale (particularly 1st ser., ii–iii, 1891–2) and in Bannister's Monumenti vaticani (1913/R) are still of immense value. The volumes of Paléographie musicale are usually accompanied by notational studies, beside which the works of Wagner (1905, 2/1912) and Suñol (1925) are the most comprehensive. Subsequent detailed studies of many regional types of chant notation are cited below. Stäblein (1975) and Corbin (1977) are modern surveys of the whole area, and Hourlier (1960) is a useful set of facsimiles with commentary.

Although the different styles of chant notation show agreement on the basic principles, they vary considerably from area to area and period to period; this variety reflects the circumstances (ecclesiastical-political, geographical, liturgical, educational) in which notation was used, and can, therefore, illuminate the history of ecclesiastical music in striking ways.

The following survey describes the principal characteristics of neumatic notation, before addressing the problem of its origins. The main regional styles of neumes are distinguished, in four historical phases: the period before the introduction of the staff; the staff notations of the 11th and 12th centuries; the less numerous forms of the 13th century onwards; and the notation of printed chant books. For each of the first three epochs a separate table of neume signs has been constructed (Table 1, 2 and 3).

Notation, §III, 1: History of Western notation: Plainchant

(ii) Principal characteristics.

In general Latin usage the word neuma meant ‘gesture, sign, movement of the hand’; in a musical sense it denoted a melodic element, often an untexted melisma. From the end of the 10th century, however, the term was also used for the graphic signs used to represent melodies, typically designating a sign or group of signs attached to one particular syllable of text (see Atkinson, 1995; see also Wagner, 1905, 2/1912, p.15).

From this period onwards also survive tables that name the signs (‘nomina notarum’ or ‘nomina neumarum’), with some variance of nomenclature depending on local traditions (see Huglo, 1954; Bautier-Regnier, 1964; Odenkirchen, 1993; Bernhard, 1997). Modern usage generally follows the practice of the tabula brevis found in a number of German sources. Several of the names appear to be of Greek origin or at least to affect a Greek derivation. The commonest are as follows (see Table 1, 2, and 3 for their melodic significance: step upwards, downwards etc.): virga (Lat.: ‘rod’, ‘staff’); punctum (Lat.: ‘point’, ‘dot’); tractulus (from Lat. trahere: ‘to draw out’); pes (Lat.: ‘foot’) – also known as podatus (probably pseudo-Gk.); clivis (from Gk. klinō: ‘I bend’, via Lat. clivus: ‘slope’) – also known as the flexa (Lat.: ‘curve’); torculus (Lat.: ‘screw of a wine-press’); porrectus (Lat.: ‘stretched out’); scandicus (from Lat. scandere: ‘to ascend’); climacus (from Gk. klimax: ‘ladder’); trigon (from Gk. trigōnos, Lat. trigonus: ‘triangular’); oriscus (possibly from Gk. horos: ‘limit’, or ōriskos: ‘little hill’); salicus (from Lat. salire: ‘to leap’); quilisma (from Gk. kyliō: ‘I roll’, kylisma: ‘a rolling’).

The signs are usually classified as simple, compound, special (sometimes called ‘ornamental’) and liquescent. The simple neumes (most of those in Tables 1–3) consist of up to three notes and can be extended or combined to make compound neumes of four to six or even more notes. Some signs, which may be modified forms of the conventional neumes or additional letters, appear to indicate special features of performing practice (articulation, ornaments, agogic nuances etc.), but the manner of their performance is often unclear today.

A further distinction touches upon the different styles of writing neumes. In some areas signs representing two or more notes in a single stroke were preferred, while in others discrete dots or short strokes for each separate note were favoured. An example of (predominantly) stroke notation is early German notation, especially the sophisticated version practised at St Gallen. (Because of the hypothesis that sees the origin of stroke neumes in the accents of classical prosody, German and French notations and all types more or less closely related to them are often referred to as ‘accent neumes’; this term will be avoided here.) Aquitaine is the best example of an area where a notation consisting primarily of points was used. Most areas, however, mixed extended strokes and dots, and the distinction has often been over-emphasized to buttress arguments concerning the origins of neumes (see below, §1(iii)).

The virga and punctum each represent a single note. In stroke notations the virga was used for notes of relatively higher pitch, the punctum for relatively lower ones. Many other notational styles make only restricted use of the virga. Sometimes the punctum was drawn in elongated form, called the ‘punctum planum’ in older literature and the ‘tractulus’ in recent writings. Some manuscripts use both punctum and tractulus and appear to distinguish rhythmically between the two, the former being shorter, the latter longer. In the important early manuscripts from the Laon/Reims area (containing Messine neumes) the punctum takes the form of a small hook or barb, called the ‘uncinus’ in recent writings. In representing passages of simple recitation on a single note some sources prefer the virga, others the punctum.

The significance of most of the simple and compound neumes is more or less clear, but many of the special neumes are difficult to interpret; manuscripts vary to the extent in which they use these signs. The oriscus seldom appears alone over a syllable, but rather as part of a group of signs, or combined in special signs: virga strata(virga+oriscus; also known as gutturalis or franculus); pes stratus (pes+oriscus), pes quassus (oriscus+virga), salicus (punctum+oriscus+virga), pressus maior and minor (virga+oriscus+punctum and oriscus+punctum respectively, the final punctum being a lower note). Although in many contexts the oriscus seems to signify the repetition of the previous note, it has also been suggested that the neume may represent a non-diatonic note, or some agogic or articulatory peculiarity. The quilisma sign usually appears between two notes a major or minor 3rd apart, but it has also been interpreted as indicating a peculiarity of delivery, for example, a chromatic glissando, a turn or a rhythmic nuance. While the last note of the trigon is relatively lower, the relationship of the first two is unclear; they may represent the same pitch, a semitone ascent or a non-diatonic interval. Some sources use strophici, which may signify a special type of articulation.

The signs known as ‘liquescent’ neumes are linked to liquid and sonant consonants and diphthongs in the text at a syllable change; they appear to involve a form of half vocalization of the note in question, passing from one syllable to the next. Two notes in ascending order, where the second is liquescent, are indicated by the epiphonus, and two notes in descending order with liquescence by the cephalicus.

Although many chant notations are recognizable at a glance, at least in a general way, their systematic investigation depends on the isolation of each sign in a particular notation and of all constituent elements within every neume, and the painstaking comparison of one source with another in the way these elements are used. Basic structural features include the direction of the script (axis) in ascending and descending strokes or groups of notes (diagonal, vertical etc.; see Tables 1, 2 and 3), and the way in which individual notes are combined in strokes or groups of signs. These are to be distinguished from calligraphic features such as the manner in which curved strokes or note-heads are drawn, or the degree of thickness of elements within a sign. The structural and the calligraphic features of a script vary according to time and place independently of each other.

Corbin (1977) introduced the concept of ‘contact neumes’, meaning a neume foreign to the area and predominant type of notation of a particular source: the neume may have been adopted by the notator of a manuscript as a result of contact with the foreign type. Corbin also used the term for a notation whose signs were derived from two or more earlier types; such a notation is here called ‘mixed’ or ‘hybrid’.

Notation, §III, 1: History of Western notation: Plainchant

(iii) Origins and earliest examples.

Precisely when and where neumes were first used in the medieval West is not known. Isidore of Seville, writing in the middle of the 7th century, stated in his Etymologiae that melodies could not be written down (GerbertS, i, 20), and no concrete evidence exists from anywhere in the West for the use of notation before the Carolingian era. Necessity being the mother of invention, the reigns of the Frankish kings Pippin the Short (751–68) and Charlemagne (768–814) are thought to be the most likely period when a pressing need for plainchant notation could first have arisen. At this time the Franks made strenuous efforts to remodel their liturgical practices along Roman lines and, during the reign of Charlemagne, initiated a wide-ranging programme of educational reform, which might have included music writing. A positive view in this regard is taken, for example, by Levy (1987 etc.) who interprets passages in several 8th-century documents as referring to notation. For example, the decrees of the Council of Clovesho in England (747) refer to ‘[cantilenae] iuxta exemplar quod videlicet scriptum de Romana habemus ecclesia’ (‘[chants] according to the written exemplar, that which we have from the Roman Church’; A.W. Haddan and W. Stubbs: Councils and Ecclesiastical Documents Relating to Great Britain and Ireland, Oxford, 1869–71, iii, 137); however it is not clear whether the written exemplar contained only chant texts or notation for them as well (see Hiley, 1993, p.297 for a negative view). Furthermore, Charlemagne's Admonitio generalis (789) decrees ‘Et ut scolae legentium puerorum fiant psalmos notas cantus compotum grammaticum per singula monasteria vel episcopia et libros catholicos bene emendate’ (‘… that schools cultivate reading by the boys: psalms, notes [notas], chant [cantus], the computus, grammar, in each monastery or bishop's school, and accurate versions of catholic books …’; MGH, Capitularia regum francorum, i, 1881, p.60); although the two words ‘notas cantus’ might be taken together to mean ‘[notational] signs of the chants’, they more probably refer to two quite separate activities: ‘writing, singing’ (see Haas, 1996, p.152). None of the extant writings of the various scholars and advisors associated with Charlemagne's court mentions music notation and the earliest definite references to neumes are by Aurelian of Réôme (c850; CSM, xxi, 1975, chap.19). By the end of the 9th century Hucbald already knew of several different styles of notation (GerbertS, i, 117); his statement is confirmed by surviving examples.

The dating of the earliest examples is fraught with uncertainty and relies in large measure on palaeographical estimates of the date when the accompanying literary text was written. Three dozen or more specimens from the 9th century have been proposed; Table 4 is a list of many of them, a few of which are no doubt dated optimistically early. Most examples are single items in books that were never intended to contain more: several are notations of the Exultet chant in a sacramentary, or of the Genealogy of Matthew or Luke in an evangeliary. Often it is difficult in such cases to decide whether the neumes were added at a later date.

The earliest surviving complete chant books with notation – the graduals F-CHRm 47, LA 239 and CH-SGs 359 – date from the end of the 9th century or the beginning of the 10th; F-LA 266 is a fragment of a cantatorium slightly older than LA 239. VAL 407 may have been copied at the same scriptorium as the gradual CHRm 47. (The sacramentary-gradual AN 91, possibly from Angers and notated with Breton neumes – see PalMus, 1st ser., i, 1889, pl.XXII and p.148 – has also occasionally been dated to the 9th century, but is more probably of the 10th.) Ten palimpsest leaves of what appears to have been a notated 9th-century gradual survive in D-Mbs Clm 14735. The existence of several 9th-century books containing the texts of Mass chants – unnotated graduals in other words – from important centres such as Corbie, Nivelles and Senlis (ed. R.-J. Hesbert: Antiphonale missarum sextuplex, Brussels, 1935) suggests that before the late 9th century such books were not normally provided with notation. On the other hand, two notated fragments dating from the late 9th century have survived from what appear to have been Office antiphoners, one with Breton neumes and one with German. These predate the earliest surviving complete notated antiphoners by a century. The possibility that Charlemagne promoted a notated archetype of the chant repertory, as argued by Levy, thus seems somewhat unlikely on chronological grounds. Although several centres were clearly versed in the practice of music notation well before the end of the 9th century (e.g. Regensburg in the first half of the century, Laon in the second, and St Amand), there is little sign of a concerted effort to establish complete notated repertories for Mass or Office during the ‘first Carolingian renaissance’.

While Palaeo-Frankish, French and German, Breton, Laon and Spanish neumes are represented on Table 4, there are no surviving examples of 9th-century notation from Aquitaine, Italy or England.

No single explanation of the origins of neumatic notation has gained wholehearted acceptance. The prosodic accents of Alexandrine grammarians (see Laum, 1920 and 1928) have frequently been cited as the ‘ancestors’ of the neumes (Coussemaker, 1852; Pothier, 1880; Mocquereau in PalMus, 1st ser., i, 1889; Suñol, 1925; Cardine, 1968). According to this theory the acute accent gave rise to the virga, the grave accent to the punctum and the circumflex to the clivis or flexa. Yet, with the exception of Palaeo-Frankish neumes, the grave accent is hardly recognizable in most notations. Only one medieval treatise explains neumes in terms of accents, the anonymous Quid est cantus? (?11th century; I-Rvat Pal.lat.235; see Wagner, 1905, 2/1912, p.355), which contains such phrases as ‘De accentibus toni oritur nota quae dicitur neuma … Ex accentibus vero toni demonstratur in acuto et gravi et circumflexo’. Atkinson (1995) has convincingly argued that the author of the treatise had Palaeo-Frankish notation in mind. Nevertheless, while the prosodic accents were certainly known in Carolingian times, they can have suggested hardly more than some rudimentary elements of a system for music notation.

The notation of the earliest graduals mentioned above, from Brittany, Laon and St Gallen, is far from rudimentary; indeed, it is of a sophistication and complexity matched by few later chant books. According to one theory these complex signs are a representation of the gestures (Gk. neuma: ‘gesture’) made by the cantor while directing a performance, in other words, they derive from the practice of Cheironomy (Huglo, RdM, 1963). The difficulties of this theory have been exposed by Hucke (1979). Cheironomy as practised in other (mostly non-Western) music cultures involves hand signs that denote exact pitches, something plainchant neumes manifestly have no intention of doing. To reconstruct a lost cheironomic practice from surviving notational signs and then to hypothesize that the signs derive from the cheironomy is inherently unsatisfactory, though the possibility should not be dismissed out of hand.

Floros (1970) proposed a wholesale adoption of Byzantine notational practice by Rome in the second half of the 7th century, claiming far-reaching correspondences between Palaeo-Byzantine notation of the Chartres type and Latin neumatic notation, including liquescent and special neumes and significative letters. But Floros's reconstruction of the early stages of Byzantine notation has been challenged (Haas, 1975), and the theory seems implausible on chronological grounds. Not until the 11th century was it customary to notate every syllable of Byzantine melodies; from the 9th century to the 11th notation was used only for particular points in the melody. And the Byzantine system developed in a quite different direction, as an interval notation, specifying intervals by signs as in a code, not representing them spatially on the page. (For further discussion of Byzantine notation see Byzantine chant, §3; on the development of the connection between vertical space on the page and a sense of higher and lower pitch in music see Duchez, 1979, and Sullivan, 1994.) However, the possibility that the concept of chant notation and some of its basic elements had a place in the interchanges between Carolingian and Byzantine church musicians of the late 8th century and the early 9th should not be dismissed completely. (The system of eight modes is ascribable to these contacts.) The names of some neumes – of which, however, no records exist before the 12th century – appear to be Greek or pseudo-Greek.

As Treitler (1982, 1984, 1992) has repeatedly stressed, neumes must not be viewed as imperfect forerunners of staff notation. Had it been desired to represent exact pitches, the means to do so would have been found. (Exactly this was indeed accomplished by Hucbald, with a letter notation adapted from Boethius, and the authors of the Enchiriadis group of treatises, with dasian signs.) Neumes remind their reader of the essential features of a melody that has already been learnt. The singer retains in his or her memory the store of typical melodic gestures implied by the genre and mode of the piece. The neumes guide the adaptation of those turns of phrase to the liturgical text in question. (See Hucke, 1988, and, for rare evidence of the system ‘under construction’, Rankin, 1984.)

The point at which this written reinforcement of the singer's memory became necessary, and where the first steps were taken in the development of notation is uncertain. Levy (1987) has favoured a relatively early date and has argued for two distinct stages in the creation of a written ‘Carolingian archetype’, two archetypes in fact. A first attempt would have been made in Palaeo-Frankish neumes, a system that appears to have achieved only modest dissemination; the second would have been made with French-German notation.

Others have argued for a later date, at least for the notation of whole chant books (van der Werf, 1983; Hiley, 1993, p.371). The wide variety of notational styles and the small but persistent differences between versions of melodies in different areas suggest the independent writing down of the repertory from memory at different times and places, after the various notational styles were already established. The fact that the whole process had to be repeated after the introduction of staff notation, again with different results in different areas, also suggests that the dissemination of an archetype was neither expected nor practicable.

Several scholars, including Stäblein (1975, diagram on p.27), have hypothesized genealogical relationships among the different neume families. The more ancient neumatic notation is believed to be, the greater the room for speculation about the organic development of the different styles. Jammers, for example, associated the point notation of Aquitanian sources with Gallican chant, and regarded stroke neumes as typically Roman. Handschin (1950, pp.81ff) distinguished between pre-Carolingian practice and a ‘“gregorianische” Neumensippe’. The sources known at present do not, however, seem to offer conclusive evidence to support such hypotheses.

Many questions, therefore, remain concerning the origins and early development of the neumatic notations. Under what circumstances could several different but equally mature types have developed by the end of the 9th century and yet more by the 11th? Is what they have in common the result of development from a common ancestor or did they evolve independently from a rather informally transmitted ‘idea’ of a written aide-mémoire for the singing-master? Is the appearance of fully notated graduals (with Mass chants) no sooner than the end of the 9th century deceptive (are earlier ones lost?), and why are the earliest fully notated antiphoners (with Office chants) no older than the end of the 10th century?

Notation, §III, 1: History of Western notation: Plainchant

(iv) Early notations, 9th–11th centuries.

(a) French and German notation including St Gallen and England.

(b) The Spanish peninsula.

(d) Palaeo-Frankish notation.

(e) Breton notation.

(f) Messine (Lorraine, Laon) notation.

(g) Aquitanian notation.

(h) Significative letters.

Notation, §III, 1(iv): Plainchant: Early notations, 9th–11th centuries

(a) French and German notation including St Gallen and England.

Despite differences in the direction of the script (from vertical in France and England to strongly inclined in south Germany) many basic similarities link the stroke notations used throughout France north of the Loire (except for Brittany and the archdiocese of Reims) and Germany.

French neumes (fig.18) were used within the area contained roughly by the four provinces of Lyons: the archbishoprics of Lyons, Rouen, Tours and Sens (Corbin, 1957). Numerous important manuscripts from such centres as St Denis, St Vaast, Dijon, Nevers, Cluny and Lyons use this notation. In the late 11th century the notation was also taken to south Italy and Sicily in the wake of the Norman conquest of those regions. The neumes typically ascend vertically and descend diagonally (the angle varies from place to place). However, this vertical direction is by no means a hard-and-fast rule in French notation, and in some sources (e.g. F-SOM 252 from St Omer: facs. in PalMus, 1st ser., iii, 1892, pl.184; and Pa 1169 from Autun: facs. in ibid., pl.183) the difference from German practice seems very slight. Other general differences from German practice are the angled form of both pes and clivis, and, from the 11th century, a tendency to add a hook or head to the upper left of the virga and pes and a foot to end of the clivis; occasional exceptions to these basic characteristics may, however, be found. The quilisma usually has three hooks; a few manuscripts, notably F-MOf H.159 from Dijon (on this source, see also §1(iv)(a)), use a descending quilisma as well. The trigon is rarely encountered. (For facs. see PalMus, 1st ser., iii, 1892, pls.181–93; Bannister, 1913, pls.10–20, 39–40, 43–9; Suñol, 1925, Fr. trans., 2/1935, pp.230–44; Jammers, Tafeln, 1965, pls.23–6, 28; Stäblein, 1975, pls.3–5; Corbin, 1977, pls.1–5, 21–6, 28–9, 40–41.)

The same general type was used in England (fig.19; see Rankin, 1987), especially in Winchester, and was imported thence to Scandinavia. The direction of the English neumes is even more markedly vertical than most French sources, for example, in the climacus where the initial virga is slightly rounded at the top and the succeeding puncta descend vertically. The rounded clivis is also more characteristic of English than French sources. (For facs. see PalMus, 1st ser., iii, 1892, pls.178–80; Bannister, 1913, pls.41b–42; Suñol, 1925, Fr. trans., 2/1935, pp.283–97; Stäblein, 1975, pls.6–9; Corbin, 1977, pls.30–31.)

A small number of 11th-century manuscripts, mostly from Normandy, use a special form of punctum like a small hook (it resembles the uncinus of Messine notation, though it is not related to the latter) for the lower note of the semitone steps (B, E and the A below B). An equivalent form is sometimes found in Aquitanian neumes (where it is usually regarded as a type of virga). After the adoption of staff notation the sign still persisted, although strictly speaking superfluous, and was used even into the 13th century. Examples of it are found in England as well as Normandy (see Corbin, 1977, pl.22; Hiley, 1993, p.424). The Aquitanian form spread as far as Portugal (Corbin, 1952).

German neumatic notations have often been referred to en bloc as ‘St Gallen’ neumes (since the time when St Gallen was believed to have received its chant directly from Rome: by implication its notation was also considered to stand at the root of the German tradition). But St Gallen is only one eminent member within a more or less clearly differentiated group. The territory of German neumatic notation includes the whole German-speaking area, and, from the 11th century onwards, some parts of north Italy (Bobbio, Moggio, the Aosta valley, Aquileia), Besançon and Remiremont, Bohemia, Hungary, Poland and parts of Scandinavia. The direction of this notation is diagonal both ascending and descending; the style of script is flexible, perfected down to the tiniest details. Both punctum and virga are used for syllabic notes and the normal form of the pes is rounded. The notation is rich in special neumes. (For facs. see PalMus, 1st ser., iii, 1892, pls.110–12, 114, 116–17; Bannister, 1913, pls.2–9; Suñol, 1925, Fr. trans., 2/1935, pp.298–304; Jammers, Tafeln, 1965, pls.6, 9–12; Stäablein, 1975, pl.58; Corbin, 1977, pls.8–9, 11–12; Möller, 1990.)

The best-documented form of this script is the notation of St Gallen itself (fig.20). A number of sources have been published in facsimile and subjected to intensive study (CH-SGs 339, 359, 390–91, E 121 and D-BAs 6). The extraordinarily rich repertory of signs includes modified forms of the basic neumes together with additional episemata and significative letters to represent agogic nuances and other features. (For facs. see PalMus, 1st ser., iii, 1892, pls.108, 113, 115; Suñol, 1925, Fr. trans., 2/1935, pp.298–304; Jammers, Tafeln, 1965, pls.7–8; PalMus, 2nd ser., i, 2/1970; Stäblein, 1975, pls.59–60; Corbin, 1977, pls.6–7.)

Numerous similar notations can be found in sources dating from the 11th century in adjacent areas as well. Rarely, however, was more than a part of the full arsenal of signs employed, and the meaning of a few signs sometimes appears to have been modified (Engels, 1994).

Many regional types within the German group have not been analysed in the same depth as St Gallen notation. One of the most important is the Echternach type, documented from the 10th century onwards (facs. of D-DS 1946; ed. Staub and others, 1982; Möller, 1988); its characteristic feature is the pressus minor resembling a question mark.

Notation, §III, 1(iv): Plainchant: Early notations, 9th–11th centuries

(b) The Spanish peninsula.

Neumes that in many ways are similar to the main French-German type were used in Spain before the Christian reconquest. There are, however, a number of distinctive signs: the scandicus proceeds upwards as a single line with loops; the pes, instead of making a simple angle, may swing upwards with a loop; and the torculus and porrectus also contain loops. This basic Spanish type was divided between two geographical areas. In northern Spain a roughly upright orientation (like that of French notation) prevailed, whereas the neumes in sources from Toledo (fig.21) are inclined drastically to the right, as it were impelling the line of music forwards. Since practically all the melodies for which these notations were chiefly used, those of the Mozarabic rite, have not survived in diastematic notation, some details of Spanish notation are not fully understood. Its age is also to some extent disputed, the possibility having been raised that it may antedate the 9th-century Frankish examples (Huglo, 1985). Thus estimates of the date of the León antiphoner (facs. in Antifonario visigótico, ed. L. Brou and J. Vives, 1953–9) vary from the 9th century to the 11th (see Mundó, 1965).

Spanish neumes were also used for some ‘Gregorian’ chant manuscripts, written after the Roman rite was brought into Spain in the 11th century (e.g. Antiphonale silense, ed. I. Fernández de la Cuesta, 1985). But the chief vehicle for the import of ‘Gregorian’ chant was Aquitanian notation.

In north-east Spain, in the area roughly corresponding to modern Catalonia, another type of notation similar to French became established, usually known as ‘Catalan’ notation.

(For discussion see esp. Suñol, 1925, Fr. trans., 2/1935, pp.311–82; also Bannister, 1913, pls.25–6; Jammers, Tafeln, 1965, pls.42–3; Stäblein, 1975, pls.86–8; Corbin, 1977, pls.37–9.)

Notation, §III, 1(iv): Plainchant: Early notations, 9th–11th centuries

(c) Italian notations.

Many different stroke notations were used in north Italy (e.g. those of Asti, Vercelli, Novara, Civate, Mantua, Reggio d'Emilia and Verona), most of which await detailed investigation (on that of Brescia see Barezzani, 1981). They have in common the use of long chain-neumes and vigorous pen strokes. Some scripts have signs also found in a few French sources (angled pes, conjunct climacus), and the direction of the script also occasionally resembles French practice.

Special subtypes include the notation of Novalesa (fig.22). Its neumes include auxiliary forms with loops and rings, and a broad curve for the clivis; the script ascends vertically (see Suñol, 1925, Fr. trans., 2/1935, pp.186–97; Corbin, 1977, pp.165–71 and pl.36).

Bologna notation (fig.23; see also PalMus, 1st ser., xviii, 1969; Kurris, 1971) probably represents the oldest north Italian notation (Hourlier, 1960, pl.30; Corbin, 1977, p.155). It is marked by vigorous diagonal up-strokes, particularly for resupini; the script ascends diagonally, descending nearly vertically. Its repertory of signs is large, with numerous variant forms reflecting agogic or melodic features. The presence of both punctum and two forms of tractulus, horizontal and slanting (planus/gravis) for single lower notes, signs with rings, and a peculiar form of quilisma are notable.

The most independent type of north Italian notation was that used in the Benedictine abbey of Nonantola near Bologna; there are also sources from Torcello (fig.24) and Verona. A peculiarity of this notation is the way in which the first note of a group or melisma is connected graphically to the corresponding vowel of the text. Notes are represented mostly by individual virgae or puncta deployed diastematically. In both climacus and scandicus the puncta are arranged vertically, but the curved virga at the start of the climacus (and related neumes) makes the direction clear. The quilisma-note is represented by two dots. The script ascends diagonally and descends vertically (almost going backwards). (For facs. see PalMus, 1st ser., ii, 1891, pls.11–14; Suñol, 1925, Fr. trans., 2/1935, pp.197–9; Jammers, Tafeln, 1965, pl.32; Stäblein, 1975, pl.15.)

The adiastematic notations used in central Italy have hardly been studied at all (see Baroffio, 1990, note 30). They are not uniform; some are akin to north Italian stroke notations (e.g. I-Rvat lat.4770; CHTd N.2: facs. in PalMus, 1st ser., xiv, 1931, pls.44–5, see also p.251; Rc 1907: facs. in PalMus, 1st ser., ii, 1891, pl.7; Lc 606: facs. in PalMus, 1st ser., xiii, 1925/R, p.94, fig.10), others already show characteristics of 12th-century staff notations (right-angled pes, prolongation of horizontal elements). Beneventan features also appear in some scripts, for example, the right-angled clivis and conjunct scandicus; their meaning, however, is not yet defined (e.g. Rvat lat.10646: facs. in Suñol, 1925, Fr. trans., 2/1935, p.209). Boe (1999) has discovered examples of adiastematic notation from Rome datable as early as around 1000, and also shown that French neumes as used at Bijon were used at the imperial abbey of Farfa in the mid-11th century.

Beneventan notation (fig.25) was used in the area corresponding roughly to the duchy of Benevento and its area of influence (including Benevento, Monte Cassino, Bari and the Dalmatian coast); it thus covered much the same territory as Beneventan literary script. (10th-century sources are listed in Corbin, 1977, p.143.) The repertory of signs is extremely rich (in PalMus, 1st ser., xv, 1937/R, Huglo listed 353 different neume forms, among them many varieties of liquescent signs). The virga has a graphic stress on the left. There are two types of punctum, one horizontal, the other slanting (planum/grave). The clivis also has two forms, one pointed (when approached from a lower note), the other right-angled (approached from the unison or a higher note). The scandicus is conjunct. The meaning of tractuli joined by a thin diagonal stroke is unclear (‘inflatilia’ with two notes, ‘gradata’ with three). Compound neumes, where long chains of notes are formed without lifting the pen from the parchment, are also prominent. The relative diastematy of this notation later developed towards an increasingly exact pitch-notation (the custos was used even before the introduction of the staff). (For facs. see PalMus, 1st ser., xiv, 1931, xv, 1937/R, xx, 1983, and xxi, 1992, which are devoted to Beneventan sources.)

Notation, §III, 1(iv): Plainchant: Early notations, 9th–11th centuries

(d) Palaeo-Frankish notation.

Palaeo-Frankish neumes (fig.26) were first discussed by Handschin (1950) and Jammers (1952; see also, Tafeln, 1965, pls.34–6); sources are surveyed by Hourlier and Huglo (1957). Their name is due to Handschin, who regarded them as the forerunner of accent neumes. The connotations of the term are, however, problematic, and with hindsight the alternative designation ‘St Amand notation’ might be more appropriate (see Huglo, 1990, p.239). The notation appears to have been used in a restricted area including several important monasteries of Picardy and Hainault – Corbie, St Bertin, Anchin, Marchiennes – with the abbey of St Amand as its possible centre and an important outpost at Corvey on the Weser. They are last found at St Amand in the 12th century. The chief distinguishing feature of the notation is that the pes and clivis are represented by a single straight or slightly curved stroke; there is thus no virga. The torculus tends to be a simple semicircle. There is no distinction between oriscus and quilisma. In this notation, if anywhere, a strong connection seems to exist to the oratorical accents of the grammarians (Atkinson, 1995). Few sources are available in facsimile, so the degree of variance in neume forms and resemblances to other types of neumes cannot yet be assessed accurately. Since the two- and three-note neumes are sometimes ‘split’ into puncta, this notation has been reckoned among the ‘rhythmic’ types, perhaps the earliest such, implying that the distinction between slower and faster delivery was present in the minds of chant scribes from the very beginning. (For a hypothetical line of development, tracing a link between Palaeo-Frankish neumes and the notations of Brittany, Aquitaine and Laon, see Hourlier and Huglo, 1957, p.218.)

Notation, §III, 1(iv): Plainchant: Early notations, 9th–11th centuries

(e) Breton notation.

Breton notation (fig.27) is found chiefly in sources from north-west France, but also in 10th- and 11th-century sources from Pavia. Huglo's survey (AcM, 1963) shows a progressive retreat from the south-west (some features appear in early manuscripts from St Martial at Limoges), the Loire valley, Chartres, Maine, and Normandy south of the Seine. It was superseded by French notation in Angers by the turn of the millennium, but survived in the backwater of Brittany until the mid-12th century. Some 10th-century sources from southern England also use Breton notation (Rankin, 1984). In view of its obvious antiquity and simplicity, Huglo (op. cit., 82) and Stäblein (1975, p.30) thought it might at one time have been propagated widely throughout the Carolingian empire. As in Palaeo-Frankish notation (from which it may derive), the same sign is used where in other notations either an oriscus or a quilisma would be employed. Since the two- and three-note neumes are sometimes ‘split’ into puncta, this notation has been reckoned among the ‘rhythmic’ types (see Ménager, 1912). One of the principal sources, F-CHRm 47 (facs. in PalMus, 1st ser., ix, 1906), may be dated as early as the late 9th century and probably comes from Rennes. (For facs. see Bannister, 1913, pls.60–62; Suñol, 1925, Fr. trans., 2/1935, pp.256–9; Jammers, Tafeln, 1965, pls.40–41).

Notation, §III, 1(iv): Plainchant: Early notations, 9th–11th centuries

(f) Messine (Lorraine, Laon) notation.

Messine notation (for illustration see fig.28) was used in north-east France, in an area including most of the archbishopric of Reims, bounded in the east by the Vosges, Eifel and Hunsrück. Towards the south and west it was not sharply detached from the area of French neumes. A special variant appeared as early as the 10th century near Lake Como (Sesini, 1932).

The earliest complete source to survive is F-LA 239 (facs. in PalMus, 1st ser., x, 1909), written in or near Laon about 930. Its repertory of signs is remarkably rich; each basic sign has variant forms (graphical variants, variants in the inner articulation of the sign, also significative letters). The basic sign for single notes is a small hook (uncinus). Characteristic signs include the clivis in the form of an Arabic ‘7’ and the cephalicus in the form of an Arabic ‘9’. The direction of the script is diagonal ascending, vertical descending.

Similarly detailed studies of other manuscripts with Messine notation are not yet available. (Jeffery, 1982, and Hourlier, 1988, both discuss other very early examples; the main survey of sources is Hourlier, 1951. See also Lipphardt, 1955 and 1957; Arbogast, 1959; Cardine, 1968, Eng. trans., 1982; Corbin, 1977, pp.87–94. For facs. see PalMus 1st ser., iii, 1892, pls.154–65; Bannister, 1913, pls.55b–59b; Suñol, 1925, Fr. trans., 2/1935, p.248–55; Stäblein, 1975, pls.63–4.)

Notation, §III, 1(iv): Plainchant: Early notations, 9th–11th centuries

(g) Aquitanian notation.

This notation (fig.29) was used over a wide area of south-west France, roughly corresponding to the Frankish province of Aquitania, and consists predominantly of discrete points. A virga, in the form of a point with a tail attached, is not found standing alone but as the final note of the pes or scandicus. The torculus is almost the only conjunct neume, formed of punctum plus virga joined to the final punctum. The quilisma is distinctive: after the initial punctum an almost vertical slash with initial hook is joined to the tail of the final virga. The earliest substantial source is the 10th-century miscellany from Limoges F-Pn lat.1240, whose principal scribes used Aquitanian notation, although some Breton and northern French neumes are also present.

Even before the end of the millennium scribes would use a dry-point line as a vertical orientation for music notation (the usual lines drawn for entering text would therefore be used alternately for text and music), usually for the 3rd above the final in authentic modes and the final in plagal modes (but F rather than E for mode 4). In some manuscripts a deliberate distinction seems to be made between dot and dash, possibly meaning shorter and longer notes respectively. In other sources the scribe seems simply to alternate the two, especially in descending climacus figures. In some sources, particularly F-Pn lat.903 (from St Yrieix; partial facs. in PalMus, 1st ser., xiii, 1925/R), alternative forms of the virga are used. A semicircular virga appears for the note on the lower step of a semitone (E, B etc.), a further type, the so-called virga cornu (‘horned’ virga), signifies the upper step of the semitone. Not dissimilar in shape to the latter is the virga strata (virga+oriscus). Even though the vertical placement of the notes is particularly exact in most sources from the mid–11th century onwards, clefs were not used, and custodes but rarely, so that in the case of non-standard pieces the aid of the virga at the semitone is often useful for determining pitch. (The principal analysis of the notation is that of Ferretti in PalMus, xiii, 1925. For facs. see PalMus, 1st ser., ii, 1891, pls.83–103; Bannister, 1913, pls.63–4; Suñol, 1925, Fr. trans., 2/1935, pp.260–82; Jammers, Tafeln, 1965, pls.29–30; Stäblein, 1975, pls.31–5; Corbin, 1977, pls.19–20.)

Notation, §III, 1(iv): Plainchant: Early notations, 9th–11th centuries

(h) Significative letters.

In some early sources letters are placed adjacent to the neumes, intended to clarify their interpretation with regard to pitch, rhythm, agogic nuance or dynamic (see Table 5). They are particularly common in a small group of 10th-century sources from St Gallen, Einsiedeln and Regensburg, and are also found in manuscripts from Laon and Chartres. Smits van Waesberghe (1938–42) counted 4156 letters in CH-SGs 359, 12,987 in SGs 390–91 (the Hartker Antiphoner) and 32,378 in E 121. Their use diminished in the 11th century. Significative letters are described by Notker of St Gallen (d 912; ed. Froger, 1962; see also MGH, Scriptores, ii, 1829, p.103), who attributed their invention to one ‘Romanus’ (a choice of name no doubt intended to heighten their authority). According to Ekkehard IV of St Gallen (d 1036) the ‘litterae alphabeti significativae’ were added by Romanus to an authentic antiphoner of St Gregory, brought to the abbey from Pope Hadrian I. Consequently they are sometimes known as ‘Romanian’ or ‘Romanus letters’. Some of the letters on Notker's list are commonly used but others are rare in chant sources. Notker's explanations (often rather fanciful) are usually devised as a mnemonic, where the significant letter is emphasized in the actual choice of words in the explanation; thus ‘g’ indicates ‘ut in gutture gradatim garruletur genuine gratulatur’. Notker's explanations are summarized in Table 5, col.2. No corresponding explanation survives for the letters used in F-LA 239, but they were elucidated in PalMus, 1st ser., x (1909; see also Billecocq, 1978; and for sources from Chartres, see PalMus, 1st ser., xi, 1912). Some of the more common meanings are explained in Table 5, col.3. The two traditions differ as to the meaning of ‘a’ and ‘f’.

Notation, §III, 1: History of Western notation: Plainchant

(v) Pitch-specific notations, 11th–12th centuries.

(a) Alphabetic notations and dasia signs.

(b) The introduction of the staff.

(d) North Italy, including Milan.

(e) Normandy, Paris and other French centres, England and Sicily.

(f) Messine (Metz, Lorraine, Laon) notation.

(g) French-Messine mixed notation.

(h) Cistercian notation.

(i) The Rhineland, Liège and the Low Countries.

(j) South Germany, Klosterneuburg, Bamberg.

(k) Hungary.

(l) German-Messine mixed notations in Germany and central Europe.

(m) The Messine notation of Prague.

(n) Cistercian and Premonstratensian notations in central Europe.

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(a) Alphabetic notations and dasia signs.

The need for pitch-specific signs was greater in theoretical texts, many of which contained music examples, than in the liturgical chant books. Treatises that dispense with music notation, such as Prologus in tonarium by Berno of Reichenau (d 1008; GerbertS, ii, 62–91), cite pitches by means of the note names of classical Greek theory (proslambanomenos, hypatē hypatōn etc.). Other treatises, however, employ simpler systems based on sets of symbols or letters of the alphabet. The series of signs known as ‘dasia’ (or ‘daseia’: see Phillips, 1984, and Hebborn, 1995) was used in the important Enchiriadis group of treatises in the 9th century. Hermannus Contractus promoted another set of letters that specified the interval between one note and the next. Of all these, only alphabetic letters seem to have been used to notate whole chant books.

The alphabetization of the individual notes of the scale was thus at first a purely theoretical procedure and was intimately connected with the use of the monochord as a teaching instrument. Boethius (d c524), the principal conduit for classical Greek music theory to the Middle Ages, demonstrated several features of the Greek systēma teleion (Greater Perfect System) by means of pitches produced on the monochord, and in one instance the notes of the diatonic scale through two octaves are marked off with the letters ‘a’ to ‘p’ (De institutione musica, iv.17).

Hucbald of St Amand, writing at the end of the 9th century, had already referred to the desirability of combining neumes with pitch-letters (GerbertS, i, 117–18; Babb, 1978, p.37; Traub, 1989, pp.62–5), although the actual pitch-letters he chose were not the a–p series but a selection from the ‘Alypian’ series transmitted by Boethius (De institutione musica, iv.3–4; see Babb, 1978, p.9). Hucbald's suggestion was not, however, taken up in this form in practical sources, although those with dual notation, such as the ‘tonary’ F-MOf H.159 (first half of the 11th century, from St Bénigne, Dijon), which also contains French neumes, do put his idea into practice. It is not clear whether the probable spiritus movens behind the copying of this manuscript, Guillaume de Dijon, knew Hucbald's work, or whether he was influenced by the late 10th-century treatise Dialogus de musica (see below).

Another series a–p, but this time representing modern c–c'', is also reported by Hucbald, and is known from several texts on the construction of organs and bells. The only known practical source utilizing this series is the Winchester manuscript with voces organales GB-Ccc 473 (late 10th- to mid-11th centuries), which attaches letters to the neumes of many sequences, making them among the earliest of all directly transcribable pieces (Holschneider, 1968 and 1978).

The dasia signs (fig.30) are known from three important texts of the 9th century and the early 10th, Musica enchiriadis, Scolica enchiriadis and Commemoratio brevis de tonis et psalmis modulandis, together with a number of others (ed. Schmid, 1981). The dasian series starts from a nucleus of four signs, representing the pitches of the four finals of Gregorian chant (D, E, F and G), which are then reversed and inverted to make further sets of four. Their intervallic disposition is so explained that the following scale results (assigning the nucleus to modern d–g; see ex.4).

The practical significance of this scale is unclear (see Phillips, 1984), since repetition at the octave is not consistently possible. (For examples of polyphony with a total range of more than an octave, the full series of dasia signs is abandoned.) Possibly we are meant to understand that b, f and c are available in all octaves, which would support the suggestion that some chants (principally offertories) ‘modulate’.

In contrast to early Western notation, the system developed to notate Byzantine chant specified intervals between notes (see Byzantine chant, §3). The same principle was adopted by Hermannus Contractus (d 1054), using the following letters: ‘s’ (semitonus) for the semitone; ‘t’ (tonus) for the tone; ‘ts’ for the minor 3rd; ‘tt’ for the major 3rd; ‘d’ (diatessaron) for the perfect 4th; ‘D’ (diapente) for the perfect 5th; ‘Ds’ for the minor 6th; ‘Dt’ for the major 6th; and ‘e’ (equaliter) for the unison. A dot under the letter indicated descending motion.

The a–p series was adopted for use in F-MOf H.159 (fig.31) and a small group of manuscripts from Normandy and Norman England (Corbin, 1954; Santasuosso, 1989). All these sources are associated with Guillaume de Dijon (William of Volpiano), the Italian abbot of St Bénigne, Dijon, who reformed most of the leading monasteries of Normandy in the early 11th century. MOf H.159 contains the complete corpus of Mass Proper chants in musical (not liturgical) order notated with both neumes and alphabetic letters in the series a–p (Guidonian A = a, Guidonian a = h, Guidonian aa = p; I = b, i = b; for the Guidonian scale, see below, ex.6). The scribes of this manuscript (see Hansen, 1974) attached special signs for liquescence, oriscus and quilisma to the letters.

A group of five special signs in F-MOf H.159 have occasioned much speculation (ex.5). They occur among the letters where a semitone step in the scale would normally be expected. According to one theory (see Gmelch, 1911) the signs represent quarter-tones or some other non-diatonic tones. Froger (1978), however, argued that the context does not necessitate the use of intervals smaller than a semitone, and there is no evidence from contemporary writings that such intervals were ever envisaged. The signs themselves seem not unlike the dasia. No fully convincing explanation for their use has yet been found.

The anonymous Dialogus de musica, written at the end of the 10th century in north Italy (see Odo, §3), proposes an alphabetic series not merely for pedagogical purposes but also as a way to notate a complete antiphoner: Γ indicates the lowest note, followed by the letters A–G then a–g for successive octaves, with ‘aa’ signifying the highest pitch. Only one fragment of such an antiphoner, however, has survived; the flyleaves of the Hereford noted breviary (GB-H P.9.vii) are from an older antiphoner with alphabetic, not neumatic notation (facs. in W.H. Frere, Bibliotheca musico-liturgica, i, London, 1901 [dated 1894]/R, pl.2). On these leaves, longer note groups in melismas are separated by dots. Guido of Arezzo also adopted this alphabetic system, extending the series to ‘ee’ (ex.6). (Santasuosso, 1989, is a study of alphabetic notation. For further facs. see Wagner, 1905, 2/1912, pp.222–9, 251–7; Bannister, 1913, pls.27–32; Suñol, 1925, Fr. trans., 2/1935, pp.392–404; Stäblein, 1975, pls.89–94.)

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(b) The introduction of the staff.

As early as the first period of medieval music notation, theoretical and pedagogical writings often specified the exact intervallic structure of music examples they cite. For this purpose, horizontal lines (varying in number) and/or letters and symbols (e.g. dasia signs) were employed. These methods, however, remained confined to theoretical texts, being too complicated for the notation of the entire contents of liturgical books. A historical turning-point was Guido of Arezzo's reform of musical notation (proposed in Aliae regulae [Prologus in antiphonarium], c1030; see Smits van Waesberghe, 1951). Based on the use of a staff, his system changed the whole relationship between writing and music in the greater part of Europe in a remarkably short space of time, and created the preconditions for developments of the greatest importance in Western music.

The rapid success of the reform may be attributed, on one level, to the simplicity and practicality of the system and to its incorporation of elements from previous systems of notation. The staff lines represent notes a 3rd apart, the intermediate notes being placed in the space between. The pitch of the lines is indicated by letter-clefs, letters of the traditional alphabet being set at the start of the respective line. In the 11th and 12th centuries the lines were normally scored into the parchment (dry-point lines), but those representing the upper note of a semitone step could be distinguished by coloured ink: red for the F-line, yellow for the c-line. Another of Guido's recommendations was the custos at the end of a staff, facilitating the progression to the next by indicating its first note. The notes themselves took the form of traditional neume shapes. Although the ‘full’ Guidonian system employed clefs, coloured lines and the custos together, in some cases not all these elements were adopted.

But it was not only the intrinsic merits of the reform that lay behind its Europe-wide success; the ecclesiastical-historical context was also favourable. When Guido explained his new ideas to Pope John XIX (1024–32), showing him how a previously unknown melody could be learnt from notation alone, Guido was commissioned to notate Roman liturgical books in staff notation – an obvious sign of papal approbation. The new ‘Guidonian’ system, therefore, also became ‘Roman’ notation, just at the beginning of an epoch when the role of the papacy and the relationship between Rome and the local Churches was changing. The dissemination of staff notation took place in the era of the crusades and the investiture struggle. Guidonian notation belonged to the arsenal of the reforms of Pope Gregory VII (1073–85); it could facilitate liturgical reform and preserve the unity of centralized uses.

Many scriptoria that adopted staff notation set their own traditional adiastematic neume shapes on the lines, which is probably what Guido himself had done. At the same time some of the previous allegiances (determined by geography or institutional connections) in respect of notational practice were relaxed or replaced. The scriptoria had three alternatives: to put their traditional neumes onto the staff; to import shapes from elsewhere along with the staff; or to create a new set of signs commensurate with the new system (naturally drawing upon previous experience).

The dissemination of staff notation across Europe did not proceed at a uniform rate. Examples in theoretical writings show that knowledge of the new notational ideal spread rapidly. But this does not necessarily mean that the transition was effected at the same time in notated liturgical books or the teaching of chant. Staff notation was introduced relatively early in central and northern Italy, including Rome: the gradual of S Cecilia in Trastevere of 1071 (CH-CObodmer 74: facs. in Lütolf, 1987; see below, fig.33) is the oldest surviving complete codex with Guidonian notation. The transition also began in central France in the 11th century, soon followed by the Low Countries (St Trond) and Lorraine. During the 12th century, liturgical books in England, Sicily and Scandinavia (all of which were under Norman influence) were supplied with staff notation. In the areas of Aquitanian and Beneventan notation, which had already displayed diastematic characteristics in the previous notational epoch, the system was taken up either rather late (south Italy) or in strongly modified form (south France). Such features of ‘classical’ Guidonian notation as clefs and coloured lines were not regarded as essential. Some conservative Beneventan scriptoria retained their own diastematic but non-Guidonian notation as late as the 13th century (e.g. I-BV 21: facs. in Kelly, 1989, pl.12; the use of the custos is characteristic). Traditional Aquitanian notation had achieved full diastematy by the end of the 11th century, without recourse to the Guidonian system (see F-Pn lat.903: facs. in PalMus, 1st ser., xiii, 1925/R). In the area of German neumes staff notation was ignored for a long time; for example, in the scriptoria of the network of churches following the secular liturgical cursus (including most of the Augustinian canons) staff notation was adopted only towards the end of the 13th century. Many conservative centres continued to use adiastematic neumes even beyond the 13th century. In Hungary Guidonian notation gained general acceptance in the last third of the 12th century, and in Bohemia and Poland during the 13th century.

The new Gregorian monastic orders also played their part in the process of assimilation of the reformed notation. The Camaldolese, Carthusians, Cistercians and Premonstratensians all chose to adopt the Guidonian system, which then spread throughout the monastic networks (in variant forms peculiar to the respective orders) across the whole of Europe. The more centralized the order, however, the less influence individual houses seem to have exerted on the scribal culture of their wider environment. In Germany, for example, the splendid Guidonian notation of the Cistercian books remained confined to the order itself. The Italian Camaldolese, on the other hand, supplied codices with staff notation to other churches.

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(c) Central and southern Italy, including Rome and Benevento.

Among the earliest centres to adopt the Guidonian reform were those of central Italy (from Perugia to the Lombard plain, Tuscany, Umbria, the Papal States, the secular churches, Camaldolese, Vallombrosians – the actual area requires more exact definition). Sources from this area usually adopt the full Guidonian system of coloured lines, clefs and custodes (Smits van Waesberghe, 1953, pp.53–6), with local variation in neume shapes. Although a systematic survey of all the material is still lacking, a number of sub-types in this notational area may be distinguished. Classic examples are those of the Camaldolese manuscripts in Lucca (see fig.32 from I-Lc 601; see also Lc 603, and 609 from S Maria di Pontetto: facs. in PalMus, 1st ser., ii, 1891, pls.34–5, and PalMus, 1st ser., ix, 1906; see also E-Tc 48.14: facs. in Smits van Waesberghe, 1953, tab.3; and I-Fl 247 and 158 – Camaldolese antiphoners of the 11th–12th centuries from Vallombrosa and Struma respectively) and those of Pistoia (I-PSc 119 and 121: facs. in Stäblein, 1975, pls.24–5). A feature of these scripts is the elongation of horizontal strokes; the liquescent virga resembles the Beneventan form. Closely related to these notations is that in the Arezzo orationale (I-ARc: facs. in PalMus, 1st ser., ii, 1891, pl.26), and, among others, a Benedictine gradual (I-Sc F.VI.15: facs. in Stäblein, 1975, pl.27). Compared with these, the finely differentiated notation of Ravenna is recognisably independent in style (I-Pc 47 and MOd O.I.7: facs. in PalMus, 1st ser., ii, 1891, pl.37; Hourlier, 1960, pl.35; see also Baroffio, 1990). The small square note-heads (virga, punctum, pes) are reminiscent of north Italian point notations. The strong right tilt of the virga in the climacus and of the initial ascending element in the pointed clivis and porrectus are also characteristic. The half-cursive notation of the Benedictine gradual from Norcia, I-Rv C.52 (facs. in PalMus, 1st ser., ii, 1891, pl.33) represents another variant of central Italian notation; Beneventan influence is apparent in some neumes (e.g. the different elements in the climacus), as indeed it seems to be for the whole group of central Italian staff notations.

Beneventan and central Italian notations seem to be most clearly differentiated from each other in the form of the scandicus. In Beneventan and in reformed Guidonian ‘Italo-Beneventan’ staff notations from central Italy all three elements are conjunct, ending in a vertical virga. Central Italian notations also use the disjunct form (inherited from adiastematic Italian systems) for the scandicus: two puncta and a virga. But the conjunct scandicus is also present in these sources and further research is needed to establish whether this is the result of Beneventan influence or whether the quilismatic scandicus is intended. Central Italian notation is further characterized by the two forms of the clivis (pointed and right-angled), the tendency to build long chains of notes, the right-inclined virga at the start of the climacus and moderation in the use of special neumes. The direction of the script is diagonal both ascending and descending, but the angle differs within the area.

The Roman basilicas, perhaps as a result of Guido's audience with John XIX, adopted the staff system (red F- and yellow c-line, letter-clefs and custos) and combined it with neumes perhaps best described as simplified Beneventan (for the literary text, however, Caroline not Beneventan script was employed). Compared to the classical forms of Beneventan notation, most of the special neumes and the variant forms of the basic signs are absent. This is the notation used to record the Old Roman chant repertory (fig.33 from CH-CObodmer 74: facs. in Lütolf, 1987; see also I-Rvat lat.5319: facs. in MMMA, ii, frontispiece; Rvat S Pietro B.79: facs. in Baroffio and Kim, 1995). It was not, however, restricted to Rome but also used in many churches in Lazio and Umbria (e.g. I-CT 12: facs. in PalMus, 1st ser., ii, 1891, pl.33; MGG1, iv, Tafel 34, pp.835–6) and was subsequently adopted for the earliest Franciscan chant books.

South Italian scriptoria in the area of Beneventan notation (Benevento, Monte Cassino, Bari; some of their manuscripts are sources of Old Beneventan chant) displayed no great enthusiasm for the Guidonian reform. Beneventan notation apparently developed towards perfect diastematy without any outside influence. At Monte Cassino this process accelerated under Abbot Desiderius in the second half of the 11th century (with the use of a staff without clefs or coloured lines but with custos), while coloured lines appeared in the 12th century (fig.34). Benevento itself was more conservative. At the end of the 12th century codices were still written without clefs, but with clear diastematy. (For facs. see Wagner, 1905, 2/1912, p.267; Kelly, 1989; PalMus, 1st ser., xv, 1937/R, and xxi, 1992; Cavallo and others, 1994.)

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(d) North Italy, including Milan.

The scriptoria of north Italy including the plain of Lombardy, with few exceptions, had adopted the Guidonian system by the beginning of the 12th century (see fig.35). In some cases neumes of the previous local type were set on the staff without much alteration (e.g. at Nonantola and in the Como area where Messine-type neumes were used), but in most cases there was a modification under central Italian influence. The notation called Milanese exists only on staves; it seems to have been newly created at the time when the staff was introduced, drawing on elements of both Italian and Messine systems. In this period there was a general tendency in north Italian notations towards the use of discrete puncta, joined with fine lines.

Nonantolan neumes were combined with the full Guidonian system (Smits van Waesberghe, 1953, p.57), adopting a vertical ascending direction in the process (for facs. see Stäblein, 1975, pl.16; PalMus, 1st ser., ii, 1891, pls.15–18; G. Iversen, ed.: Corpus troporum, iv: Tropes de l'Agnus Dei, Stockholm, 1980, pls.XXX–XXXI). In Vercelli, by contrast, the notation had become diastematic by the 12th century, but can hardly be described as Guidonian, using only a custos (for facs. see Stäblein, 1975, pl.20; Iversen, op. cit., pls.XXVII–XXVIII; see also I-VCd 70 and 161). Characteristic of a large number of sources whose notation is generally closer to central Italian practice are: two types of clivis, pointed and right-angled; both disjunct and conjunct scandicus; right-facing virga at the start of the climacus. (For facs. see G. Iversen, ed.: Corpus troporum, vii: Tropes du Sanctus, Stockholm, 1990, pls.XXV–XXVI; MGG1, viii, Tafel 48 after p.1026; Stäblein, 1956, pl.7; PalMus, 1st ser., ii, 1891, pls.36, 37B.)

Milanese staff notation (fig.36) employed Guidonian coloured lines. Its characteristics include: conjunct scandicus, right-angled clivis, pes pointing right, no independent virga, tractuli for all single notes, climacus appearing as a clivis combined with a punctum, a tendency to construct long chains of notes, and an individual shape for torculus and porrectus. Like other notations of the region, neumes tended to be constructed out of points joined with thin lines. (Examples include GB-Lbl 34209: facs. in PalMus, 1st ser., v, 1896; and I-MZ c.14/77: facs. in PalMus, 1st ser., ii, 1891, pl.40; see also Stäblein, 1975, pl.21; Huglo and others, 1956, Tav.VII.)

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(e) Normandy, Paris and other French centres, England and Sicily.

The beautiful chant manuscripts with square notation produced in Paris workshops in the 13th century (and taken as models by the designers of the type for the Solesmes-Vatican books at the end of the 19th century and the beginning of the 20th) are often regarded as the outcome of a development initiated in Paris itself. But this is not the case. During the 12th century many centres in northern France, especially Normandy, and England began to make the punctum like a small square and used a small square head or foot on the virga, clivis and so on. They also adopted the Guidonian staff. Hesbert (1954) has traced this development within the manuscripts from the Norman abbey of Jumièges, and the same could be done for other centres. There are naturally some small differences between scriptoria: in Paris, for example, manuscripts from the late 12th century with staff notation have a pes subbipunctus with head turned right, instead of left as in ‘classical’ square notation of the 13th century (e.g. F-Psg 93, R 249 from St Victor, also Pn lat.17328 from St Corneille at Compiègne).

As already remarked, several 12th-century Norman and English manuscripts (e.g. F-Pn lat.10508 from St Evroult) use the special punctum at the semitone step. In Norman Sicily it seems that when the generation of scribes using neumatic notation had passed away, a form of proto-quadratic staff notation with mostly French but also one or two Italian elements (such as an Italian pes) was introduced. (See Suñol, 1925, Fr. trans., 2/1935, pp.145–7.)

No sources from these areas with staff notation are known to date from the 11th century, and many centres continued to use adiastematic neumes well into the 12th century. 12th-century manuscripts with staff notation survive from Angers and Fleury; Chelles, Paris, St Denis and St Maur-des-Fossés; the Norman monasteries of Fécamp, Jumièges and St Evroult; St Albans, Worcester and Downpatrick; Palermo and Catania; and Jerusalem. (For facs. see PalMus, 1st ser., ii, 1891, pls.43, 194; Bannister, 1913, pls.94, 96; Stäblein, 1975, pls.41, 65; Bernard, 1965, pls.xvii-xxvi; Bernard, 1974, pls.ix–x, xxxvii–xlv.)

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(f) Messine (Metz, Lorraine, Laon) notation.

The Guidonian staff spread to the area of Messine notation during the 12th century, co-existing briefly with notation in campo aperto. Even before the introduction of the staff, attempts at a more precise diastematy are visible. Scriptoria in this area, principally those in monastic centres, adapted the Guidonian system along their own lines, and little homogeneity can be observed. As in other parts of France, no need to apply all aspects of the system was felt, resulting in much variety in respect of coloured lines, custodes and letter-clefs. From the 13th century, however, Lorraine neumes regularly appear on staves of four red or black lines; some of the earliest preserved examples are those from the seat of the archbishopric in that area, Reims (see fig.37 from F-RSc 221; see also RSc 261: facs. in PalMus, 1st ser., iii, 1892, pl.167; and F-Pn lat.833 and 18008, both from the end of the 12th century).

The vocabulary of Messine neumes was somewhat simplified for the staff. The disjunct neume forms (used to signify agogic prolongation) receded, similarly the virga and most of the special neumes: the quilisma was replaced by a scandicus, the oriscus became a normal note or was simply omitted. Some scriptoria continued to use strophici, and of the liquescent neumes only the cephalicus and epiphonus. The basic single note remained the hook-shaped punctum (uncinus), whose form varied from place to place. The representation of the scandicus and climacus continued to be variable. From the 12th century onwards the climacus tended to descend not vertically but diagonally to the right, perhaps under French or German influence. During this century the area of Messine notation gradually narrowed under French influence – F-CA 193 (olim 188) f.151r, from Cambrai (facs. in PalMus, 1st ser., iii, 1892, pl.168B), for example, includes a French pes among Messine neumes). However, the Messine system exercised considerable influence on almost all notations in the German area that adopted staff notation. (I-VEcap CLXX, a noted breviary from Namur, early 13th century, is a classic example of Messine notation; for facs. see also Suñol, 1925, Fr. trans., 2/1935, p.254–5; Bannister, 1913, pls.55b–59b; PalMus, 1st ser., iii, 1892, pls.166–73; Hourlier, 1960, pl.19; Wagner, 1905, 2/1912, p.322). A complete codex with Messine staff notation (with some German features), the noted missal F-VN 759 of the 13th century, has appeared in facsimile (ed. Saulnier, 1995).

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(g) French-Messine mixed notation.

With the introduction of staff notation, scriptoria in central France developed their own variety of the system (in respect of coloured lines, clef letters and custodes; see fig.38); among manuscripts following Guidonian practice strictly are those of Nevers (e.g. F-Pn n.a.lat.1235–6; for facs. see PalMus, 1st ser., iii, 1892, pl.195B; Stäblein, 1956, pl.3; M. Huglo: ‘Un nouveau prosaire nivernais (Paris, B.N. nouv.acq.lat.3126)’, Ephemerides liturgicae, lxxi, 1957, pp.3–30; G. Iversen, ed.: Corpus troporum, iv: Tropes de l'Agnus Dei, Stockholm, 1980, pls.X–XI). The French-Messine system is an example of a ‘hybrid’ notation (Corbin, 1977, p.127). Most neumes are French, but beside the French clivis there is a right-angled clivis, which Corbin thought had been borrowed from Messine notation (although Italian influence, or perhaps even a music-theoretical source, cannot be ruled out entirely), and which is used where the first note of the clivis is at the same pitch as, or lower than, the preceding note. From the area east of Sens many such examples of French-Messine mixed notations may be found in this period (Corbin, 1977, map 2; manuscripts from Troyes, St Florentin, Auxerre, Vézelay, Dijon, Langres; for facs. see PalMus, 1st ser., iii, 1892, pl.198A; Bernard, 1965, pl.VI).

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(h) Cistercian notation.

The first great houses of the Cistercians (Clairvaux, Morimond and Pontigny) were founded in the area in which the French-Messine hybrid notations were used. Cistercian notation used the staff from the very beginning (Marosszéki, 1952, p.31) and employed a mixture of French and Messine neumes. Beside the French virga, pes, scandicus, climacus, clivis and cephalicus, occur the Messine clivis and porrectus. No special neumes are used. While there is some regional variety among French Cistercian scriptoria in respect of the appearance of the staff, those in Italy, Germany and central Europe followed rather strict Guidonian practice. (For facs. of F-Dm 114, the 12th-century standard Cistercian compendium see MGG1, xiv, Tafel 73 after col.1344.)

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(i) The Rhineland, Liège and the Low Countries.

The Rhineland down to the Low Countries was one of the first areas to use staff notation, which was employed from the late 11th century onwards (staff notation was known in St Trond in 1099; see Smits van Waesberghe, 1969, p.27). Aachen (see fig.39 from D-AAm 13), Liège and Cologne seem to be among the earliest centres that adopted the system, with Utrecht, the Münster area, Mainz and even further south along the Rhine within the area of influence. Later, staff notation spread north-east, following, for example, the path of the Teutonic Knights. Many neume shapes were derived from earlier German forms, but the virga was provided with a small diamond-shaped head (later to grow into the ‘Hufnagel’). The first element of the pes sometimes became an upward-arching semicircle (pes à ergot), a form found in French or Messine scripts but previously rare in German sources. Special neumes and liquescents were also used. The direction of the script no longer slanted as much as it had done previously, but the script retained much of its rounded contours. Red and yellow lines for F and c respectively are common, the F-clef is often a simple point and the custos is absent from early manuscripts. Some sources appear to have borrowed signs from French or Messine notation, for example, the right-angled clivis or the epiphonus with a closed ring. Typical examples available in facsimile are from Ratingen or Gaesdonck (D-Mbs Clm 10075; facs. in Hourlier, 1960, pl.5), the abbey of St Jacques, Liège (F-Pe B-A: facs. in Bernard, 1974, pl.XVII), Maastricht (NL-DHk 76.F.3: facs. in MGG1, viii, Tafel 72 after col.1410), Stavelot (GB-Lbl 18031–2: facs. in PalMus, 1st ser., iii, 1892, pl.131), Trier (D-Ds 664: facs. in PalMus, 1st ser., iii, 1892, pl.132; D-TRs 2254: facs. in ibid., pl.133), Aachen (D-AAm 13: facs. in MGG1, v, Tafel 14 before col.321 and Haug, 1995, pl.93–9) and Utrecht (NL-Uu 417: facs. in Haug, 1995, pp.131–3; Uu 406: facs. in Loos, Downey and Steiner, 1997). Variant forms in the Mainz area use a vertical virga and a pes with a left-facing head. Such forms are also to be found in the Hildegard-Codex (Dendermonde, Benedictine Abbey, MS 9: facs. van Poucke, 1991) and a Koblenz missal (Wirzenborn [nr Montabaur], f.260r Kirchenarchiv: facs. in PalMus, 1st ser., iii, 1892, pl.137). Its influence may have reached further south, being felt in such books as the Zwiefalten antiphoner (D-KA 60, second scribe, f.260r), the gradual D-Au Öttingen-Wallersteinische Bibliothek, Maihingen I.2.4^o.13, and an antiphoner fragment A-Ws C 1.

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(j) South Germany, Klosterneuburg, Bamberg.

Adiastematic notation was still dominant in south Germany during the 12th century. However, two types of staff notation developed under special circumstances, employed in comparatively few books. These types are referred to as ‘south German’ staff notation and ‘Klosterneuburg’ notation, respectively.

In a number of Benedictine scriptoria traditional south German neumes were placed on the staff, with differences in the use of clefs and coloured lines. Perhaps the oldest preserved source is the fragment of a monastic antiphoner from the end of the 11th century, A-LIs 623, with coloured lines and clef-pairs D-a, F-c or a-e. Important 12th-century sources include the Einsiedeln hymnal (CH-E 366 with red F-line, clef-pair F-c: facs. in Stäblein, 1975, pl.62), fragments from Hirsau (e.g. D-Sl Cod.fragm.53 with coloured lines, clefs on all lines, pes like an Arabic ‘3’) and from Prüfening near Regensburg, affiliated to Hirsau, including the most extensive fragment, Mbs lat.10086 (see fig.40) with red F- and green c-line, clefs a 5th apart (also from Prüfening come D-Mbs lat.23037, f.240 with clefs on all lines and a pes sometimes like an Arabic ‘3’; and Mbs Clm 13021 and 12027). Some sources with mostly south German neumes and script-direction appear to borrow from Messine practice (cephalicus like an Arabic ‘9’, right-pointing virga), for example, D-Mbs lat.9921 (f.40v, from Ottobeuren) and D-KA 60 (f.267r, from Zwiefalten).

Closely related to these is the distinctive notation in 12th-century Bamberg sources. Its typical features are a right-leaning virga like an Arabic ‘1’, an elongated tractulus (punctum planum), both pointed and right-angled clivis forms, the latter with a long first element. (This type of clivis can already be seen in the late adiastematic notation of Bamberg sources, e.g. D-BAs 24 and 26, both of the 13th century.) Early examples include the 12th-century music theory manuscript D-Mbs Clm 14965b (f.30r; see Smits van Waesberghe, 1969, p.97) and two fragments of monastic antiphoners from the turn of the 12th century (A-KN F8 and F19). This script evolved further in 13th-century sources such as D-BAs 25 (an antiphoner, first notation, f.2r) and 12 (gradual frag., f.8r).

Messine (Lorraine) features are predominant in Klosterneuburg notation, which also seems to be of south German Benedictine origin. Only the clivis and the special neumes (strophici, oriscus, virga strata, liquescents) are German. The direction of the script (ascending diagonally, descending vertically) is also Messine. The old, wavy quilisma is replaced by a form similar to the conjunct scandicus, while the normal form of the scandicus contains three Messine tractuli (uncini). Red F- and yellow c-lines are used consistently, all lines have clefs, but the custos is avoided. Sources include D-Mbs lat.9921 (ff.1, 54–7; see Smits van Waesberghe, 1969, p.111), from Ottobeuren, and three from Augsburg: A-Wn 573 (ff.19–25; see Berschin, 1975); D-Mbs lat.22025 (flyleaf); and D-W Gud.lat.334 (olim 4641). The most important group of completely preserved codices are those from the house of Augustinian canons at Klosterneuburg, including a gradual from the first third of the 12th century, A-Gu 807 (facs. in PalMus, 1st ser., xix, 1974) and the antiphoners from later in the century, for example, A-KN 1010, 1012 and 1013.

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(k) Hungary.

In the 12th century, when the Guidonian reform was carried out, Hungary was politically and ecclesiastically an independent kingdom. The notational reform may have been part of more general changes to the liturgy. Older Hungarian codices used south German neumes. At this time a deliberate campaign seems to have been carried out to create a new, reformed notation. Neumes of Messine and Italian origin were combined in a unique synthesis and set on the staff to create an independent notational type, known as ‘Esztergom’ or ‘Graner’ notation (see fig.41 from H-Bn MNy 1, 13th-century additions; see also Szendrei, 1988). Some remnants of the German neumes found in 12th-century sources gradually disappeared: only the supple appearance and careful calligraphy are reminiscent of the superseded German models. The characteristic features of the Esztergom notation are: tractulus rather than punctum; right-facing pes; right-angled clivis; vertically descending climacus – often starting with a stereotyped wave like a double-note; and a conjunct scandicus (the last two after Italian models). Liquescent and other special signs are rare. 12th-century sources include H-Bn MNy 1 (first notation), HR-ŠIBf 10 (binding) and H-Bu U.Fr.1.m.214; from the 13th century date A-GÜ 1/43 and CZ-Ps DE.I.7; and SK-BRm EC Lad.3 and EL18 were copied in the early 14th century. TR-Itks 42 dates from around 1360 (facs., Szendrei, 1999).

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(l) German-Messine mixed notations in Germany and central Europe.

The change to staff notation was somewhat delayed in non-monastic scriptoria using German neumes. Only after the mid-13th century did sources with staff notation appear regularly east of Mainz or in the south German dioceses. Palaeographically these notations belong together, for they are all characterized by a fusion of German and Messine forms (in differing combinations, some an equal mix, others predominantly one or the other). The direction of the script is German (ascending and descending diagonally). The rhomboid single note typical of the whole region is a stylized evolution of the Messine punctum (uncinus). Since these developments were relatively late, the appearance of the notations was influenced by gothic scribal characteristics. Until the sources have been more comprehensively investigated it is not possible to say if these notations were disseminated initially from one centre or represent simultaneous and independent developments.

The earliest among the preserved sources is the Quedlinburg gradual D-Bsb 40078 (fig.42), from the start of the 13th century (sometimes dated to the end of the 12th; facs. in Haug, 1995, pp.109–12). The usual form for a single note is a virga with short stem and left-facing head (showing Messine influence on German form). The other neumes are of German or Messine type. There are coloured lines, but clefs are found only in the middle of lines for a change of register, not at the beginning. 13th-century manuscripts where there is also a balance between German and Messine forms include those of Brunswick (see Härting, 1963) and Leipzig (e.g. D-LEu 391: facs. in Wagner, 1930; see also the 13th-century gradual CZ-Ps DF.I.8).

A number of notations more decidedly Messine in character are found from the mid-13th century onwards. The shape of the neumes is always articulated, consisting of rhomb for the noteheads connected by thick Gothic strokes. Examples are common in Austrian and Moravian sources (A-Wn 1925; Olomouc, Kapitulni Knihovna CO 3; CZ-Bam 6/11 and 19/27). Staff notation is known to have been introduced in the Moravian diocese (suffragan of Mainz until 1344) by Baldwin, Dean of Olomouc (d 1203; see Pokorný, 1980, p.42).

A mixed Messine-German staff notation was adopted in the south Polish diocese of Kraków, with sources dating as early as the 13th century (additions in PL-Kk 51), although the first complete sources are later. Messine elements predominate in a gradual of about 1300 from Wislica in the Kraków diocese (Kielce, Biblioteka Seminarium Duchownego RL 1), rather as in Moravian and Austrian sources just mentioned.

Besides the forms incorporating the stylized Messine rhomb, square note-heads were also used in some scriptoria of the region (see A-KN 629 and 1021, Olomouc, Kapitulni Kninovna CO 7). For example, the Benedictine scriptorium of Tyniec in southern Poland, developed an individual notation combining square and rhomboid forms (e.g. PL-Wn Akc.10810; see Szendrei, ‘Notacja liniowa’, 1999).

Silesian notation, one of the most individual as well as best-documented notations of this area, is also dominated by Messine forms. The earliest sources already rely on the Messine punctum (uncinus) for the single note, and for the pes and scandicus when the interval of only a 2nd is involved (larger intervals end with a virga). There are no special neumes. This notation developed independently until the 16th century. Sources include the missal CZ-Pnm XIII.B.17 from the end of the 13th century (facs. in Hutter, 1926, Abb.VI-VII) and the following 14th-century manuscripts: PL-WRu Br.Mus.K.21; Ms.Muz.51322 (olim K.24); I.F.386; and R 503.

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(m) The Messine notation of Prague.

Apart from some monastic houses with affiliations outside Bohemia, scriptoria of the Prague diocese used German neumes until staff notation was introduced by Vitus (d 1271), dean of Prague Cathedral. (German adiastematic neumes are still found in some Prague cathedral manuscripts as late as the early 14th century.) The manuscripts commissioned by Vitus, dating from between 1235 and 1253, use classical Messine forms, though the direction of the script is diagonal descending as well as ascending; the custos is absent (see fig.43 from CZ-Pak A 26-2, dated 1253; facs. in Spunar, 1957, pl.14c). The Premonstratensians probably played a part in this importation of Messine notation. Codices written under Bishop Tobias (1279–96) witness its further assimilation. The following examples may be cited: CZ-Pak Cim.4 (dated 1235, ninth gathering: facs. in Spunar, 1957, pl.14b); Pak LXI.2 (Evangeliary of Bishop Tobias, dated 1293); Pak P.3 (Agenda of Bishop Tobias, 1294: facs. in Hutter, 1926, pls.IV–V); and Pu XIV.A.19. Both staffless German neumes and Messine staff notation are found in Pu IV.D.9 (Liber ordinarius S Viti, 13th–14th century).

Notation, §III, 1(v): Plainchant: Pitch-specific notations, 11th–12th centuries

(n) Cistercian and Premonstratensian notations in central Europe.

Cistercian monasteries in central Europe used staff notation much earlier than other churches of the region, in fact from the time of their foundation in the 12th century. They used the French-Messine mixed notation as it had been developed in the Burgundian homeland of the order. This Cistercian system was more or less isolated from the traditions of its new environment, but gradually assimilated a few gothic features.

Premonstratensian notation in this area was less autonomous. The early houses of the order used Messine neumes, and the Premonstratensians were probably influential in introducing Messine staff notation to central Europe. Later sources with staff notation tended to assume characteristics of the local region. The first two notational layers of the troper CZ-Pak Cim.4 are probably Premonstratensian (see Vlhova, 1993). (See also the Polish Premonstratensian antiphoner of c1200, MS Arch.Norbertanek 1 in the convent library of Klasztor Norbertanek, Imbramowice, Poland: facs. in Miazga, 1984, p.235; and the German gradual from Arnstein, Trier diocese, D-DS 868, dated 1208–15: facs. in Miazga, 1979, p.120, facs.19).

Notation, §III, 1: History of Western notation: Plainchant

(vi) Pitch-specific notations, 13th–16th centuries.

(a) Square notation.

The development of square notation may be seen as the result of changes in both the conception and the function of chant notation. The resolution of stroke notation into a series of discrete squares linked by thin lines suggests that chant was thought of more in terms of individual pitches than of lines and phrases, perhaps because of its role as static tenor beneath more mobile upper parts in polyphony. Because of the easier visibility of individual notes, it facilitated singing from a codex by a group of singers (the increasing size of manuscripts also reflects the trend towards singing from a book instead of from memory, at least in some centres). To notate in this way, with thick horizontal and hair-thin vertical strokes, required a different pen-hold from that used for writing literary texts. These new requirements and techniques led to the separation of cursive notation (for private musical jottings) from formal book notation (for official use).

The ‘classical’ square notation best known from Parisian books of the mid-13th century onwards was a development of the French notations used in northern France (especially the Ile de France) in the 12th century. Thus the virga, pes and porrectus have a left-facing head and the clivis has a thin initial upstroke; the direction of the script is vertical ascending and diagonal descending. The scandicus consists of a punctum combined with a pes, or a pes with a virga; and the two puncta of the climacus take the form of small rhombs. A four-line staff (sometimes red) is normal; the custos is usually absent, as it had been in the Paris area in the 12th century. (For facs. see PalMus, 1st ser., iii, 1892, pl.204A)

Square notation was adopted with greater or lesser promptness in wide areas of western and southern Europe, Britain and Scandinavia in the 13th century, occasionally (though not always) replacing a different notational type (e.g. in some centres where Messine notation had been used). Sometimes Parisian books were imitated fairly exactly, no doubt as a result of the general political, intellectual and cultural importance of Paris in the 13th century. But many regional centres assimilated square forms into their traditional notation (e.g. retaining the original direction of their script) without adopting all features of Parisian practice. Many of these local varieties await thorough investigation. Aquitanian scriptoria furnished many examples of this (Stäblein, 1975, p.161, pls.43a–c), so also the Carthusians (PalMus, 1st ser., ii, 1891, pl.105; iii, 1892, pl.206A) or northern French centres such as Beauvais (Bernard, 1965, pl.xix–xx; Stäblein, 1975, p.159, pls.41a–b). Thus old notational boundaries retained some of their effectiveness even in the 13th century. Milanese notation, presumably because of the different chant repertory it represented, remained individual throughout the Middle Ages.

Homogenizing and standardizing forces were nevertheless at work. Chant books could be commissioned from professional scriptoria and executed by scribes unfamiliar with local (provincial) idiosyncrasies. The new religious orders of the Franciscans, Dominicans and Augustinian hermits made square notation obligatory for their chant books (see Huglo, 1967; Van Dijk, 1963, ii, p.359); the correctoria of the Dominicans were written in Paris in the mid-13th century (PalMus, 1st ser., iii, 1892, pls.200A–B). When the Franciscan Pope Nicholas III (1277–80) ordered the destruction of older chant books in Rome and their replacement with new ones after the Franciscan model, square notation acquired the semi-official status of a ‘Roman’ notation. Thereafter it made rapid headway, especially in Italy, where Beneventan notation, for example, was shortly superseded. It also penetrated Germany and central Europe, mainly as the preserve of the religious orders.

(b) ‘Gothic’ notations.

Gothic notations were not a new notational type but a change to the surface appearance of traditional neume shapes. Something similar had happened with the establishment of square notation, but whereas there the pen was held parallel to the line, in gothic style it remained diagonal. The horizontal and in particular the vertical down-strokes are strongly marked, the diagonal up-strokes fine. Whereas elegant, curved shapes were still common in the 13th century, by the 15th century thick, often uninterrupted chains of geometrically regular strokes were used. The basic shapes, however, are those of the German and central European notations already established in the 12th and 13th centuries, with the variety already described above, at least at first. The number of types diminished with time. Cistercian notation and that of Bamberg (except for its distinctive clivis) were eventually assimilated into the regional types with which they coexisted. Klosterneuburg notation disappeared after the 14th century. But the Esztergom notation in Hungary, and the notations of Prague and Silesia retained their independence. The rest of Germany and central Europe used either the (west) German or the mixed Messine-(east) German type. The former predominated as before in the area from the Rhineland up to the Low Countries, the latter in eastern and southern Germany, Austria, Switzerland and Poland (the geographical boundaries have not been precisely determined).

The chief difference between the (west) German and the Messine lies their preference as regards in the sign for single notes. In the former both the punctum (as always, for lower notes) and the virga (for higher notes and recitation) are used. Here the head of the virga is shaped like a horseshoe nail (Ger. ‘Hufnagel’, hence the common designation of this notation as Hufnagelschrift; see fig.44). On the other hand, the mixed Messine-German notation preferred the rhomb (lozenge, diamond, derived from the uncinus; see fig.45) for single notes. In German notation the rounded clivis with initial vertical shaft was preferred, in Messine-German the right-angled clivis. The westerly scriptoria cultivated more rounded shapes and placed less emphasis on the individual note-head, and liquescents – the strophici, even the quilisma – are still to be found. (PalMus, 1st ser., iii, 1892, pl.141; Hourlier, 1960, pl.7.) Messine-German notation appears to place more emphasis on the individual note. Liquescents remained but other special neumes disappeared.

In neither family is uniformity to be expected; for example, D-W 528, from Minden, is basically Messine-German but has a virga with its head on the right-hand side – a kind of compromise between Hufnagel and Messine rhomb (Haug, 1995, pp.156–60). Some Messine-German sources occasionally (but inconsistently) use a virga for a single higher note (e.g. San Cándido Stiftsbibliothek, VII a 7: facs. in Haug, 1995, pp.129–30; D-Mu 2° 156: facs. in Hiley, 1996).

Within the general areas of dissemination of the types mentioned above, notational ‘islands’ are discernible, where a tradition other than the prevailing regional system was employed. The Benedictines of the Abbey of St George in Prague, no doubt because of their connection with Hirsau in the Black Forest, used German staff notation in the very heartland of Prague-Messine notation. The Order of Teutonic Knights brought (west) German notation (together with the Dominican liturgy) into the north-eastern areas of Europe they colonized (e.g. the 14th-century antiphoner PL-PE L 19; see also Szendrei, 1994, and ‘Notacja liniowa’, 1999).

Professional workshops producing manuscripts to order were responsible for a gradual simplification and standardization of the notational picture, although some local scriptoria continued to produce codices of more individual appearance. In the late Middle Ages the number of sources made for private purposes (as informal music notebooks and school music books) increased. The appearance of the cursive notations in this class of music manuscripts naturally differs radically from the highly artistic books for official use.

(c) Esztergom, Prague and Wrocław.

Three larger enclaves of independent notations persisted to the end of the Middle Ages in Hungary, Bohemia and Silesia, respectively.

Esztergom notation was uniquely long lived. Although losing ground fractionally to Messine-German notation, it retained all its essential characteristics, its arsenal of signs and typical direction, even beyond the Middle Ages (see fig.46; survey with facs. in Szendrei, 1988). In surface appearance it acquired some gothic features. In a few scriptoria a new mixed notation incorporating some Messine-German elements was practised for luxury manuscripts (for facs. see Szendrei, 1990–93).

Prague notation continued to develop during the 14th and 15th centuries. After Prague became canonically independent of Mainz in 1344, its status as seat of the archbishopric, the imperial power and the university demanded the production of numerous splendid presentation codices; in such books the way in which every note is represented by a rhomb, joined by hair-thin lines (in traditional Messine combinations) is particularly noticeable (fig.47). When Olomouc became suffragan of Prague the local notation disappeared in favour of the latter's notation, which also spread beyond the borders of Bohemia and Moravia, influencing practice in Kraków in the 14th century and other areas in the 15th, during the time of the Hussite ascendency. (For facs. see Hutter, 1930, and Plocek, 1973.)

In Silesia the notation of Wrocław (Breslau) attained its fullest individuality in the second half of the 15th century (fig.48). Here, too, rhombs were used for pes and scandicus with intervals of a 2nd, and they predominate as component elements in other neumes as well, joined by lines of varying slenderness. (For facs. see Miazga, 1984, pls.71, 81, 91; Musica Medii Aevi, iv, 1973, pls.16–17; ibid., viii, 1991, pls.11–12.)

Notation, §III, 1: History of Western notation: Plainchant

(vii) Printed notations.

Early printed chant sources have been surveyed by Riemann (1896) and Molitor (1904). They precede the earliest printed polyphonic music by over two decades. Some 270 books with printed music were published by 1500 (King, 1964, p.8), almost all liturgical. Some of the earliest examples are in missals where only some of the priest's chants are provided with music. The first known book of this kind is the missal printed in Rome in 1476 by Ulrich Han from Ingolstadt. The earliest choirbook is even older, a gradual probably printed in Konstanz in 1473. The gradual uses ‘gothic’ notation with a pleasing repertory of shapes, even including the distropha and custos. The Roman print uses square notation. Printers displayed considerable ingenuity in devising appropriate note-forms, with German printers generally approaching the flexibility of handwritten neumes more successfully than their Latin counterparts, who often relied on the square and lozenge, or even the square alone.

Even before the advent of music printing, plainchant notations occasionally adopted features of mensural notation. Manuscripts with signs such as the semibrevis and minima are not uncommon in the 16th century in the south of the German-speaking regions. These were not used for traditional melodies but for new compositions, particularly melodies for the Mass Ordinary (e.g. the pieces in CH-SGs 546: ed. Marxer, 1908; also Sigl, 1911). Mensural notational signs were then taken up in some printed chant books; for example, books printed in Venice by Francis de Bruges regularly include the mensural Credo known as the ‘Credo cardinale’ (Tack, 1960, p.50).

Mensural signs were also adopted in Giovanni Guidetti's influential Directorium chori (1582), which includes the simple tones of the Mass and Office. There is a fourfold distinction between lozenge (semibrevis, short), square (brevis), square surmounted by an arc, and square with fermata (longest value), in the ratio 1:2:3:4 (see ex.7). A ‘dotted rhythm’ is always indicated by using 3 with 1. Such shapes were then widely adopted in later books, particularly for the notation of the new chants produced in profusion in France as part of the ‘neo-Gallican’ ecclesiastical movement.

(See Plainchant, §9(i);Plain-chant musical; and Neo-Gallican chant.)

In printed chant books of the 19th century various styles were used, which were derived and developed from earlier printing practice, often incorporating mensural features. The melodies thus notated, when not actually new compositions, were the result of much revision and recasting, whose principal monument was the gradual in the ‘Medicean edition’ (1614–15) composed by Felice Anerio and Francesco Soriano. When the Benedictines of Solesmes made new editions of the chant melodies in their medieval form they decided to develop a new font incorporating as many features as possible of the ‘classical’ quadratic notation of the 13th century, but also including a sign for the quilisma, which by the 13th century was no longer in use. In the Solesmes Antiphonale monasticum (Tournai, 1935) a sign for the oriscus was introduced. More recent books (Liber hymnarius cum invitatoriis & aliquibus responsoriis, Solesmes, 1983) have developed further signs to represent other features of the early chant manuscripts (a greater variety of liquescent signs, apostropha, pes with light first note etc.: see Liber hymnarius, p.xii).

Research at Solesmes had made it clear that the notation of early St Gallen and Laon manuscripts was particularly rich in rhythmic detail. The question as to whether such indications should be represented in the Vatican editions caused a rift in the commission appointed to prepare the new books. Pothier, the chairman of the commission, saw them as a local and temporary phenomenon that need not become part of an official edition with claims to universal validity (see Pothier, 1880; David, 1927; Bescond, 1972). Eventually two parallel editions appeared, that of the Vatican was ‘plain’, that of Solesmes contained supplementary horizontal bars (known as ‘episemata’) over certain notes and dots after others, to indicate lengthening. The Solesmes version became particularly well known after the publication of the compendium Liber usualis (Solesmes, 1921), and was propagated in numerous explanations of the ‘Solesmes method’ (Suñol, 1905 etc.; Gajard, 1951) as well as in Mocquereau's weighty treatise, Le nombre musical (1908–27).

An interesting development has been the re-publication by the Benedictines of Solesmes of older chant editions with the addition of hand-drawn reproductions of the neumes of F-LA 239, CH-SGs 359, E 121 and so on in the Graduale triplex and Offertoriale triplex. The purpose of such editions is to enable performers to take the notation of the early sources into account. Starting with the writings of Cardine (esp. 1968), a large body of literature has been created to support theories of chant performance based on details of these neumatic notations (see Performing practice, §II, 2(i)).

Notation, §III, 1: History of Western notation: Plainchant

BIBLIOGRAPHY

A General: (i) General studies and facsimile collections (ii) Principal characteristics (iii) Origins. B Regional notations: (i) French (ii) English (iii) German and St Gallen (iv) Central European (v) Spanish (vi) Italian (vii) Palaeo-Frankish (viii) Breton (ix) Messine/Laon/Lorraine (x) Aquitanian. C Significative letters, D Pitch-specific systems. E Staff notations: (i) Introduction (ii) France, England and Spain (iii) Low Countries and Germany (iv) Italy (v) Hungary, Bohemia and Poland. F Printed notations.

a: general

b: regional notations

c: significative letters

d: pitch-specific systems

e: staff notations

e. printed notations

a: general

(i) General studies and facsimile collections

MGG2 (‘Notation IV: Neumen’; M. Haas)

Paléographie musicale: les principaux manuscrits de chant grégorien, ambrosien, mozarabe, gallican (Solesmes, 1889–) [for details of individual vols. see Solesmes, §4]

P. Wagner: Neumenkunde: Paläographie des liturgischen Gesanges (Leipzig, 1905, 2/1912/R)

J.B. Thibaut: Monuments de la notation ekphonétique et neumatique de l'église latine (St Petersburg, 1912/R)

H.M. Bannister: Monumenti vaticani di paleografia musicale latina (Leipzig, 1913/R)

G.M. Suñol: Introducció a la paleografia musical gregoriana (Montserrat, 1925; Fr. trans., enlarged, 1935)

J. Hourlier, ed.: La notation musicale des chants liturgiques latins présentée par les moines de Solesmes (Solesmes, 1960)

F. Tack: Der gregorianische Choral, Mw, xviii (1960; Eng. trans., 1960)

M. Bernard: Bibliothèque Sainte-Geneviève, Paris, Répertoire de manuscrits médiévaux contenant des notations musicales, i (Paris, 1965)

E. Jammers: Tafeln zur Neumenschrift (Tutzing, 1965)

M. Bernard: Bibliothèque Mazarine, Paris, Répertoire de manuscrits médiévaux contenant des notations musicales, ii (Paris, 1966)

M. Bernard: Bibliothèques Parisiennes: Arsenal, Nationale (musique), Universitaire, Ecole des beaux-arts et fonds privés, Répertoire de manuscrits médiévaux contenant des notations musicales, iii (Paris, 1974)

B. Stäblein: Schriftbild der einstimmigen Musik, Musikgeschichte in Bildern, iii/4 (Leipzig,1975)

S. Corbin: Die Neumen (Cologne, 1977)

M. Huglo: ‘Bilan de 50 années de recherches (1939–1989) sur les notations musicales de 850 à 1300’, AcM, lxii (1990), 224–59

D. Hiley: Western Plainchant: a Handbook (Oxford, 1993)

(ii) Principal characteristics

E. de Coussemaker: Histoire de l'harmonie au Moyen Age (Paris, 1852)

F. Raillard: Explication des neumes ou anciens signes de notation musicale pour servir à la restauration complète du chant grégorien (Paris, 1852)

J. Pothier: Les mélodies grégoriennes d'après la tradition (Tournai, 1880)

A. Mocquereau: ‘Origine et classement de differentes écritures neumatiques: 1. Notation oratoire ou chironomique, 2. Notation musicale ou diastématique’, Le codex 339 de la Bibliothèque de Saint-Gall, PalMus, 1st ser., i (1889), 96–160

A. Mocquereau: ‘Neumes-accents liquescents ou sémi-vocaux’, Le répons-graduel Justus ut palma, PalMus, 1st ser., ii (1891), 37–86

H. Freistedt: Die liqueszierenden Noten des gregorianischen Chorals (Fribourg, 1929)

M. Huglo: ‘Les noms des neumes et leur origine’, EG, i (1954), 53–67

W. Wiesli: Das Quilisma im Codex 359 der Stiftsbibliothek St. Gallen: eine paläographisch-semiologische Studie (Immensee, 1966)

E. Cardine: Semiologia gregoriana (Rome, 1968; Eng. trans., 1982); Fr. trans. in EG, xi (1970), 1–158, and also pubd separately (Solesmes, 1970)

C. Thompson: ‘La traduction mélodique du trigon dans les pièces authentiques du Graduale romanum’, EG, x (1969), 29–85

J.B. Göschl: Semiologische Untersuchungen zum Phänomen der gregorianischen Liqueszenz: der isolierte dreistufige Epiphonus praepunctis, ein Sonderproblem der Liqueszenzforschung (Vienna, 1980)

W. Arlt: ‘Anschaulichkeit und analytischer Charakter: Kriterien der Beschreibung und Analyse früher Neumenschriften’, Musicologie médiévale: Paris 1982, 29–55

D. Hiley: ‘The Plica and Liquescence’, Gordon Athol Anderson, 1929–1981, in memoriam, ed. L.A. Dittmer (Henryville, PA, 1984), 379–91

J.B. Göschl: ‘Der gegenwärtige Stand der semiologischen Forschung’, Beiträge zur Gregorianik, i (1985), 43–102

A. Haug: ‘Zur Interpretation der Liqueszenzneumen’, AMw, (1993), 85–100

A. Odenkirchen: ‘13 Neumentafeln in tabellarischer Übersicht’, De musica et cantu: Helmut Hucke zum 60. Geburtstag, ed. P. Cahn and A.-K. Heimer (Hildesheim, 1993), 257–62

(iii) Origins

F. Steffens: Lateinische Paläographie (Freiburg, Switzerland, 1903)

J.B. Thibaut: Origine byzantine de la notation neumatique de l'église latine (Paris, 1907)

R. Beer, ed.: Monumenta palaeographica vindobonensia: Denkmäler der Schreibkunst aus der Handschriftensammlung des Habsburg-Lothringischen Erzhauses, ii (Leipzig,1913)

B. Laum: ‘Alexandrinisches und byzantinisches Akzentuationssystem’, Rheinisches Museum für Philologie, new ser., lxxiii (1920–24), 1–34

B. Laum: Das alexandrinische Akzentuationssystem unter Zugrundelegung der theoretischen Lehren der Grammatiker und mit Heranziehung der praktischen Verwendung in den Papyri (Paderborn, 1928)

E. Jammers: ‘Zur Entwicklung der Neumenschrift im Karolingerreich’, Otto Glauning zum 60. Geburtstag, ed. H. Schreiber (Leipzig, 1938), 89–98

J. Handschin: ‘Eine alte Neumenschrift’, AcM, xxii (1950), 69–97; xxv (1953), 87–8

L. Brou: ‘Notes de paléographie musicale mozarabe’, AnM, vii (1952), 51–76

S. Corbin: ‘Les notations neumatiques à l'époque carolingienne’, Revue d'histoire de l'église de France, xxxviii (1952), 225–32

E. Jammers: Die Essener Neumenhandschriften der Landes- und Stadtbibliothek Düsseldorf (Ratingen, 1952)

E. Jammers: ‘Die paläofrankische Neumenschrift’, Scriptorium, vii (1953), 235–59 [repr. in Hammerstein, 1969]

E. Jammers: ‘Die materiellen und geistigen Voraussetzungen für die Entstehung der Neumenschrift’, Deutsche Vierteljahrsschrift für Literaturwissenschaft und Geistesgeschichte, xxxii (1958), 554–75

B. Stäblein: ‘Zur Frühgeschichte der Sequenz’, AMw, xviii (1961), 1–33

K. Gamber: Codices liturgici Latini antiquiores (Fribourg, 1963, 2/1968, suppl. ed. B. Baroffio and others, 1988)

M. Huglo: ‘La chironomie médiévale’, RdM, xlix (1963), 155–71

A.-M. Bautier-Regnier: ‘A propos du sens de neuma et de nota en latin médiéval’, RBM, xviii (1964), 1–9

E. Jammers: ‘Studien zu Neumenschriften, Neumenhandschriften und neumierter Musik’, Bibliothek und Wissenschaft, ii (1965), 85–161

E. Jammers: ‘Rhythmen und Hymnen in einer St. Galler Handschrift des 9. Jahrhunderts’, Festschrift Bruno Stäblein zum 70. Geburtstag, ed. M. Ruhnke (Kassel, 1967), 134–42

E. Hammerstein, ed.: Schrift, Ordnung und Gestalt: gesammelte Aufsätze zur älteren Musikgeschichte (Berne, 1969) [writings of E. Jammers]

C. Floros: Universale Neumenkunde (Kassel, 1970)

K. Gamber: ‘Sacramentaria praehadriana: neue Zeugnisse der süddeutschen Überlieferung des vorhadrianischen Sacramentarium Gregorianum im 8.–9. Jh.’, Scriptorium, xxvii (1973), 3–15

M. Haas: ‘Probleme einer “Universale Neumenkunde”’, Forum musicologicum, i (1975), 305–22

B. Stäblein: Schriftbild der einstimmigen Musik, Musikgeschichte in Bildern, iii/4 (Leipzig, 1975)

M.-E. Duchez: ‘La représentation spatio-verticale du caractère musical grave-aigu et l'élaboration de la notion de hauteur de son dans la conscience occidentale’, AcM, li (1979), 54–73

H. Hucke: ‘Die Cheironomie und die Entstehung der Neumenschrift’, Mf, xxxii (1979), 1–16

K. Gamber: ‘Fragmentblätter eines Regensburger Evangeliars aus dem Ende des 8. Jahrhunderts’, Scriptorium, xxxiv (1980), 72–7

P. Jeffery: ‘An Early Cantatorium Fragment Related to MS Laon 239’, Scriptorium, xxxvi (1982), 245–52

L. Treitler: ‘The Early History of Music Writing in the West’, JAMS, xxxv (1982), 237–79

H. van der Werf: The Emergence of Gregorian Chant, i (Rochester, NY, 1983)

S.K. Rankin: ‘From Memory to Record: Musical Notations in Manuscripts from Exeter’, Anglo-Saxon England, xiii (1984), 97–112

L. Treitler: ‘Reading and Singing: on the Genesis of Occidental Music-Writing’, EMH, iv (1984), 135–208

H. Hucke: ‘Die Anfänge der abendländischen Notenschrift’, Festschrift Rudolf Elvers, ed. H. Herttrich and H. Schneider (Tutzing, 1985), 271–88

H. Möller: ‘Die Prosula “Psalle modulamina” (Mü 9543) und ihre musikhistorische Bedeutung’, La tradizione dei tropi liturgici: Paris 1985 and Perugia 1987, 279–96

F. Unterkircher: ‘Fragmente eines karolingischen Chorantiphonars mit Neumen (Wien, Österreichische Nationalbibliothek, Cod. Ser. n. 3645 und München, Bayerische Staatsbibliothek, Vorsatzblätter in Cgm 6943)’, Codices manuscripti: Zeitschrift für Handschriftenkunde, xi (1985), 97–109

M. Huglo: ‘Les évangiles de Landévennec (New York, Public Library, De Ricci 115)’, Landévennec et le monachisme breton dans le haut Moyen Age: Landévennec 1985 (Landévennec, 1986), 245–52

K.J. Levy: ‘On the Origin of Neumes’, EMH, vii (1987), 59–90

C.M. Atkinson: ‘From “Vitium” to “Tonus acquisitus”: on the Evolution of the Notational Matrix of Medieval Chant’, Cantus Planus III: Tihány 1988, 181–97

J. Hourlier: ‘Trois fragments de Laon’, EG, xxii (1988), 31–42

H. Hucke: ‘Gregorianische Fragen’, Mf, xliv (1988), 304–30

M. Bielitz: Die Neumen in Otfrids Evangelienharmonie: zum Verhältnis von Geistlich und Weltlich in der Musik des frühen Mittelalters sowie zur Entstehung der raumanalogen Notenschrift (Heidelberg, 1989)

K. Levy: ‘On Gregorian Orality’, JAMS, xliii (1990), 185–227

L. Treitler: ‘The “Unwritten” and “Written Transmission” of Medieval Chant and the Start-Up of Musical Notation’, JM, x (1992), 131–91

B. Sullivan: Grammar and Harmony: the Written Representation of Musical Sound in Carolingian Treatises (diss., U. of California, 1994)

C.M. Atkinson: ‘De accentibus toni oritur nota quae dicitur neuma: Prosodic Accents, the Accent Theory, and the Paleofrankish Script’, Essays on Medieval Music: in Honor of David G. Hughes, ed. G.M. Boone (Cambridge, MA, 1995), 17–42

M. Haas: Mündliche Überlieferung und altrömischer Choral: historische und analytische computergestützte Untersuchungen (Berne, 1996)

M. Bernhard: ‘Die Überlieferung der Neumennamen im lateinischen Mittelalter’, Quellen und Studien zur Musiktheorie des Mïttelalters, ed. M. Bernhard, ii (Munich, 1997), 13–91

b: regional notations

(i) French

Antiphonarium tonale missarum, XIe siècle: codex H. 159 de la Bibliothèque de l'Ecole de médicine de Montpellier, PalMus, 1st ser., viii (1901–5/R)

W.H. Frere, ed.: Pars antiphonarii (London, 1923) [facs. of GB-DRc B.iii.11]

J. Hourlier: ‘Remarques sur la notation clunisienne’, Revue grégorienne, xxx (1951), 231–40

R.-J. Hesbert, ed.: Les manuscrits musicaux de Jumièges (Mâcon, 1954)

Le manuscrit du Mont-Renaud, Xe siècle: graduel et antiphonaire de Noyon, PalMus, 1st ser., xvi (1955)

S. Corbin: La notation musicale neumatique des quatre provinces lyonnaises: Lyon, Rouen, Tours et Sens (diss., U. of Paris, 1957)

Fragments des manuscrits de Chartres, PalMus, 1st ser., xvii (1958)

D. Escudier: Le scriptorium de Saint-Vaast d'Arras, des origines au XIIe siècle: contribution à l'étude des notations neumatiques du Nord de la France (diss., Ecole des Chartes, Paris, 1970)

R.-J. Hesbert, ed.: Le graduel de St. Denis (Paris, 1981) [F-Pm 384]

D. Escudier: ‘La notation musicale de St. Vaast: étude d'une particularité graphique’, Musicologie médiévale: Paris 1982, 107–18

(ii) English

W.H. Frere: The Winchester Troper from MSS of the Xth and XIth Centuries (London, 1894)

L. Gjerløw: Adoratio crucis, the Regularis concordia and the Decreta Lanfranci: Manuscript Studies in the Early Medieval Church of Norway (Oslo, 1961)

A. Holschneider: Die Organa von Winchester: Studien zum ältesten Repertoire polyphoner Musik (Hildesheim, 1968)

S.K. Rankin: ‘Neumatic Notations in Anglo-Saxon England’, Musicologie médiévale: Paris 1982, 129–44

S.K. Rankin: ‘From Memory to Record: Musical Notations in Manuscripts from Exeter’, Anglo-Saxon England, xiii (1984), 97–112

(iii) German and St Gallen

Le codex 339 de la Bibliothèque de Saint-Gall (Xe siècle): antiphonale missarum sancti Gregorii, PalMus, 1st ser., i (1889)

Le codex 121 de la Bibliothèque d' Einsiedeln (IXe–XIe siècle): antiphonale missarum sancti Gregorii, PalMus, 1st ser., iv (1894)

Antiphonaire de l'office monastique transcrit par Hartker: MSS. Saint-Gall 390–391 (980–1011), PalMus, 2nd ser., i (1900/R)

Cantatorium, IXe siècle: no. 359 de la Bibliothèque de Saint-Gall, PalMus, 2nd ser., ii (1924/R)

H. Malloth: ‘Die ältesten Kärnter Tondenkmäler’, Carinthia I, clvi (1966), 203–52

H. Malloth: ‘Kärnter Tondenkmäler des Hoch- und Spätmittelalters’, Carinthia I, clvii (1967), 542

F. Unterkircher and O. Demus, eds.: Antiphonar von St. Peter (Graz, 1969–74) [A-Wn s.n.2700; colour facs.]

K. Biegaņski and J. Woronczak, eds.: Missale plenarium Bib.Capit.Gnesnensis Ms. 149 (Warsaw and Graz, 1970–72) [facs.]

S. Corbin: ‘Le fonds d' Echternach à la Bibliothèque nationale de Paris’, Ecole pratique des hautes études: annuaire, iv (1971–2), 371–9

K.H. Staub, P. Ulveling and F. Unterkircher, eds.: Echternacher Sakramentar und Antiphonar: vollständige Faksimile-Ausgabe im Originalformat der Handschrift 1946 aus dem Besitz der Hessischen Landes- und Hochschulbibliothek Darmstadt (Graz, 1982) [colour facs.]

Die Handschrift Bamberg Staatsbibliothek Lit. 6, Monumenta palaeographica Gregoriana, ii (Münsterschwarzach, 1986) [facs.]

G.M. Paucker, ed.: Das Graduale Msc. Lit. 6 der Staatsbibliothek Bamberg: eine Handschriften-Monographie unter besonderer Berücksichtigung des Repertoires und der Notation (Regensburg, 1986)

A. Haug: Gesungene und schriftlich dargestellte Sequenz: Beobachtungen zum Schriftbild der ältesten ostfränkischen Sequenzenhandschriften (Neuhausen-Stuttgart, 1987)

H. Möller: ‘Deutsche Neumen – St. Galler Neumen: zur Einordnung der Echternacher Neumenschrift’, SMH, xxx (1988), 415–30

F.C. Lochner: ‘La “notation d'Echternach” reconsidérée’, RBM, xliv (1990), 41–55

H. Möller, ed.: Das Quedlinburger Antiphonar (Berlin, Staatsbibliothek Preussischer Kulturbesitz Mus. ms. 40047) (Tutzing, 1990) [facs.]

F.K. Prassl: ‘Beobachtungen zur adiastematischen Notation in Missalehandschriften des 12. Jahrhunderts aus dem Augustiner-Chorherrenstift Seckau’, Cantus Planus IV: Pécs 1990, 31–54

E. Höchtl: Die adiastematisch notierten Fragmente aus den Handschriften der Stiftsbibliothek Melk: Versuch einer Bestandsaufnahme (diss., U. of Vienna, 1992)

H. Möller: ‘Deutsche Neumenschriften ausserhalb St. Gallens’, De musica et cantu: Helmut Hucke zum 60. Geburtstag, ed. P. Cahn and A.-K. Heimer (Hildesheim, 1993), 225–42

K. Schlager and A. Haug, eds.: Tropi carminum: Liber hymnorum Notkeri Balbuli: Berlin, Ehem. Preussische Staatsbibliothek, Ms.theol.lat.qu.11 (z.Zt. Kraków, Biblioteka Jagiellónska, Deposit) (Munich,1993)

M. Czernin: ‘Beobachtungen zur Neumenschrift der Handschrift CC 28 der Stiftsbibliothek von Kremsmünster’, SMw, xliii (1994), 7–35

S. Engels: Das Antiphonar von St. Peter in Salzburg: Codex ONB Ser. Nov. 2700 (Paderborn, 1994)

A. Hänggi and P. Ladner, eds.: Missale basileense saec. XI (Codex Gressly) (Fribourg, 1994) [facs.]

W. Arlt and S. Rankin, eds.: Stiftsbibliothek Sankt Gallen Codices 484 & 381, i: Kommentar, ii: Codex Sangallensis 484, iii: Codex Sangallensis 381 (Winterthur, 1996) [colour facs.]

(iv) Central European

J. Hutter: Česká notace [Czech notation]: Neumy (Prague, 1926) [with Fr. summary]

J. Hutter: Notationis bohemicae antiquae specimina selecta e codicibus bohemicis, i: Neumae (Prague, 1931)

Z. Falvy and L. Mezey, eds.: Codex albensis: ein Antiphonar aus dem 12. Jahrhundert (Budapest and Graz, 1963) [facs. of Graz, Universitätsbibliothek, 211]

B. Bujić: ‘Zadarski neumatski fragmenti v Oxfordu’ [Neumatic fragments from Zadar in Oxford], Muzikološki zbornik, iv (1968), 28–33

J. Szendrei: Középkori hangjegyírások Magyarországon [Medieval notation in Hungary] (Budapest, 1983) [with Ger. summary]

(v) Spanish

MGG2(‘Mozarabischer Gesang’; I. Fernández de la Cuesta)

J. Moll: ‘Nuevos hallazgos de manuscritos mozárabes con neumas musicales’, AnM, v (1950), 11–14

L. Brou: ‘Fragments d'un antiphonaire mozarabe du monastère de San Juan de la Peña’, Hispania sacra, v (1952), 35–65

L. Brou: ‘Un antiphonaire mozarabe de Silos d'après les fragments du British Museum (Mss. add. 11695, fol. 1r–4v)’, Hispania sacra, v (1952), 341–66

L. Brou: ‘Notes de paléographie musicale mozarabe’, AnM, vii (1952), 51–76; x (1955), 23–44

L. Brou and J.Vives, eds.: Antifonario visigótico-mozárabe de la Catedral de León (Barcelona, 1953–9)

L. Brou: ‘Le joyau des antiphonaires latins’, Archivos leonenses, viii (1954), 7–114

A.M. Mundó: ‘La datación de los códices litúrgicos visigóticos toledanos’, Hispania sacra, xviii (1965), 1–25

I. Fernández de la Cuesta, ed.: Antiphonale silense: British Library Mss.Add.30850: introducción, indices y edición (Madrid, 1985) [facs.]

M. Huglo: ‘La notation wisigothique est-elle plus ancienne que les autres notations européennes?’España en la música de occidente: Salamanca 1985, 19–26

Antiphonale hispaniae vetus (s. X–XI): Biblioteca de la Universidad de Zaragoza (Zaragoza, 1986)

A. Durán, R. Moragas and J. Villarreal, eds.: Hymnarium oscense (s. XI), i: Edición facsímil, ii: Estudios (Zaragoza, 1987)

J. Mas: ‘La notation catalane’, RdMc, xi (1988), 11–30

(vi) Italian

Le codex 10673 de la Bibliothèque vaticane fonds latin (XIe siècle): graduel Bénéventain, PalMus, 1st ser., xiv (1931)

Le codex VI. 34 de la Bibliothèque capitulaire de Bénévent (XIe–XIIe siècle): graduel de Bénévent avec prosaire et tropaire, PalMus, 1st ser., xv (1937/R) [incl. J. Hourlier: ‘Etude sur la notation bénéventaine’, 71–161]

R. Arnese: I codici notati della Biblioteca nazionale di Napoli (Florence, 1967)

Le codex 123 de la Bibliothèque angelica de Rome (XIe siècle): graduel et tropaire de Bologne, PalMus, 1st ser., xviii (1969)

A. Moderini: La notazione neumatica di Nonantola (Cremona, 1970)

A.M.W.J. Kurris: ‘Les coupures expressives dans la notation du manuscrit Angelica 123’, EG, xii (1971), 13–63

M.T.R. Barezzani: La notazione neumatica di un codice Bresciano (secolo XI) (Cremona, 1981)

Le manuscrit VI.33, Archivio arcivescovile Benevento: missel de Bénévent (début du XIe siècle), PalMus, 1st ser., xx (1983)

J. Boe: ‘The Beneventan Apostrophus in South Italian Notation, A.D. 1000–1100’, EMH, iii (1983), 43–66

T.F. Kelly: The Beneventan Chant (Cambridge, 1989)

T.F. Kelly: Les témoins manuscrits du chant bénéventain, PalMus, 1st ser., xxi (1992)

J. Boe: ‘Chant Notation in Eleventh-Century Roman Manuscripts’, Essays on Medieval Music: in Honor of David G. Hughes, ed. G.M. Boone (Cambridge, MA,1995), 43–57

M.T.R. Barezzani and G. Ropa, eds.: Codex angelicus 123: studi sul graduale-tropario bolognese del secolo XI e sui manoscritti collegati (Cremona, 1996)

J. Boe: ‘Music Notations in Archivio San Pietro C 105 and in the Farfa Breviary, Chigi C.VI.177’, EMH, xviii (1999), 1–45

(vii) Palaeo-Frankish

J. Handschin: ‘Eine alte Neumenschrift’, AcM, xxii (1950), 69–97; xxv (1953), 87–8

E. Jammers: Die Essener Neumenhandschriften der Landes- und Stadtbibliothek Düsseldorf (Ratingen, 1952)

E. Jammers: ‘Die paläofrankische Neumenschrift’, Scriptorium, vii (1953), 235–59

J. Hourlier and M. Huglo: ‘La notation paléofranque’, EG, ii (1957), 212–19

(viii) Breton

Antiphonale missarum Sancti Gregorii, Xe siècle: codex 47 de la Bibliothèque de Chartres, PalMus, 1st ser., xi (1912) [incl. A. Ménager: ‘Etude sur la notation du manuscrit 47 de Chartres’, 41–131]

M. Huglo: ‘Le domaine de la notation bretonne’, AcM, xxxv (1963), 53–84; rev. with plates and index as Britannia Christiana, i, ed. J.-L. Deuffic and A. Dennery (Daoulas, 1982)

(ix) Messine/Lorraine/Laon

Antiphonale missarum Sancti Gregorii, IXe–Xe siècle: codex 239 de la Bibliothèque de Laon, PalMus, 1st ser., x (1909) [incl. A. Ménager: ‘Aperçu sur la notation du manuscrit 239 de Laon: sa concordance avec les codices rythmiques sangalliens’, 177–211]

U. Sesini: La notazione comasca del cod. Ambrosiano E.68 sup. (Milan, 1932)

J. Hourlier: ‘Le domaine de la notation messine’, Revue grégorienne, xxx (1951), 96–113, 150–58

W. Lipphardt: ‘Punctum und Pes in Codex Laon 239’, KJb, xxxix (1955), 10–40

W. Lipphardt: ‘Flexa und Torculus in Codex Laon 239’, KJb, xli (1957), 9–15

P.M. Arbogast: ‘The Small Punctum as Isolated Note in Codex Laon 239’, EG, iii (1959), 83–133

P. Jeffery: ‘An Early Cantatorium Fragment Related to MS. Laon 239’, Scriptorium, xxxvi (1982), 245–52 [F-LA 266, ff.A–B]

J. Hourlier: ‘Trois fragments de Laon’, EG, xxii (1988), 31–42 [F-LA 9, 121, 266]

(x) Aquitanian

Le codex 903 de la Bibliothèque nationale de Paris (XIe siècle): graduel de Saint-Yrieix, PalMus, 1st ser., xiii (1925/R) [incl. P. Ferretti: ‘Etude sur la notation aquitaine d'après le graduel de Saint-Yrieix’, 54–211]

M.-N. Colette: ‘La notation du demi-ton dans le manuscrit Paris, B.N.Lat.1139 et dans quelques manuscrits du Sud de la France’, La tradizione dei tropi liturgici: Paris 1985 and Perugia 1987, 297–311

B. Gillingham, ed.: Paris, Bibliothèque nationale, fonds latin 1139 (Ottawa, 1987) [facs.]

c: significative letters

R.-J. Hesbert: ‘L'interprétation de l'equaliter dans les manuscrits sangalliens’, Revue grégorienne, xviii (1938), 161–73

J. Smits van Waesberghe: Muziekgeschiedenis der Middeleeuwen (Tilburg, 1938–42)

E. Cardine: ‘Le sens de iusum et inferius’, EG, i (1954), 159–60

J. Froger: ‘L'épître de Notker sur les “lettres significatives”’, EG, v (1962), 23–72

M.-C. Billecocq: ‘Lettres ajoutées à la notation neumatique du codex 239 de Laon’, EG, xvii (1978), 7–144

d: pitch-specific systems

J. Gmelch: Die Vierteltonstufen im Messtonale von Montpellier (Eichstätt, 1911)

S. Corbin: ‘Valeur et sens de la notation alphabétique à Jumièges et en Normandie’, Jumièges … XIIIe centenaire: Rouen 1954, 913–24

J. Smits van Waesberghe: ‘Les origines de la notation alphabétique au Moyen-Age’, AnM, xii (1957), 3–14

F.E. Hansen, ed.: H 159 Montpellier: Tonary of St. Bénigne of Dijon (Copenhagen, 1974)

W. Babb, C.V. Palisca and A.E. Planchart, eds.: Hucbald, Guido, and John on Music: Three Medieval Treatises (New Haven, CT, 1978)

J. Froger: ‘Les prétendus quarts de ton dans le chant grégorien et les symboles du ms. H.159 de Montpellier’, EG, xvii (1978), 145–79

A. Holschneider: ‘Die instrumentalen Tonbuchstaben im Winchester Troper’, Festschrift Georg von Dadelsen zum 60. Geburtstag, ed. T. Kohlhase and V. Scherliess (Neuhausen-Stuttgart, 1978), 155–66

R.L. Crocker: ‘Alphabet Notations for Early Medieval Music’, Saints, Scholars, and Heroes: Studies in Medieval Culture in Honor of Charles W. Jones, ed. M.H. King and W.M. Stevens (Collegeville, MN, 1979), ii, 79–104

A.C. Browne: ‘The a–p System of Letter Notation’, MD, xxxv (1981), 5–54

H. Schmid, ed.: Musica et Scolica enchiriadis una cum aliquibus tractatulis adiunctis (Munich,1981)

N. Phillips: ‘The Dasia Notation and its Manuscript Tradition’, Musicologie médiévale: Paris 1982, 157–73

N. Phillips: Musica et Scolica enchiriadis: its Literary, Theoretical, and Musical Sources (diss., New York U., 1984)

A.C. Santasuosso: Letter Notations in the Middle Ages (Ottawa, 1989)

A. Traub: ‘Hucbald von Saint-Amand “De harmonica institutione”’, Beiträge zur Gregorianik, vii (1989), 3–101 [whole issue]

W. Arlt: ‘Die Intervallnotation des Hermannus Contractus in Gradualien des 11. und 12. Jahrhunderts: das Basler Fragment N I 6 Nr.63 und der Engelberger Codex 1003’, De musica et cantu: Helmut Hucke zum 60. Geburtstag, ed. P. Cahn and A.-K. Heimer (Hildesheim, 1993), 243–56

B. Hebborn: Die Dasia-Notation (Bonn, 1995)

e: staff notations

(i) Introduction

J. Smits van Waesberghe: ‘The Musical Notation of Guido of Arezzo’, MD, v (1951), 15–53

J. Smits van Waesberghe: De musico-paedagogico et theoretico Guidone Aretino eiusque vita et moribus (Florence, 1953)

S.J.P. van Dijk: Sources of the Modern Roman Liturgy: the Ordinals by Haymo of Faversham and Related Documents (1243–1307) (Leiden, 1963)

M. Huglo: ‘Règlement du XIIIe siècle pour la transcription de livres notés’, Festschrift Bruno Stäblein zum 70. Geburtstag, ed. M. Ruhnke (Kassel, 1967), 121–33

J. Smits van Waesberghe: Musikerziehung: Lehre und Theorie der Musik im Mittelalter, Musikgeschichte in Bildern, iii/3 (Leipzig, 1969)

(ii) France, England and Spain

W.H. Frere, ed.: Graduale Sarisburiense (London, 1894/R) [facs. of GB-Lbl Add.12194]

W.H. Frere, ed.: Antiphonale Sarisburiense (London, 1901–24/R) [facs.]

H. Loriquet, J. Pothier and A.K. Collette, eds.: Le graduel de l'église cathédrale de Rouen au XIIIe siècle (Rouen, 1907) [facs. of F-Pn lat.904]

Antiphonaire monastique, XIIIe siècle: codex F. 160 de la Bibliothèque de la cathédrale de Worcester, PalMus, 1st ser., xii (1922/R)

W.M. Whitehill, J. Carro García and G. Prado, eds.: Liber Sancti Jacobi: Codex Calixtinus (Santiago de Compostela, 1944) [facs.]

S. Corbin: Essai sur la musique religieuse portugaise au Moyen Age (1100–1385) (Paris, 1952)

R.-J. Hesbert, ed.: Le prosaire de la Sainte-Chapelle (Mâcon, 1952) [part of I-BAca 1]

S.R. Marosszéki: ‘Les origines du chant cistercien: recherches sur les réformes du plain-chant cistercien au XIIe siècle’, Analecta sacri Ordinis Cisterciensis, viii (1952), 1–179

R.-J. Hesbert, ed.: Le tropaire-prosaire de Dublin: manuscrit Add. 710 de l'Université de Cambridge (vers 1360) (Rouen, 1966)

Jacobus: Codex Calixtinus de la catedral de Santiago de Compostela (Madrid, 1993) [colour facs.]

D. Hiley, ed.: Oxford Bodleian Library MS. Lat.liturg.b.5 (Ottawa, 1995) [facs.]

D. Saulnier, ed.: Verdun, Bibliothèque municipale, 759. Missale (Padua, 1995) [facs.]

O.T. Edwards, ed.: National Library of Wales MS. 20541 E: the Penpont Antiphonal (Ottawa, 1997) [facs.]

(iii) Low Countries and Germany

O. Marxer: Zur spätmittelalterlichen Choralgeschichte St. Gallens: der Codex 546 der St. Galler Stiftsbibliothek (St Gallen, 1908)

M. Sigl: Zur Geschichte des Ordinarium Missae in der deutschen Choralüberlieferung (Regensburg, 1911)

P. Wagner, ed.: Das Graduale der St. Thomaskirche zu Leipzig (14. Jahrhundert) (Leipzig, 1930–32/R)

R.-J. Hesbert, ed.: Le prosaire d'Aix-la-Chapelle (Rouen, 1961) [part of D-AAm 13 (XII)]

M. Härting: Der Messgesang im Braunschweiger Domstift St. Blasii (Handschrift Niedersächsisches Staatsarchiv in Wolfenbüttel VII B Hs 175) (Regensburg, 1963)

Le manuscrit 807, Universitätsbibliothek Graz (XIIe siècle): graduel de Klosterneuburg, PalMus, 1st ser., xix (1974)

W. Berschin: ‘Historia S. Kuonradi’, Freiburger Diözesan-Archiv, xcv (1975), 107–28

W. Arlt and M. Stauffacher, eds.: Engelberg Stiftsbibliothek Codex 314 (Winterthur, 1986)

J. Szendrei: ‘Linienschriften des zwölften Jahrhunderts auf süddeutschem Gebiet’, Cantus Planus IV: Pécs 1990, 17–30

P. van Poucke, ed.: Hildegard von Bingen, Symphonia harmoniae caelestium revelationum: Dendermonde, St.-Pieters & Paulusabdij, ms. cod.9 (Peer, 1991) [facs.]

A. Haug: Troparia tardiva: Repertorium später Tropenquellen aus dem deutschsprachigen Raum, MMMA, Subsidia, i (1995)

H. Möller, ed.: Antiphonarium: Karlsruhe, Badische Landesbibliothek, Aug.perg.60 (Munich, 1995) [facs.]

J. Szendrei: ‘Prager Quellen zum Hirsauer Choral’, Cantus Planus VII: Sopron 1995, 555–74

D. Hiley, ed.: Moosburger Graduale: München, Universitätsbibliothek, 2° Cod. ms. 156 (Tutzing, 1996) [facs.]

I. de Loos, C. Downey and R. Steiner, eds.: Utrecht, Bibliotheek der Rijksuniversiteit, MS 406 (3.J.7) (Ottawa, 1997) [facs.]

(iv) Italy

Antiphonarium ambrosianum du Musée britannique (XIIe siècle): codex additional 34209, PalMus, 1st ser., v (1896)

Antiphonaire monastique, XIIe siècle: codex 601 de la Bibliothèque capitulaire de Lucques, PalMus, 1st ser., ix (1906)

P. Ferretti: ‘I manoscritti musicale gregoriani dell’ Archivio di Montecassino’, Casinensia, i (1929), 187–203

G. Vecchi, ed.: Troparium sequentiarum nonantulanum (Cod. Casanat. 1741), MLMI, Latina, i (1955)

M. Huglo and others, eds.: Fonti e paleografia del canto ambrosiano (Milan, 1956)

B. Stäblein: Hymnen, I: die mittelalterliche Hymnenmelodien des Abendlandes, MMMA, i (Kassel, 1956; repr. 1995 with additional appendix)

M. Lütolf, ed.: Das Graduale von Santa Cecilia in Trastevere (Cod. Bodmer 74) (Cologny-Geneva, 1987) [facs.]

B.G. Baroffio: ‘Le grafie musicali nei manoscritti liturgici del secolo XII nell'Italia settentrionale: avvio a una ricerca’, Cantus Planus IV: Pècs 1990, 1–16

G. Cattin: Musica e liturgia a San Marco: testi e melodie per la liturgia delle ore dal XII al XVII secolo (Venice, 1990–92)

N. Albarosa and A. Turco, eds.: Benevento, Biblioteca capitolare 40, graduale (Padua, 1991) [facs., incl. essays by J. Mallet, A. Thibaut, R. Fischer, T. Kelly]

G. Cavallo, G. Orofino and O. Pecere: Exultet: rotoli liturgici del medioevo meridionale (Rome, 1994)

B.G. Baroffio and Soo Jung Kim, eds.: Biblioteca apostolica vaticana, Archivio S. Pietro B 79: antifonario della Basilica di S. Pietro (Sec. XII) (Rome, 1995) [facs.]

R. Camilot-Oswald: Die Liturgischen Musikhandschriften aus dem mittelalterlichen Patriarchat Aquileia, MMMA, Subsidia, ii (1997)

C. Ruini: I manoscritti liturgici della Biblioteca musicale L. Feininger presso il Castello del Buonconsiglio di Trento (Trent, 1998)

(v) Hungary, Bohemia and Poland

J. Hutter: Česká notace [Czech notation], ii: Nota choralis (Prague, 1930) [with Fr. summary]

J. Hutter: Notationis bohemicae antiquae specimina selecta e codicibus bohemicis, ii: Nota choralis (Prague, 1931)

P. Spunar: ‘Das Troparium des Prager Dekans Vit (Prag, Kapitelbibliothek, Cim 4)’, Scriptorium, ix (1957), 50–62

K. Szigeti: ‘Denkmäler des gregorianischen Chorals aus dem ungarischen Mittelalter’, SMH, iv (1963), 129–72

V. Plocek: Catalogus codicum notis musicis instructorum qui in Bibliotheca publica rei publicae Bohemicae socialisticae in Bibliotheca universitatis pragensis servantur (Prague, 1973) [describes 243 MS sources with musical notation in CZ-Pu]

T. Miazga: Die Gesänge zur Osterprozession in den handschriftlichen Überlieferungen vom 10. bis zum 19. Jahrhundert (Graz, 1979)

F. Pokorný: ‘Mährens Musik im Mittelalter’, Hudební veda, xvii/1 (1980), 36–52

J. Szendrei and R. Rybarič, eds.: Missale notatum strigoniense ante 1341 in Posonio (Budapest, 1982)

J. Szendrei: Középkori hangjegyírások Magyarorzágon [Medieval notation in Hungary] (Budapest, 1983) [with Ger. summary]

T. Miazga: Notacja gregoriańska w świetle polskich rekopisów liturgicznych (Graz, 1984)

J. Szendrei: ‘The Introduction of Staff Notation into Middle Europe’, SMH, xxviii (1986), 303–19

J. Szendrei: ‘Die Geschichte der Graner Choralnotation’, SMH, xxx (1988), 5–234

L. Dobszay: ‘Plainchant in Medieval Hungary’, Journal of the Plainsong and Medieval Music Society, xiii (1990), 49–78

J. Szendrey, ed.: Graduale strigoniense: s.XV/XVI (Budapest, 1990–93)

L. Dobszay: A gregorián ének kézikönyve [Handbook of Gregorian chant] (Budapest, 1993)

H. Vlhová: ‘Die Ordinarium-Tropen im Troparium des Prager Dekans Vít’, Cantus Planus VI: Éger 1993, 763–79

J. Szendrei: ‘Choral notationen in Polen’, Musica antiqua X: Bydgoszcz 1994, 257–74

A. Haug: Troparia tardiva: Repertorium später Tropenquellen aus dem deutschsprachigen Raum, MMMA, Subsidia, i (1995)

J. Morawski: Recytatyw liturgiczny [Liturgical recitative] (Warsaw, 1996)

J. Szendrei, ed.: The Istanbul Antiphoner (Budapest, 1999) [facs. of TR-Itks 42]

J. Szendrei: ‘Notacja liniowa w polskich żródłach chorałowych XII–XVI wieku’ [Staff notation of Gregorian chant in Polish sources from the 12th to 16th centuries], Notae musicae artis: notacja muzyczna W żródłach polskich XI–XVI wieku, ed. E. Witkowska-Zaremba (Kraków, 1999), 187–281

e. printed notations

H. Riemann: Notenschrift und Notendruck (Leipzig, 1896)

R. Molitor: Deutsche Choral-Wiegendrucke: ein Beitrag zur Geschichte des Chorals und des Notendruckes in Deutschland (Regensburg, 1904)

G.M. Suñol: Método completo para tres cursos de canto gregoriano segun la escuela de Solesmes (Montserrat, 1905; Eng. trans., 1930)

A. Mocquereau: Le nombre musical grégorien ou rythmique grégorienne: théorie et pratique, i (Tournai, 1908; Eng. trans., 1932); ii (Tournai, 1927)

L. David: ‘La restauration du chant grégorien et le mensuralisme’, Ephemerides liturgicae, xli (1927), 245–77, 349

J. Gajard: La méthode de Solesmes, ses principes constitutifs, ses règles pratiques d'interprétation (Tournai, 1951)

A.H. King: Four Hundred Years of Music Printing (London, 1964)

A.J. Bescond: Le chant grégorien (Paris, 1972)

Graduale triplex, seu Graduale romanum Pauli PP. VI cura recognitum & rhythimicis signis a Solesmensibus monachis ornatum, neumis laudunensibus (cod. 239) et sangallensibus (cod. San Gallensis 359 et Einsidlensis 121) nunc auctum (Solesmes, 1979)

Offertoriale triplex cum versiculis (Solesmes,1985) [with neumes of F-LA 239 and E 121]

(i) Neume patterns in Aquitanian polyphony, c1100–c1200.

2. Polyphony and secular monophony to c1260.

This section is devoted almost exclusively to the notation of rhythm, an emphasis borne out by the theoretical sources from later in this period. Apart from the Aquitanian manuscripts mentioned below, which display the neume dialect particular to this region, the music is notated in the square notation of plainchant (see above, §III, 1(vi)), which originally had no rhythmic significance, but acquired durational values for use in polyphony. Detailed descriptions of the sources of early polyphony discussed below may be found in Sources, MS, §IV; manuscripts containing secular monophony are treated in Sources, MS, §III.

(ii) Pre-modal rhythm.

(iii) The system of modal rhythm.

(iv) Coniuncturae, plicae and strokes.

(v) Modal rhythm in practice.

(vi) Organum purum, modus non rectus and irregular modes.

(vii) English practice.

(viii) Mensural notation before Franco.

(ix) The rhythmic interpretation of polyphonic and monophonic conductus.

(x) The rhythmic interpretation of secular monophony.

Notation, §III, 2: Polyphony and secular monophony to c1260

(i) Neume patterns in Aquitanian polyphony, c1100–c1200.

Several conspicuous features emerge in the notation of Aquitanian polyphony, including the Codex Calixtinus (E-SC, copied in central France c1150–80; see Huglo, 1995). One is a predilection for stronger consonance at the ends of neume-against-neume or note-against-neume units; another is the use of patterned melismas (e.g. strings of two- or three-note neumes). Stäblein (1963) and Karp (1992) proposed that rhythmic configurations akin to those of the later modal system may be present. Ex.5 is an example of Aquitanian/Compostelan polyphony with a hypothetical rhythmic transcription.

The preference for consonance at the ends of neumes is particularly striking in texted sections of conductus, versus and Benedicamus settings, where it belies the supposed pitch alignment and syllable placement implied by the sources; regular neumatic patternings are prominent in final melismas (or caudas), and also appear in organal voices of chant settings. A connection with Parisian polyphony is possible, although no theoretical witness supports such an association. One of the pieces in the Codex Calixtinus is attributed to Magister Albertus Parisiensis (d 1177), who has been identified with a cantor of Notre Dame; this ascription, however, is not certain.

Notation, §III, 2: Polyphony and secular monophony to c1260

(ii) Pre-modal rhythm.

As with interpretations of the Aquitanian repertory, the first manifestations of rhythmic indications in the Parisian corpus are difficult to construe (for a recent attempt, see Roesner, 1990). The period proposed for the musical activity is between about 1160 and 1250, while the surviving manuscript sources and theoretical testimony date from between about 1230 and 1300; this disjunction has meant that the historical picture is largely speculative and in dispute. It is evident, however, that at some point during the composition of the Notre Dame repertory certain portions of organa and conductus (discant passages, copulas, caudas and clausulas) were subject to rhythmic realization and recorded in a notation that conveyed the essence of this practice. Temporal durations were indicated by grouping the notes together as ligatures, rather than by discrete shapes.

The earliest evidence of this practice occurs in the opening portion of the anonymous treatise Discantus positio vulgaris (c1225–40), which advises that two-note ligatures represent a short–long (i.e. breve–long, or B–L) gesture, three-note groups signify long–breve–long (L–B–L) and those with four notes are all short; when more than four notes are found in a ligature they are executed at the discretion of the performer and not according to any specific criteria. The ratio of the long value to the short is 2:1, with greater or lesser durations described as ‘beyond measure’ (ultra mensuram). Although such lengths are strictly inexpressible as ‘long’ or ‘short’, they were not alien to the rhythmic practice. For example, single notes, such as those employed for a chant tenor in a discant passage or as a solitary figure within a ligatured portion, are described as having the duration of a long and a breve combined, that is, a ternary (later ‘perfect’) long value. In addition, the treatise implies that durations in ligatures are flexible; they may communicate different values depending on their position in a melodic phrase (e.g. a three-note ligature may have a value of B–B–L when preceded by a long). Such basic rules of thumb as given in the Discantus form the starting point for interpreting the rhythmic properties of Parisian polyphony. However, they neither suggest a fully developed system nor invoke the terminology of the rhythmic modes that was to be a staple of later theoretical works.

Notation, §III, 2: Polyphony and secular monophony to c1260

(iii) The system of modal rhythm.

At some point between the composition of the early part of the Discantus positio vulgaris and the treatise ascribed to Johannes de Garlandia (c1240–60) the diverse rhythms of Parisian polyphony were abstracted into a series of repetitive patterns, analogous perhaps to the modern function of a time signature. These underlying patterns, termed ‘modes’ (Lat. modi, sing. modus; Garlandia: manieres), formed the principal means of signifying ligature rhythms until the advent of mensural clarifications to their shapes (see Rhythmic modes). The following list names authors whose works include discussions of modal rhythm. However, it is important to realize that mensural doctrines appear in treatises as early even as Garlandia's text. Furthermore, occasional inconsistency exists in these theoretical works as to the number of the modes, their ordering and the depiction of particular ligature shapes.Anonymous: Discantus positio vulgaris (c1230–40: survives only in a partly revised form; see Reckow, AcM, 1976, p.137, n.81); ed. Cserba, 1935, pp.189–94
Johannes de Garlandia: De mensurabili musica (c1240–60: portions may stem from an anonymous earlier treatise; the final chapter of the work as it survives in F-Pn lat.16663, ed. in CoussemakerS, i, postdates Franco); ed. Reimer, 1972
Bruges Organum Treatise (possibly earlier than Garlandia); ed. Pinegar, 1992
Anonymus 7 (certain portions identical to the Bruges treatise; others may postdate Franco; see Reimer, 1972, i, p.31, n.20); CoussemakerS, i, 378–83, and CSM, xxxvi
Amerus/Aluredus: De musica libellus (1271); ed. Kromolicki, 1909, and CSM, xxv
Anonymus 4 (after 1272); ed. Reckow, 1967
Dietricus: Regule super discantum (c1275); ed. Müller, 1886
Magister Lambertus: Tractatus de musica (c1275); CoussemakerS, i, 251–81
Anonymus of St Emmeram (1279); ed. Sowa, 1930, and Yudkin, 1988
Franco of Cologne: Ars cantus mensurabilis (c1280: see Frobenius, 1970); CSM, xviii
Walter Odington: Summa de speculatione musicae (before 1300); CSM, xiv

Table 6 shows the six commonest rhythmic modes in their most conventional numerical ordering together with their associated ligature patterns (indicated by brackets over the notes). Each has a fundamental recurrent pulse equivalent to the ultra mensuram long (= dotted crotchet), and each pulse divides into three smaller time units (tempora/breves = quaver). Several important distinctions among the patterns are defined by whether the main pulse falls on the last note of the ligature (i.e. 1, 3a–b, 6a–b) or on the first (2, 4, 6c), whether the pulse is divided L–B (1a–b, 3b, 6b) or B–L (2, 3a, 4, 6c) and whether a ternary ligature extends over one, two or three pulses. (The value of the three-note ligature is the most equivocal and in the 5th mode is restricted largely to the tenor part in discant passages; the 4th mode, curiously, appears to be a theoretical construction not encountered in practice.) In all these important distinctions, the note shapes as they appear in the manuscript sources remain ambiguous; harmonic consonance, the succession of ligatures and the proportions between parts all contribute to define (or confound) the intended rhythm. This ambiguity appears to have prompted the writing of many of the treatises listed above, as their authors tried to clarify the intended durations by modifications to the standard, chant-based notational figures.

Notation, §III, 2: Polyphony and secular monophony to c1260

(iv) Coniuncturae, plicae and strokes.

One of the most ambiguous of all modal figures was the climacus, which was drawn with lozenges in square notation. These were called currentes (Lat.: ‘running’) by Anonymus 4, probably as an extended use of a term that originally referred to the descending scales found in Aquitanian as well as Parisian polyphony. Johannes de Garlandia did not mention them at all, possibly because they could be confused with the rhomboid semibreve. Franco of Cologne called the figure the coniunctura (Lat.: ‘joined [note]’), and even in his most rational system it eluded rhythmic codification.

Liquescent forms of neumes also appeared in melismatic polyphony in modal rhythm. Usually they indicated an added breve on a weak beat (see modes 6b–c), although other values were possible according to the prevailing rhythmic framework and the length of the host note. Because a single liquescent note was usually written like a ‘U’ or an inverted ‘U’, it was termed Plica (Lat.: ‘fold’). A vertical stroke added to the end of ligatures made them ‘plicata’. The liquescent neume, however, did not abandon its original function in such texted music as conductus, secular monophony and in chant settings if the cantus firmus demanded it.

Vertical strokes were used for two different purposes: as indications of changes of syllable and to signify rests. For the first purpose 12th-century scribes drew a roughly vertical line through both staves, although in Parisian sources this shrank to a small stroke through one or two lines only. Where a rest was intended its duration was not specified, although it frequently corresponded to the penultimate value of the modal pattern.

Whereas former repertories tended to preserve the ligatures of cantus firmi, undifferentiated single notes were typical for tenors in the early Parisian corpus, whether the tenor held long notes in Organum or moved with the pulse in discant (see Discant, §I). Only in the later layers of discant did tenors include ligatures with breves. Although a stroke generally appears after each note of the tenor in organum, the pitch seems to have been sustained beneath the continuing organal voices. Anonymus 4 called this a burdo (Lat.: ‘support’, ‘drone’).

Notation, §III, 2: Polyphony and secular monophony to c1260

(v) Modal rhythm in practice.

The system of modal rhythm outlined by the theorists is an intellectual abstraction from flexible practice. The rudimentary patterns of the modes they cited are of course frequently encountered in the late 12th- and early 13th-century repertory, and are particularly clear in tenors of late clausulas and motets. But in practice they are often so extensively intermingled, not merely vertically in different voices but successively in single parts, that they are only of limited descriptive use if treated strictly. Modal integrity can be compromised not only by the insertion of unligated long notes within a phrase, but also by the practice of fractio modi (Lat.: ‘breaking of the mode’) – the introduction of shorter note values than normal. Such deviations alter the expected sequence of ligatures in a particular pattern. Fractio modi may have prompted an early formation of the 6th mode (6a) from the 1st, as the typical series of two-note ligatures succeeding an initial ternary figure in mode 1 is, in mode 6, replaced by three-note figures following an initial four-note gesture. In such cases the final note of the ligature tends to retain its normal value within the prevailing mode as far as is feasible, with the added notes splitting the other elements of the pattern. Even with this provision, however, the profusion of ‘non-modal’ ligatures in an ornate passage of fractio modi can seriously obscure a clear reading of the rhythm. Fig.49 gives some of the patterns described by Anonymus 4.

Ambiguities within the modal system may be demonstrated by two examples. Ex.9 gives the opening of the verse section of Perotinus's Alleluia, Posui adiutorium (I-Fl Plut.29.1, f.36v). Judging from the ligature patterns, both upper parts appear closest in form to the 2nd mode; yet the duplum lacks a final three-note ligature to match the triplum (which, contrary to the rules, ends with a two-note ligature followed by a single note). In this case, the penultimate note may reasonably be interpreted as a long. Consonances between the second note of each ligature, however, are greater in number than between the first – a transcription in the 1st mode thus seems more appropriate, so that each pulse is coincident with a consonance.

Ex.10 is from a Benedicamus Domino (I-Fl Plut.29.1, f.41r). Because of the prevalence of repeated notes, which defy ligation, the passage may be transcribed in the 6th mode (as in Husmann, 1940) as easily as in the 3rd. But most of the rest of the piece is in the 1st mode, so that a reading in the ‘alternative’ 3rd mode (3b) probably causes the least disruption. The consideration of variants in the concordant sources also influences interpretation, as, for example, in the third phrase where I-Fl Plut.29.1 notates the duplum in a 2nd-mode pattern, whereas D-W Guelf.628 (677) uses the 1st mode. Furthemore, cadences such as that in ex.10 frequently present problems of interpretation; the transcriptions given here are only a few out of many justifiable readings.

Notation, §III, 2: Polyphony and secular monophony to c1260

(vi) Organum purum, modus non rectus and irregular modes.

Particular segments of sustained-tone organum duplum (termed organum purum by Anonymus 4, and organum in speciali or organum per se by Garlandia) present serious problems regarding the extent and type of rhythmic interpretation and have caused much disagreement among scholars. Unlike discant or copula passages, whose unfolding often suggests a ‘straightforward’ (rectus) rhythmic mode, the ligature formations of organum purum defy such easy categorization. Garlandia's representative discussion of the rhythmic component, with its emphasis on oppositional construction, demonstrates vividly how the subsequent imposition of the modal system failed to reflect accurately the capricious style of organum purum:

Organum purum is said to be that performed according to a certain mode that is not rectus but non rectus. A rectus mode is used here to mean that by which discant is performed. … But in non rectus [measure] the long and breve are taken not in the first way, but according to the context (ex contingenti).

Just what contexts might affect the performance appear in a later paragraph:

Longs and breves in organum are recognized in this way, that is to say through [concord], through notation, through the penultimate. Whence the rule: each thing [?duplum note] that falls upon something [?tenor pitch] in compliance with the strength of the [consonances] is said to be long. Another rule: whatever is notated long according to the organa before a rest or in [?the] place [of a concord] is said to be long. Another rule: whatever is accepted before a long rest or before a perfect concord is said to be long.

Perhaps because of the vagueness of such passages, no agreement on the rhythmic realization of organum purum has yet been reached. Does the first rule imply that every harmonic interval between duplum and tenor owes its length to consonance, or only the contact points between the two parts at the start and close of major sections? Does the last rule apply to all perfect concords, or only particular ones? And what is the role of the notational component? What purpose do the duplum ligatures serve and how are they to be coordinated with the other strictures mentioned by Garlandia? Finally, and perhaps most importantly, there is the question of whether the theoretical information and manuscript sources reflect or recast a performing tradition that began at least a half-century earlier. Faced with such dilemmas it is easy to understand why editors of this repertory often choose a non-committal approach to organum purum by using stemless note heads, although several transcriptions with specified durations are also available (e.g. Waite, 1954; Tischler, 1988; Payne, 1996).

Another perplexing phenomenon are the ‘modi irregulares’ mentioned by Anonymus 4 (fig.50). While the first two appear to be rhythmically sharper versions of the normal 1st and 2nd modes, interpretations of the others ranges from binary mensuration of the long to mere nuances of tempo.

Notation, §III, 2: Polyphony and secular monophony to c1260

(vii) English practice.

Sanders (1962) has convincingly demonstrated that pairs or longer chains of lozenges (‘English breves’) used in English manuscripts dating up to about 1300 signify 1st-mode rhythms (L–B, L–B etc.). Such breves appear in D-W Guelf.628 (677) (even in the non-English works: for facs. of Perotinus's Sederunt see Sources, MS, §IV, fig.30), GB-Lbl Harl.978 (in which some pieces have been ‘reformed’ by adding tails to alternate lozenges to make them longs) and the Worcester Fragments (earlier layers). Johannes de Garlandia and Anonymus 4 both reported that the English interpreted ternary ligatures in what has become known as ‘alternative 3rd mode’ (3b in Table 6. Similarly, Wibberly (EECM, xxvi) argued that certain nuances in the slanting of ligatured notes by English scribes may reflect an attempt to distinguish between complementary insular and continental rhythmic practices.

Notation, §III, 2: Polyphony and secular monophony to c1260

(viii) Mensural notation before Franco.

Clarification of ambiguities in modal notation already appears in the earliest Parisian sources, though inconsistently, and in the theory of Johannes de Garlandia. Such specifications affected the appearance of discrete note shapes, ligatures and to a lesser extent rests.

The pressure towards the codification of note forms seems indebted to the motet (see Motet, §I). Many early 13th-century motets were clausulas with text added to their upper voice or voices; because the text usually set a separate syllable to every pitch, the ligatures of clausulas were thus split into single notes. Hence in older sources the music of motets was often available in melismatic notations as clausulas, but in texted form with undifferentiated note heads.

All the chief sources of Parisian polyphony up to about 1260 may distinguish between a single long and a single breve in instances involving repeated notes (the long with a downward stem attached to its right-hand side, the breve without). The opening of the organum quadruplum Sederunt has already been cited; another example is the clausula Mulierum (Apel, 1942, facs.52a). Double longs are also frequently distinguished by horizontal elongation (see above, ex.6).

In mensural sources certain conventions regarding the value of the discrete notes were observed. A long contained three tempora if followed by another long (as in mode 5), and two tempora if succeeded (mode 1) or preceded (mode 2) by a breve; pairs of breves (mode 3) were interpreted in the order brevis recta (one tempus) – brevis altera (two tempora), except by the English, who preferred the opposite interpretation (see above, §2(vii)).

The semibreve (single lozenge) attained its shape at about the time of De mensurabili musica (c1240–60); but it is rare in sources from this period. (Both Garlandia and Anonymus 4, however, used the term semibrevis to refer to half a brevis altera; see Sanders, 1962, p.267.) The earliest surviving manuscripts clearly and consistently making the distinction are rather later: F-Pn n.a.fr.13521 (‘La Clayette MS’) and GB-Lbl 30091, from the end of the 13th century. Other important steps concerned the clarification of ligatures. Theorists conferred qualities of ‘propriety’ (proprietas) and ‘perfection’ (perfectio) on the traditional chant-based shapes of modal rhythm. The former term referred to the first note of the ligature – whether it was drawn ‘properly’ (cum proprietate) or not (sine proprietate) – the latter originally specified whether the note shape concluded in a regular manner (cum perfectione) or denoted a ‘broken’ or ‘unfinished’ figure (hence ‘imperfect’, sine perfectione). Fig.51 gives the basic shapes and their alterations. The meaning of the modifications (as well as the default forms) depended on the individual theorist. Garlandia, for example, held that lack of propriety reversed the default values of an entire two- or three-note ligature (a proper, perfect B–L thus became L–B, and L–B–L inverted to B–L–B), whereas imperfect ligatures needed to be reconstituted to perfect forms according to the context of the phrase. Franco's innovation was to specify undeviating values for ligatures of all types and to equate propriety and perfection respectively with the durations of only the first and last notes of a figure. (For a comparative table drawn from several theorists, see Reimer, 1972, i, 56.)

The ligature that became known as ‘having opposite propriety’ (cum opposita proprietate), written with an ascending stroke to the left, is first seen in D-W 1099. Garlandia was the earliest theorist to describe such a ligature, but whereas he interpreted it in a manner akin to fractio modi (with the last note as a long and all others equal to a breve), later practice was to read the first two notes as semibreves and the remainder according to the rules of perfection (see below, §III, 3). An alternative form of the descending ligature cum opposita proprietate had three lozenges with a tail descending obliquely from the left of the first, and is found in some French and many English manuscripts.

Johannes de Garlandia used a stroke through one space of the staff for a breve rest and a stroke through two or more for a long (number of tempora undifferentiated). Magister Lambertus used a stroke through one space for the semibreve rest, through two for the brevis recta, three for the brevis altera and longa imperfecta, and four for the longa perfecta (a practice found in D-BAs lit.115). Franco used strokes through the lower portion of a space for semibreve rests, and one complete space for each tempus. The duration of the two-tailed plica might also be differentiated. The plicated breve had either a very short tail to the right or a single tail to the left, the plicated long a long tail to the right and a shorter one to the left. English scribes used a lozenge with a tail descending obliquely to the left for a semibreve.

Notation, §III, 2: Polyphony and secular monophony to c1260

(ix) The rhythmic interpretation of polyphonic and monophonic conductus.

The caudas of the more complex Parisian conductus were usually written in the ligature notation associated with modal rhythm. Realization of the syllabic sections, however, is far less certain. As with the texted versions of early motets, the note values set to conductus verses are ambiguous in the major sources; but in contrast to the motet the routine absence of melismatically or mensurally notated forms of the music compounds the problems of interpretation. Often it is presumed that the texts themselves provide clues for performance in a rhythmic mode. However, there are several methodological problems with such a premise. Firstly, datable examples of Parisian conductus indicate that the genre was cultivated from about 1160 to about 1240, well before the codification of the modal system and only briefly coincident with the imposition of its strictures; it is therefore questionable whether modal interpretations of conductus poetry should apply to the entire repertory, if at all. Secondly, the modal system originated as a means of interpreting ligatures; it cannot be assumed that its successive long and breve durations apply equally to syllabic passages before the advent of the motet. Lastly, although the poetry of conductus is ‘rhythmic’ in the specific sense that it relies on lines with set numbers of syllables, the accentual configurations within each line do not approach the regularity of poetic metre and can frustrate a performance that adheres too strictly to a modal pattern.

The series of transcriptions of the opening of Hac in anni ianua (ex.11) reflects the diversity of possible solutions (see also Apel, 1942, p.258). Exx.11a–d treat each syllable as occupying the same length of time. 11a interprets the ligatures in binary rhythm (perhaps the least justifiable) and 11b in ternary, both within the 1st mode; 11c gives a strict reading in mode 1, as if there were no text (compare the treatment of Aquitanian versus in ex.8), and 11d is a strict reading in mode 2. Exx.11e–f abandon the principle of giving equal time to each syllable: 11e interprets the text as in the 1st mode; 11f as in the 2nd. On the other hand, ex.11g gives the closing cauda of the piece; its ligatures suggest the 3rd mode (although the alternative mode 3 could serve equally well), which could influence the choice of rhythm for the rest of the work. Page (1997) has suggested rendering the syllabic portions of all conductus with unmeasured values.

Given the difficulties of transcribing polyphonic conductus, where the rhythm might be expected to be evident from the relationship between the parts, it is not surprising that monophonic conductus presents even greater problems. In several of the more elaborate works, interpretations with equal syllables are often complicated by the presence of compound neumes of six or more notes (these are occasionally present in polyphonic conductus also). As an illustration, ex.12 gives a rhythmic rendition of the opening of one of the most ornate works in the Parisian corpus, Turmas arment christicolas, on the murder of Adalbert of Leuven, Bishop of Liège, by German knights in 1192. The principle of equal syllables has been applied wherever a syllable carries one, two or three notes; where it has four or more its value has been extended to two or more dotted crotchets. If such an interpretation was originally intended, it displays nothing of the regular ligature patterns characteristic of the organa tripla and quadrupla of this period, and the stress of the text is not complemented. Interestingly, the ligatures and melodic content of monophonic conductus often suggest the modus non rectus of organum purum rather than the clearer forms of the rhythmic modes. As a result, transcription in unmeasured values for this repertory, as well as for other types of monophony from the period, has become standard practice.

Notation, §III, 2: Polyphony and secular monophony to c1260

(x) The rhythmic interpretation of secular monophony.

The same cautions exercised in the treatment of conductus rhythm apply to the secular monophonic repertory, but with even more circumspection. The application of modal rhythms before the codification of the system and outside the Parisian orbit is highly questionable (this includes the majority of troubadour and trouvère songs), the texts are non-metrical and therefore not conducive to patterned rhythms, and, except for a handful of songs in F-Pn fr.846 and a few in other manuscripts, mensural notation is not used, even though the bulk of the sources of secular monophony dates from after c1250. In retrospect, the suggestion that troubadour and trouvère melodies might be transcribed in rhythmic patterns resembling those of the rhythmic modes (see Sanders, 1985) seems to have been adopted with excessive zeal, although it still has its adherents.

Yet even with a preference for unmeasured transcriptions, opinions are divided on the fundamental procedures for interpreting the songs. Among recent treatments, van der Werf (1972 etc.) suggested an essential rhythmic equality for each pitch that could be adapted to accommodate rhetorical features of the poem. Stevens (1986) proposed a single elastic rhythmic unit for each syllable, and along with Page (1987) recommended the recognition of various registers (high/courtly versus low/popular styles) among songs – distinctions that could affect the imposition of rhythm as well as the use of instruments in performance. Aubrey's approach (1996) is the most flexible and inclusive, eschewing single, systematic procedures and suggesting that the different contexts in which songs were performed might have significantly altered the presentation of even the same piece by the same executor. This method favours the investigation of each piece on its own terms to uncover patterns of musical structure and emphasis that can inform the rhythmic treatment.

Notation, §III, 2: Polyphony and secular monophony to c1260

BIBLIOGRAPHY

theoretical sources

monophony to c1260: studies

polyphony to c1260: studies

Notation, §III, 2: Polyphony and secular monophony to c1260: Bibliography

theoretical sources

listed alphabetically as items largely undatable

Amerus: Practica artis musice, ed. J. Kromolicki: Die Practica artis musicae des Amerus und ihre Stellung in der Musiktheorie des Mittelalters(Berlin, 1909); ed. C. Ruini, CSM, xxv (1977)

Anonymous: Ad organum faciendum [Milan organum treatise (prose and verse); Berlin treatises A and B; Montpellier treatise], ed. H.H. Eggebrecht and F. Zaminer:Ad organum faciendum: Lehrschriften der Mehrstimmigkeit in nachguidonischer Zeit (Mainz, 1970) [Lat. with Ger. trans.]; Eng. trans. of Milan and Berlin B, J.A. Huff, Music Theorists in Translation, viii (Brooklyn, 1963)

Anonymous: Discantus positio vulgaris, CoussemakerS, i, 94–7; ed. S.M. Cserba:Hieronymus de Moravia O.P.: Tractatus de musica (Regensburg, 1935), 189–94; Eng. trans., J. Knapp, JMT, vi (1962), 203–7

Anonymous: Musica enchiriadis, Scolica enchiriadis, GerbertS, i, 152–73, 173–212; ed. H. Schmid: Musica et scolica enchiriadis (Munich,1981); Eng. trans., R. Erickson: Musica enchiriadis and Scolica enchiriadis, ed. C.V. Palisca (New Haven, CT, 1995)

Anonymous [St Emmeram anonymus], ed. H. Sowa: Ein anonymer glossierter Mensuraltraktat 1279 (Kassel, 1930); Eng. trans., Yudkin (1990)

Anonymous [Vatican organum treatise], ed. F. Zaminer: Der Vatikanischen Organum-Traktat (Tutzing, 1959); ed. I. Godt and B. Rivera: ‘The Vatican Organum Treatise: a Colour Reproduction, Transcription, and Translation into English’, Gordon Athol Anderson, 1929–81, in memoriam, ed. L.A. Dittmer (Henryville, PA, 1984), ii, 264–345

Anonymus 4 [CoussemakerS, i]: De mensuris et cantu, CoussemakerS, i, 327–65; ed. F. Reckow:Der Musiktraktat des Anonymus 4: Edition und Interpretation der Organum purum-Lehre (1967), i; Eng. trans., Yudkin (1985)

Anonymus 7 [CoussemakerS, i]: De musica libellus, CoussemakerS, i, 378–83; ed. G. Reaney,CSM, xxxvi (1996), 19–35; Eng. trans., J. Knapp: ‘Two 13th-Century Treatises on Modal Rhythm and the Discant’, JMT, vi (1962), 200–215 [see also Pinegar, 1992, for edn of Bruges organum treatise]

Dietricus: Regule super discantum, ed. H. Müller: Eine Abhandlung über Mensuralmusik (Leipzig, 1886)

Franco of Cologne: Ars cantus mensurabilis, CoussemakerS, i, 117–36; GerbertS, iii, 1–16; ed. G. Reaney and A. Gilles, CSM, xviii (1974); ed. F. Gennrich, Musikwissenschaftliche Studien-Bibliothek, xv–xvi (Darmstadt, 1957)

Guido frater: Ars musice mensurate, ed. F.A. Gallo: Mensurabilis musicae tractatuli, AntMI, Scriptores, i/1 (1966), 17–40

Guido of Arezzo: Micrologus, GerbertS, ii, 2–24; ed. J. Smits van Waesberghe, CSM, iv (1955); Eng. trans., W. Babb, in Hucbald, Guido and John on Music: Three Medieval Treatises, ed. C.V. Palisca (New Haven, CT, 1977)

Hieronymus de Moravia: Tractatus de musica, CoussemakerS, i, 1–94; ed. S.M. Cserba: Hieronymus de Moravia O.P.: Tractatus de musica (Regensburg, 1935)

Jacobus of Liège: Speculum musice, CoussemakerS, ii, 193–433 [attrib. Johannes de Muris]; ed. R. Bragard, CSM, iii (1955–73)

Johannes de Garlandia: De mensurabili musica, CoussemakerS, i, 175–82; later version as De musica mensurabili positio, CoussemakerS, i, 97–117; ed. E. Reimer (Wiesbaden, 1972); Eng. trans., S. Birnbaum (Colorado Springs, CO, 1978)

Magister Lambertus [Pseudo-Aristoteles]: Tractatus de musica,CoussemakerS, i, 251–81; CSM (forthcoming)

W. Odington: Summa de speculatione musicae, CoussemakerS, i, 182–250; ed. F.F. Hammond, CSM, xiv (1970); Eng. trans. of pt.vi, J.A. Huff, MSD, xxxi (1973)

For further bibliography seeOrganum and discant: bibliography, §III, 2.

Notation, §III, 2: Polyphony and secular monophony to c1260: Bibliography

monophony to c1260: studies

J.B. Beck: Die Melodien der Troubadours (Strasbourg, 1908/R)

P. Aubry: Trouvères et troubadours (Paris, 1909, 2/1910; Eng. trans., 1914/R)

F. Ludwig: ‘Zur “modalen Interpretation” von Melodien des 12. und 13. Jahrhunderts’, ZIMG, xi (1909–10), 379–82

P. Aubry and A. Jeanroy, eds.: Le chansonnier de l'Arsenal (trouvères du XIIe–XIIIe siècle) (Paris, 1909–12)

J.B. Beck: La musique des troubadours (Paris, 1910/R)

E. Jammers: ‘Untersuchungen über die Rhythmik und Melodik der Melodien der Jenaer Liederhandschrift’, ZMw, vii (1924–5), 265–304

R. Lach: ‘Zur Frage der Rhythmik des altfranzösischen und altprovenzalischen Liedverses’, Zeitschrift für französische Sprache und Literatur, xlvii (1924–5), 35–59

J.B. Beck, ed.: Le chansonnier Cangé: manuscrit français no.846 de la Bibliothèque nationale de Paris, Corpus cantilenarum medii aevi, 1st ser., i (Paris and Philadelphia, 1927/R) [facs.]

J. Handschin: ‘Die Modaltheorie und Carl Appels Ausgabe der Gesänge von Bernart de Ventadorn’, Medium aevum, iv (1935), 69–82

J.B. Beck and L. Beck, eds.: Le manuscrit du roi: fonds français no.844 de la Bibliothèque nationale de Paris, Corpus cantilenarum medii aevi, 1st ser., ii (London and Philadelphia, 1938/R) [facs.]

H. Anglès: ‘Der Rhythmus der monodischen Lyrik des Mittelalters und seine Probleme’, IMSCR IV: Basle 1949, 45–50

H. Husmann: ‘Zur Grundlegung der musikalischen Rhythmik des mittellateinischen Liedes’, AMw, ix (1952), 3–26

H. Husmann: ‘Zur Rhythmik des Trouvèregesanges’, Mf, v (1952), 110–31

H. Husmann: ‘Die musikalische Behandlung der Versarten im Troubadourgesang der Notre Dame-Zeit’, AcM, xxv (1953), 1–20

H. Husmann: ‘Das Prinzip der Silbenzählung im Lied des zentralen Mittelalters’, Mf, vi (1953), 8–23

F. Gennrich: ‘Grundsätzliches zur Rhythmik der mittelalterlichen Monodie’, Mf, vii (1954), 150–76

H. Husmann: ‘Das System der modalen Rhythmik’, AMw, xi (1954), 1–38

F. Gennrich: ‘Ist der mittelalterliche Liedvers arhythmisch?’, Cultura neolatina, xv (1955), 109–31

F. Gennrich: Musica sine littera: Notenzeichen und Rhythmik der Gruppennotation (Darmstadt, 1956)

F. Gennrich: ‘Wer ist der Initiator der “Modaltheorie”? Suum cuique’, Miscelánea en homenaje a Monseñor Higinio Anglés (Barcelona, 1958–61), 315–30

H. Anglès: ‘Die volkstümlichen Melodien bei den Trouvères’, Festgabe für Joseph Müller-Blattau, ed. W. Salmen (Saarbrücken, 1960, 2/1962), 15–22

H. Anglès: ‘Der Rhythmus in der Melodik mittelalterlicher Lyrik’, IMSCR VIII: New York 1961, i, 3–11

B. Kippenberg: Der Rhythmus im Minnesang: eine Kritik der literar- und musikhistorischen Forschung (Munich, 1962)

H. van der Werf: ‘The Trouvère Chansons as Creations of a Notationless Musical Culture’, CMc, no.1 (1965), 61–8

H. van der Werf: ‘Deklamatorischer Rhythmus in den Chansons der Trouvères’, Mf, xx (1967), 122–44

H. van der Werf: The Chansons of the Troubadours and Trouvères: a Study of the Melodies and their Relation to the Poems (Utrecht, 1972)

E. Jammers: Aufzeichnungsweisen der einstimmigen ausserliturgischen Musik des Mittelalters, Palaeographie der Musik, i/4 (Cologne, 1975)

B. Stäblein: Schriftbild der einstimmigen Musik, Musikgeschichte in Bildern, iii/4 (Leipzig, 1975)

T. Karp: ‘Three Trouvère Chansons in Mensural Notation’, Gordon Athol Anderson, 1929–1981, in memoriam ed. L.A. Dittmer (Henryville, PA, 1984), 474–94

H. van der Werf: The Extant Troubadour Melodies: Transcriptions and Essays for Performers and Scholars (Rochester, NY, 1984)

C. Page: Voices and Instruments of the Middle Ages: Instrumental Practice and Songs in France, 1100–1300 (Berkeley, 1986)

J. Stevens: Words and Music in the Middle Ages: Song, Narrative, Dance and Drama, 1050–1350 (Cambridge, 1986)

E. Aubrey: The Music of the Troubadours (Bloomington, IN, 1996)

Notation, §III, 2: Polyphony and secular monophony to c1260: Bibliography

polyphony to c1260: studies

G. Jacobsthal: Die Mensuralnotenschrift des zwölften und dreizehnten Jahrhunderts (Berlin, 1871/R)

W. Niemann: Über die abweichende Bedeutung der Ligaturen in der Mensuraltheorie der Zeit vor Johannes de Garlandia (Leipzig, 1902/R)

F. Ludwig: Repertorium organorum recentioris et motetorum vetustissimi stili, i/1 (Halle, 1910/R), 42–57

A.M. Michalitschke: Theorie des Modus: eine Darstellung der Entwicklung des musikrhythmischen Modus und der entsprechenden mensuralen Schreibung (Regensburg, 1923)

J. Handschin: ‘Zur Notre Dame-Rhythmik’, ZMw, vii (1924–5), 386–9

A.M. Michalitschke: ‘Zur Frage der Longa in der Mensuraltheorie des 13. Jahrhunderts’, ZMw, viii (1925–6), 103–9

A.M. Michalitschke: ‘Studien zur Entstehung und Frühentwicklung der Mensuralnotation’, ZMw, xii (1929–30), 257–79

H. Sowa: ‘Zur Weiterentwicklung der modalen Rhythmik’, ZMw, xv (1932–3), 422–7

H. Husmann, ed.: Die drei- und vierstimmigen Notre-Dame-Organa: kritische Gesamtausgabe, Publikationen älterer Musik, xi (Leipzig, 1940/R)

W. Apel: The Notation of Polyphonic Music, 900–1600 (Cambridge, MA, 1942, rev. 5/1961; Ger. trans., rev., 1970)

R. von Ficker: ‘Probleme der modalen Notation (zur kritischen Gesamtausgabe der drei- und vierstimmigen Organa)’, AcM, xviii–xix (1946–7), 2–16

M. Bukofzer: ‘Rhythm and Meter in the Notre Dame Conductus’, BAMS 1948, 63–5

F. Gennrich: ‘Perotins Beata viscera Mariae virginis und die “Modaltheorie”’, Mf, i (1948), 225–41

W. Apel: ‘From St. Martial to Notre Dame’, JAMS, ii (1949), 145–58

J. Handschin: ‘Zur Frage der Conductus-Rhythmik’, AcM, xxiv (1952), 113–30

W. Waite: ‘Discantus, Copula, Organum’, JAMS, v (1952), 77–87

C. Parrish: ‘Some Rhythmical Problems of the Notre Dame Organa and Conductus’, JAMS, vi (1953), 89–90

H. Husmann: ‘Das System der modalen Rhythmik’, AMw, xi (1954), 1–38

W.G. Waite: The Rhythm of Twelfth-Century Polyphony: its Theory and Practice (New Haven, CT, 1954/R)

H. Husmann: ‘Les époques de la musique provençale au Moyen Áge’, Actes et mémoires du ler congrès international de langue et littérature du Midi de la France: Avignon 1955 (Avignon, 1957), 197–201

C. Parrish: The Notation of Medieval Music (New York, 1957, 2/1959/R), chaps.3–4

H. Tischler: ‘Ligatures, Plicae and Vertical Bars in Premensural Notation’, RBM, xi (1957), 83–92

H. Tischler: ‘A propos the Notation of the Parisian Organa’, JAMS, xiv (1961), 1–8

E.H. Sanders: ‘Duple Rhythm and Alternate Third Mode in the 13th Century’, JAMS, xv (1962), 249–91

B. Stäblein: ‘Modale Rhythmen im Saint-Martial-Repertoire?’, Festschrift Friedrich Blume, ed. A.A. Abert and W. Pfannkuch (Kassel, 1963), 340–62

E.F. Flindell: ‘Aspekte der Modalnotation’, Mf, xvii (1964), 353–73

F. Reckow: Der Musiktraktat des Anonymus 4, ii: Interpretation der Organum purum-Lehre (Wiesbaden, 1967)

F. Reckow: ‘Proprietas und perfectio: zur Geschichte des Rhythmus, seiner Aufzeichnung und Terminologie im 13. Jahrhundert’, AcM, xxxix (1967), 115–43

G.A. Anderson: ‘Mode and Change of Mode in Notre Dame Conductus’, AcM, xl (1968), 92–114

G.A. Anderson, ed.: The Latin Compositions in Fascicules VII and VIII of the Notre Dame Manuscript Wolfenbüttel Helmstadt 1099 (1206), pt.i: Critical Commentary, Translation of the Texts and Historical Observations (New York, 1968–76)

R. Flotzinger: Der Discantussatz im Magnus liber und seiner Nachfolge (Vienna, 1969)

S. Fuller: Aquitanian Polyphony of the Eleventh and Twelfth Centuries (diss., U. of California, Berkeley, 1969)

R.A. Rasch: Iohannes de Garlandia en de ontwikkeling van de voor-Franconische notatie (New York, 1969) [with Eng. and Ger. summaries]

H.H. Eggebrecht and F. Zaminer, eds.: Ad organum faciendum: Lehrschriften der Mehrstimmigkeit in nachguidonischer Zeit (Mainz, 1970)

W. Frobenius: ‘Zur Datierung von Francos Ars cantus mensurabilis’, AMw, xxvii (1970), 122–7

J. Stenzl: Die vierzig Clausulae der Handschrift Paris, Bibliothèque nationale latin 15139 (Saint Victor-Clausulae)(Berne, 1970)

H.H. Eggebrecht: ‘Organum purum’, Musikalische Edition im Wandel des historischen Bewusstseins, ed. T.G. Georgiades (Kassel, 1971), 93–112

W. Frobenius: ‘Longa–Brevis’, ‘Minima’, ‘Modus (Rhythmuslehre)’, ‘Perfectio’, ‘Prolatio’, ‘Proprietas (Notationslehre)’, ‘Semibrevis’, ‘Semiminima’, (1971–4), HMT

R. Flotzinger: ‘Zur Frage der Modalrhythmik als Antike-Rezeption’, AMw, xxix (1972), 203–8

E. Reimer: Johannes de Garlandia: De mensurabili musica, ii: Kommentar und Interpretation der Notationslehre (Wiesbaden, 1972)

G.A. Anderson: ‘Magister Lambertus and Nine Rhythmic Modes’, AcM, xlv (1973), 57–73

G.A. Anderson: ‘The Rhythm of cum littera Sections of Polyphonic Conductus in Mensural Sources’, JAMS, xxvi (1973), 288–304

R. Baltzer: Notation, Rhythm, and Style in the Two-Voice Notre Dame Clausula (diss., Boston U., 1974)

K.-J. Sachs: ‘Punctus’ (1974), HMT

G.A. Anderson: ‘The Notation of the Bamberg and Las Huelgas Manuscripts’, MD, xxxii (1978), 19–67

G.A. Anderson: ‘The Rhythm of the Monophonic Conductus in the Florence Manuscript as Indicated in Parallel Sources’, JAMS, xxxi (1978), 480–89

J. Knapp: ‘Musical Declamation and Poetic Rhythm in an Early Layer of Notre Dame Conductus’, JAMS, xxxii (1979), 383–407

E. Roesner: ‘The Performance of Parisian Organum’, EMc, vii (1979), 174–89

L. Treitler: ‘Regarding Rhythm and Meter in the Ars Antiqua’, MQ, lxv (1979), 524–58

E.H. Sanders: ‘Consonance and Rhythm in the Organum of the 12th and 13th Centuries’, JAMS, xxxiii (1980), 264–86 [see comments by Reckow and reply, ibid., xxxiv, 1981, pp.588–9]

H. Tischler: ‘Versmass und musikalischer Rhythmus in Notre-Dame-Conductus’, AMw, xxxvii (1980), 292–304

J. Yudkin: ‘The Copula According to Johannes de Garlandia’, MD, xxxiv (1980), 67–84

C. Morin: ‘Mise en place de l'écriture polyphonique: l'école de Notre-Dame’, EG, xx (1981), pp.69–76

R. Rastall: The Notation of Western Music: an Introduction (New York, 1982)

E.H. Roesner: ‘Johannes de Garlandia on organum in speciale’, EMH, ii (1982), 129–60

H. Tischler: ‘A Propos Meter and Rhythm in the Ars Antiqua’, JMT, xxvi (1982), 313–30

L. Treitler: ‘Regarding “A Propos Meter and Rhythm in the Ars Antiqua”’, JMT, xxvii (1983), 215–22

J. Yudkin: ‘The Rhythm of Organum Purum’, JM, ii (1983), 355–76

M. Haas: ‘Die Musiklehre im 13. Jahrhundert von Johannes de Garlandia bis Franco’, Geschichte der Musiktheorie, ed. F. Zaminer, v (Darmstadt, 1984), 91–158

D. Hiley: ‘The Plica and Liquescence’, Gordon Athol Anderson, 1929–1981, in memoriam, ed. L.A. Dittmer (Henryville, PA, 1984), 379–92

E.H. Sanders: ‘Sine littera and Cum littera in Medieval Polyphony’, Music and Civilization: Essays in Honor of Paul Henry Lang, ed. E. Strainchamps, M.R. Maniates and C. Hatch (New York, 1984), 215–31

H. Tischler: ‘Gordon Anderson's Conductus Edition and the Rhythm of Conductus’, Gordon Athol Anderson, 1929–1981, in memoriam, ed. L.A. Dittmer (Henryville, PA, 1984), 561–73

J. Yudkin: ‘The Anonymous of St. Emmeram and Anonymous IV on the Copula’, MQ, lxx (1984), 1–22

E.H. Sanders: ‘Conductus and Modal Rhythm’, JAMS, xxxviii (1985), 439–69

L.C.H. Spottswood: Accents in Texted Ligatures: the Influence of Old French on the Rhythm and Notation of the Polyphonic Conductus (diss., U. of Maryland, 1985)

J. Yudkin: The Music Treatise of Anonymous IV: a New Translation (Neuhausen-Stuttgart,1985)

B. Gillingham: Modal Rhythm (Ottawa, 1986)

H. Ristory: ‘Ein Kurztraktat mit Binärmensuration und praefranconischem Gepräge’, Studi musicali, xv (1986), 151–66

E. Apfel: Die Lehre vom Organum, Diskant, Kontrapunkt und von der Komposition bis um 1480 (Saarbrücken, 1987, 4/1997)

M.E. Fassler: ‘Accent, Meter, and Rhythm in Medieval Treatises “De rithmis”’, JM, v (1987), 164–90

M. Huglo: ‘La notation franconienne: antécédents et devenir’, Cahiers de civilisation médiévale, xxxi (1988), 123–32

M. Lütolf: ‘Les notations des XIIe–XIIIe siècles et leur transcription: difficultés d'interprétation’, Cahiers de civilisation médiévale, xxxi (1988), 151–60

M. Pérès: ‘L'interprétation des polyphonies vocales du XIIe siècle et les limites de la paléographie et de la sémiologie’, Cahiers de civilisation médiévale, xxxi (1988), 169–78

H. Tischler, ed.: The Parisian Two-Part Organa (New York, 1988)

G. Le Vot: ‘La notation et l'oralité des musiques polyphoniques aux XIIe et XIIIe siècles’, Cahiers de civilisation médiévale, xxxi (1988), 133–50, 179–81

M.E. Wolinski: The Montpellier Codex: its Compilation, Notation, and Implications for the Chronology of the Thirteenth-Century Motet (diss., Brandeis U., 1988)

C.M. Atkinson: ‘Franco of Cologne on the Rhythm of Organum Purum’, EMH, ix (1989), 1–26

L. Lera: ‘Grammatici della notazione di Notre-Dame’, AcM, lxi (1989), 150–74

R.L. Crocker: ‘Rhythm in Early Polyphony’, CMc, nos.45–7 (1990), 147–77

N.E. Smith: ‘The Notation of Fractio modi’, CMc, nos.45–7 (1990), 283–304

J. Knapp: ‘Polyphony at Notre Dame of Paris’, NOHM, ii (2/1990), 557–635

E.H. Roesner: ‘The Emergence of Musica mensurabilis’, Studies in Musical Sources and Style: Essays in Honor of Jan LaRue, ed. E.K. Wolf and E. Roesner (Madison, WI, 1990), 41–74

L.C.H. Spottswood: ‘The Influence of Old French on Latin Text Settings in Early Measured Polyphony’, Beyond the Moon: Festschrift Luther Dittmer, ed. B. Gillingham and P. Merkley (Ottawa, 1990), 163–82

H. Tischler: ‘Words and Music in the Middle Ages: a Critique of John Stevens' “Words and Music in the Middle Ages: Song, Narrative, Dance and Drama, 1050–1350”’, De musica hispana et aliis: miscelánea en honor al Prof. Dr. José Lopez-Calo, ed. E. Caseres and C. Villanueva (Santiago de Compostela, 1990), 181–96

J. Yudkin, ed. and trans.: De musica mensurata: the Anonymous of St. Emmeram: Complete Critical Edition, Translation, and Commentary (Bloomington, IN, 1990)

S. Pinegar: Textual and Conceptual Relationships among Theoretical Writings on Measurable Music from the Thirteenth and Early Fourteenth Centuries (diss., Columbia U., 1991)

J. Yudkin: ‘The Anonymous Music Treatise of 1279: Why St. Emmeram?’, ML, lxxii (1991), 177–96

T. Karp, ed.: The Polyphony of Saint Martial and Santiago de Compostela (Oxford, 1992)

S. Pinegar: ‘Exploring the Margins: a Second Source for Anonymous 7’, JMR, xii (1992), 213–43

E.H. Roesner, ed.: Les quadrupla et tripla de Paris, Le magnus liber organi de Notre-Dame de Paris, i (Les Remparts, 1993) [see esp. ‘Introduction: the Interpretation of Rhythm’]

E.H. Sanders: ‘The Earliest Phases of Measured Polyphony’, Music Theory and the Exploration of the Past, ed. C. Hatch and D.W. Bernstein (Chicago, 1993), 41–58

M. Huglo: ‘The Origin of the Monodic Chants in the Codex Calixtinus’, Essays on Medieval Music in Honor of David G. Hughes, ed. G.M. Boone (Cambridge, MA,1995), 195–206

E.H. Sanders: ‘Rithmus’, Essays on Medieval Music in Honor of David G. Hughes, ed. G.M. Boone (Cambridge, MA, 1995), 415–40

A.M. Busse Berger: ‘Mnemotechnics and Notre Dame Polyphony’, JM, xiv (1996), 263–98

T.B. Payne, ed.: Les organa à deux voix du manuscrit de Wolfenbüttel, Herzog August Bibliothek, cod. Guelf. 1099 Helmst., Le magnus liber organi de Notre-Dame de Paris, vi (Les Remparts, 1996) [incl. ‘Introduction: the Interpretation of Rhythm’]

C. Page: Latin Poetry and Conductus Rhythm in Medieval France (London, 1997)

For further bibliography seeOrganum and discant: bibliography.

(ii) Franconian notation.

3. Polyphonic mensural notation, c1260–1500.

(i) General.

(iii) French 14th-century notation.

(iv) Italian 14th-century notation.

(v) Late 14th-century notation.

(vi) English 14th-century notation.

(vii) 15th-century notation.

Notation, §III, 3: Polyphonic mensural notation, c1260–1500

(i) General.

Well before this period the notation of pitch had lost all ambiguity apart from occasional uses of the Plica and the operation of the rules of musica recta and Musica ficta. The four-line staff used for plainchant was still sometimes retained in polyphony, especially for a voice presenting plainchant, but the five-line staff had come to be used for polyphonic voices. A six-line staff became normal for the 14th-century Italian repertory, and was occasionally used outside it. Additional staff-lines were provided throughout the period wherever the range of a voice demanded, though the leger line itself was rare. The most commonly used clef was the C (on any line), as in plainchant, and its position was readily movable from line to line when range or a copying error made this expedient. Of the other two clefs used in plainchant the F came increasingly into use with the gradual extension of the lower pitch register, but the B – that is, the sign used on its own as a clef – was rare in polyphony, probably because of the growing use of the same symbol to supply what would later be called a key signature. The treble G clef appeared in the 14th century; it came increasingly into use, especially in England, again in connection with extension of range; bass G and D clefs are rare. (See Staff and Clef.)

Score notation had disappeared by about 1260, except for late copies of the organum and conductus repertory, and certain categories of composition in England, for which it was retained late into the 15th century (including carols, homophonic sequences and cantilenas, and English discant). Notation in separate voices reflected their new rhythmic independence.

Throughout the period there were three principal signs for what are now called accidentals. They did not function as modern accidentals do, in that they did not signify the automatic raising or lowering of an otherwise ‘natural’ note by a semitone. They were adjuncts of the solmization system: the signs in fig.52a (alternative forms adopted by different scribes) designated the note following it to be sung to the syllable mi, and fig.52b designated it to be sung to the syllable fa. Fig.52c was often used simply as an alternative to fig.52b, though it seems to have been used by some scribes to refer to notes in the upper octave of a given voice range. In consequence, the note F, for example, would be rendered not flat but F by the placing of the ‘flat’ sign (fig.52b) before it; a ‘sharp’ or hard b() sign before the note E would render it E. Ambiguity could arise with A and D as to whether a flat sign meant natural or flat, and with G and D as to whether a sharp sign meant natural or sharp; but this ambiguity could usually be resolved by consideration of context. Significantly, the three clef signs discussed above were all indications of fa in the three basic hexachords (based on G, C and F respectively).

See Accidental; Score, §3; Solmization, §I; Sources, MS, §I.

Notation, §III, 3: Polyphonic mensural notation, c1260–1500

(ii) Franconian notation.

The development of notation during the period c1260–1500 was almost exclusively in the realm of rhythm, and specifically concerned with achieving precise notation for note values shorter than the long and breve. The 13th century saw the gradual adoption of graphic distinctions between the long and the breve, both as isolated note shapes (simplices) and as they appear within ligatures. The forms of square note with and without stem had been used arbitrarily in the Florence manuscript (I-Fl Plut.29.1), but were used throughout the next generation of sources, including the Montpellier manuscript (F-MOf H196), to indicate long and breve respectively (see Sources, MS, §V for these manuscripts). Ligatures began to have fixed evaluations regardless of their modal context, even though they still often adhered to modal patterns and though the values assigned to them derived from their modal interpretations. These and other fundamental changes can be traced in the musical sources, and are mentioned in the theoretical writings (c1240) ascribed to Johannes de Garlandia, Magister Lambertus (before 1279) and the St Emmeram anonymus [Sowa anon. 1930] (1279), all of which are now dated earlier than the main formulation of these changes by Franco of Cologne (?c1280) on whose rules the following summary is based.

The Franconian system required that note symbols should be capable of indicating the rhythmic modes rather than being determined by them. Under this system, each of the three principal note values had two states. The long was either ‘perfect’ or ‘imperfect’, there was also a duplex long, worth two longs, which Franco explained as a means of avoiding repeated notes. The breve was either recta or altera (‘other’ – Robert de Handlo in 1326 proposed that the breve be thought of as alterata, ‘altered’, CoussemakerS, i, 385). The semibreve could be either ‘major’ or ‘minor’.

The perfect long was worth three breves. The imperfect long was worth two breves, as had been the earlier long, and was used in combination with a preceding or following breve; it could not stand on its own (i.e. only triple time was allowed on the level of the long), and hence could not be called longa recta (but see Johannes de Garlandia, ed. Reimer, i, 37). When a long preceded a second long the first must always be perfect (thus, in terms of breves, 3–3 or 3–2).

The brevis altera was worth two recta breves. It arose as the second breve in the context breve–breve–long (1–2–3 breve units respectively): see fig.53a (in the upper voice the first breve is subdivided into semibreves). Although identical in duration with the imperfect long it could not be written thus because of the preceding rule. Where a long followed by a breve would normally be imperfect, it could be rendered perfect by the placing immediately after it of a dot or stroke, variously called tractulus, signum perfectionis or divisio modi, as in fig.53b. A long followed by two breves was perfect unless preceded by a single breve. The following set of patterns illustrates the operation of the system (numerals represent multiples of breve-values; primes represent signs of perfection):

LBLB	= 2–1–2–1

L'BLB	= 3–1–2–1

LBBL	= 3–1–2–3

BLBBL	= 1–2–1–2–3

LB'BL	= 2–1–1–2

LBBBL	= 3–1–1–1–3

LB'BBL	= 2–1–1–2–3

LBBBBL	= 2–1–1–1–1–3

L'BBBBL	= 3–1–1–1–1–2

The brevis recta might contain not more than three semibreves and not fewer than two. If three, they would be equal and all minor; if two, they would be minor–major (1–2). Franco made no provision for two equal semibreves, though several earlier theorists did not specify the value of a pair of semibreves when it constituted a breve nor did they recognize a group of three (Johannes de Garlandia, ed. Reimer, i, 50; Dietricus, ed. Müller, 5; Amerus, p.II). (The semibreve pairs in F-MOfh196 and D-BAs ED.N.6, and possibly other sources, in most cases lend themselves much more comfortably to equal performance, and it is not always certain that Franco’s rules apply.)

There is no provision as yet for the breve to be imperfected by the semibreve, or for the semibreve to stand alone: the breve-semibreve relationship was not at that stage analogous to that of the long-breve. This meant also that the principle of ‘alteration’ did not apply. A breve preceding a second breve is not said to be perfect, because there is no question of its being imperfected. Similarly, the second of a pair of semibreves is not said to be ‘altered’ before a breve, because a pair of semibreves is rendered iambically, regardless of what follows. Hence the following patterns (numerals represent multiples of semibreve-values):

BSSSS	= 3–1–2–1–2

SSS'SS	= 1–1–1–1–2

Several of Franco’s contemporaries (e.g. St Emmeram anonymus, 1279) added to the semibreve-pair rule ‘and vice versa’, implying the reverse interpretation (2–1); and one later writer, the author of the Quatuor principalia (CoussemakerS, iv; see also John of Tewkesbury), even attributed this interpretation directly to Franco.

Franco defined ascending and descending plicae for the long and breve. Plicae continued in use in the 14th century, but their pitch and rhythmic evaluation are sometimes open to question (see Handlo’s evaluations, CoussemakerS, i, 383ff; also ed. in Lefferts). They were obsolete before 1400, by which time any surviving plica shapes no longer have the former significance of a plica.

Franco took over the existing ligature shapes with their connotations of propriety and perfection depending on the presence or absence of stems (see §III, 2). He provided evaluations that were mostly consistent with the earlier system but which could stand independent of their modal meanings. The first note of a ligature ‘with propriety’ was a breve, the last note of a ligature ‘with perfection’ was a long. He opened the door to many hitherto unused ligature shapes and provided a means of evaluating them, simple for anyone familiar with the existing shapes. A ligature with a stem ascending from the first note was described as having ‘opposite propriety’: it signified two semibreves. All notes other than the first and last were breves. In practice, downward stems were occasionally used to create a long in the middle of a ligature; the upward stem could occur elsewhere than at the beginning to create two semibreves; and the long body of the duplex long or maxima could be used to create this value anywhere in the ligature. These are later modifications to Franco’s system. Notes in ligature were subject to the same rules for imperfection and alteration as single notes, but in practice grouping in ligatures tended to favour certain groupings as strongly as did a divisio modi.

Franco advocated the use of ligatures where possible; if possibility here implies absence of constraints from word underlay, he did not say so. However, it remains generally true (with a few exceptions) that two syllables do not have to be fitted to one ligature. On the other hand, Franco disallowed the pre-Franconian practice of notating 5th-mode tenors in motets as three-note ligatures and insisted on a succession of separate longs. Fig.54 shows the principal ligature shapes of the Franconian system. (An oblique shape involves only two pitches: the first and last covered by the ligature.) In evaluating ligatures of more than two notes, the first and last were treated as though each formed a two-note ligature with its neighbour. Middle notes were breves unless modified by stems making them longs or semibreves, or by extension of the note body to make a duplex long or maxima (see fig.55).

Fig.56 shows the rests given by Franco, together with their values in terms of recta breves. They are respectively the perfect long, the imperfect long and brevis altera, the brevis recta, the major semibreve, the minor semibreve and the finis punctorum, which marked the end of a section or piece and was immeasurable. All these rests were fixed in value, not subject to imperfection or alteration.

Franco made no provision for a binary division of the long, though it is generally agreed that some pre-Franconian compositions require this. Such a division became common in the following generation (see Sanders, 1962). After Franco the breve was further subdivided, being replaceable by more than three semibreves. The evaluation of these smaller semibreves differed, both in theory and in practice, in the separate 14th-century traditions of France, Italy and England, and the resulting rhythmic differences contributed largely to the musical distinctness of the three styles. Franco was the starting-point for all three. In none of them was a primary division of the breve into more than three semibreves called for: smaller note values were achieved by further subdivision of the primary divisions – subdivisions that were still regarded as types of semibreve, and were written without differentiation as semibreves. In addition, French and Italian theorists introduced imperfect time, with two equal semibreves constituting one breve, on an equal footing with perfect time.

Jacobus of Liège alleged that Petrus de Cruce had used up to seven semibreves in the space of a breve. He said that ‘another’ had used up to nine semibreves, and Robert de Handlo and John Hanboys said the same of a ‘Johannes de Garlandia’ (CoussemakerS, i, 389; see also edn by Lefferts); both cite pre-Ars Nova motets (F-MOf H196) in support. They do not specify the semibreves’ values. But Petrus seems to have earned Jacobus’s approval for staying within the Franconian tradition and distinguishing the semibreves adequately from each other without recourse to stems; and Robert de Handlo attributed to him the orthodox Franconian division of the breve into two unequal or three equal semibreves. In view of these two facts, there is no compelling reason to assume that his shorter notes were anything other than forerunners of one of the 14th-century systems, all of which arranged the shorter notes, according to rules prescribed in increasing detail as the century progressed, within the primary perfect or imperfect division. (Apel’s claim (1942, 5/1961, p.319) that Petrus introduced a system without precedent or progeny using five or seven equal semibreves is based on a misreading of Jacobus, who would surely have condemned such temerity.) There is no mention of Petrus in the early French or Italian treatises.

Notation, §III, 3: Polyphonic mensural notation, c1260–1500

(iii) French 14th-century notation.

The first theoretical formulations of French 14th-century notation were those of Philippe de Vitry and Johannes de Muris dating from the early 1320s. Their starting-point was explicitly the teaching of Franco. In addition to the triple division of the breve permitted by the latter, they reintroduced duple division and further subdivided these semibreves into shorter notes, which were regarded as different orders of semibreves, and were at first not differentiated graphically except for the occasional lengthening downstem. The first surviving musical instances of this practice are some of the motets interpolated between about 1317 and 1319 into one copy of the Roman de Fauvel (F-Pn fr.146). Some are cited in Ars nova, and Vitry may well have been the composer of them, for composer and theorist alike were concerned mainly with a metrical scheme in which the breve was divided into two equal semibreves each of which was in turn subdivided into three smaller values. Fig.57 shows the interpretation of the contents of the breve when subdivided by two, three, four and five semibreves respectively. Other musical sources of these motets corroborate these interpretations by distinguishing the shorter order of semibreve with an upward stem, thereby converting them into a new level of note value known as the minima. Italian theorists of the time (see §iv below) also gave these interpretations.

Vitry’s Ars nova established the following hierarchy of five possible subdivisions of the breve: ‘minimum perfect time’ (i.e. Franconian, although he stated that interpretation of semibreve pairs as 2–1 had been superseded by that of 1–2, and thus departed from Franconian practice in his only statement about perfect time), three semibreves; ‘minimum imperfect time’, two semibreves each comprising two minims; ‘medium perfect time’, three semibreves each comprising two minims; ‘major perfect time’, three semibreves each comprising three minims; ‘major imperfect time’, two semibreves each comprising three minims (Roesner, Avril and Regalado, 30–38).

Taken together with later treatises embodying the theory of the Ars Nova as it developed (including Johannes de Muris’s later treatise, Libellus cantus mensurabilis, c1340, and Anonymus 5 of CoussemakerS, iii), the French system can be summarized as follows. There was a graphic distinction of the minim by an upward stem from approximately the time of Vitry’s treatise. The four principal levels of note value, the long, breve, semibreve and minim, were thus visually distinct. The relationships between these four levels of note value were given names: modus (‘mode’ or ‘mood’) for the long-breve relationship, tempus (‘time’) for breve-semibreve, prolatio (‘prolation’) for semibreve-minim. Each of these relationships might be binary or ternary. The various relationships of mode, time and prolation came to be termed ‘mensurations’. The four combinations of tempus and prolatio were attributed to Vitry as the ‘quatre prolacions’. Various special signs were proposed for the available mensurations, but none was much used during the 14th century. Their appearance in the later part of the century reflected the existence in composition of a wider range of possibilities and therefore the need to specify which combination of relationships was in force. Yet they were in practice confined, with few exceptions, to the circle for perfect tempus and the half-circle for imperfect tempus, with a dot in the centre to designate major prolatio (its absence designated minor).

The existing range of symbols for rests was extended. The semibreve rest became a short vertical bar suspended from a staff-line, and the minim a similar bar placed upon a staff-line. These rests, like Franco’s, were fixed in value. Within a given mensuration, which established the value of each rest as perfect or imperfect, no rest was imperfectible or alterable – a situation that did not apply in either Italy or England.

Dots were used to mark off groups of notes according to tempus, that is according to breves’-worth, by extension of Franco’s principle, and also to indicate perfection. This led in later treatises towards the idea of a ‘dot of addition’ which added half again to the value of an imperfect note. At first this concept was expressed in terms of showing the perfection of an imperfect note. Muris stated that an imperfect note might be made perfect by the addition of half its value (Libellus; no dot is mentioned there, but one source of the treatise has a musical example with a dotted breve in imperfect time). Anonymus 5 stated that ‘a dot, when it perfects, always adds to the note after which it is placed the neighbouring part’ (i.e. the next note value down).

Vitry prescribed red notes for various purposes. Where black notes were perfect, red indicated imperfect mode or imperfect mode and time. The roles of black and red could also be reversed. Red could be used to prevent individual notes from being perfect or altered (i.e. to fix their value regardless of context). Red could effect octave transposition (though no surviving examples are known) or pick out a plainchant voice.

Franco’s rules for imperfection of the long were now also applied to the breve and semibreve, and his rules for alteration of the breve to the semibreve and minim. The precise evaluation of any note depended on the governing mensuration and on the context.

Not only could the long be imperfected by the breve, the breve by the semibreve and the semibreve by the minim, but imperfection by non-adjacent values was permitted – for example the long by the semibreve and the breve by the minim. A note could be imperfected to a varying extent: a breve might be imperfected by one minim or two. Vitry specified four types of semibreve: the major (i.e. altera), equal to six minims, the ‘semimajor’ or imperfect equal to four or five, the recta or vera equal to three, and the minor equal to two. The minim was often described as a semibrevis minima, the lowest value that a semibreve could have.

Franco’s rule that a long preceding a long was always perfect came to be strictly applied to breves and semibreves, and was later formulated as the rule similis ante similem perfecta (‘like before like is perfect’). Particular contexts yielded fixed values for certain notes by requiring them to be perfect: for example, the semibreve shown in fig.58a could be imperfect, yet the first semibreve in fig.58b had to be perfect, so that only by means of the minima altera could the rhythm given in fig.58c be shown. Such alteration of the minim became possible only when the minim was graphically distinct: a pair of unstemmed semibreves, according to Vitry, was trochaic. The full application of these relationships on all levels was not yet in operation at the time of Vitry’s treatise.

Syncopation was discussed by theorists, and was allowed by Johannes de Muris in perfect or imperfect mood, time and prolation. Although it was not discussed systematically, it seems clear from the musical sources that the means of syncopation were notes or rests of fixed value (e.g. any rest, or a note imperfected by coloration or perfected by a dot). Dots of syncopation are in effect dots of division unusually positioned to show displacement. A note set off by two dots, as found in later 14th-century sources, is thus isolated as the agent of displacement or prevented from alteration.

Notation, §III, 3: Polyphonic mensural notation, c1260–1500

(iv) Italian 14th-century notation.

The early development of Italian Trecento notational theory has been clarified by reference to treatises which apparently antedate Marchetto da Padova, who had long been regarded as its first exponent (Gallo, La teoria della notazione, 1966). Amerus, in 1271, recognized exclusively binary division of the long with each of the two breves further subdivided into two semibreves. Guido frater (?1326–30) showed the systematic fusion of this binary tradition with Franconian teaching, dealing with perfect and imperfect time, and agreed in most essential points with Marchetto’s Pomerium.

In perfect time the breve was divided into three ‘major’ semibreves (the use of the term is different from Vitry’s). Each of these might be divided into two ‘minor’ semibreves (as in fig.59a), and each of those into two ‘minimum’ semibreves, totalling 12 minimum semibreves or minims (Guido: semibreves minime; Marchetto: minime). Alternatively, each major semibreve might be divided into three, making nine in all; Guido, unlike Marchetto, spoke of this as a French practice. (Guido called the resulting nine notes minimum semibreves, whereas Marchetto called them minor semibreves.) In imperfect time the breve was divided into two equal major semibreves and was defined as two-thirds the value of the breve of perfect time. Each of these two major semibreves might be divided into two minor semibreves, and each of those into two minims, making eight minims in all (Guido: semibreves minime; Marchetto: minime in secundo gradu; see fig.59b, bars 1–3, 6–8). Guido and Marchetto both called this manner of division the ‘Italian way’. Alternatively, each of the two major semibreves might be divided into three minims (Marchetto: minime in primo gradu), making six minims in all (as in fig.59b, bars 4–5); this Guido and Marchetto call the ‘French way’ (their evaluations are shown in fig.60). Marchetto admitted, but did not enlarge upon, the further division of the six minims of imperfect time into two to make 12, and into three to make 18.

Unstemmed semibreves (naturales) were evaluated according to certain prescriptions which could be overruled artificially (via artis) by means of stems. Downward stems (as in fig.59b, bar 3) indicated longer notes whose precise value depended on context as well as on the ‘division’ (approximately equivalent to the French ‘mensuration’) that was in operation. Upward stems indicated the minim, whose value was fixed within any division that contained that level of note. The use of these stems was not necessary, even that of stems for minims, if what was required was the normal arrangement of a certain number of notes within a certain division. It became necessary only with abnormal arrangements of notes.

The primary division of perfect time placed the longer of two notes at the end of the tempus unless a downward stem was attached to the first note (as in fig.59a, bars 1, 8). This is not the same as alteration in French notation, since here a semibreve in such a position need not precede a breve; the procedure is Franconian. Whenever unequal division of notes within an ‘Italian’ division was called for, the longer note (or notes) was again placed at the end (as in fig.59a, bars 2–3) unless modified by stems. But the ‘French’ divisions, whose evaluations as given in the right-hand column of fig.60 are taken from Guido, normally placed the shorter notes after the longer. Though not entirely consistent, and thus in defiance of Marchetto’s attempt to impute superior logic to the French system, they are the rhythms most commonly encountered in contemporary French music.

Unless bounded by a breve or ligature, each tempus group of semibreves was marked off by a dot. Any ligature comprising two semibreves occupied a full tempus. Although Guido provided two forms of semibreve rest (both standing on the staff-line), one occupying a quarter, the other a third of the space between two staff-lines (ed. Gallo, 27), he did not equate these with the three levels of semibreve. In practice, rests were inconsistently indicated and were as much subject to variation in value as the notes to which they corresponded; this was diametrically opposed to the French use of rests, to which however Italian notation moved closer as the century progressed.

The breve could not be imperfected: the rhythm that French notation rendered as an imperfect breve followed by a semibreve (2–1) was represented in Italian notation by a semibreve with a downward stem followed by a plain semibreve: that is, a semibreve prolonged by via artis to two-thirds of a tempus followed by a major semibreve. Hence, since a semibreve could not occupy a tempus alone, no semibreve could be used alone. That also derives from Franco.

Marchetto proposed that the initial letters of certain modi and divisions be used to identify them. This was the counterpart to the French mensuration signs (see (iii) above), which found no place in the Italian tradition until it merged with the French later in the century. Marchetto advocated ‘.i.’ and ‘.p.’ for ‘imperfect’ and ‘perfect’ modus (see figs.59b and a), not for the divisions of senaria imperfecta and perfecta (see fig.61) which had not yet acquired these names. The letters ‘.b.’ and ‘.t.’ were to indicate the binary and ternary divisions of the breve (CSM, vi, 164). The letters ‘Y’ and ‘G’ were to indicate the Italian and French (literally ‘Gallic’) manners in imperfect time. In addition, the letters ‘S.G.’ were used presumably for secundum gallicos or senaria gallica in I-Rvat Rossi 215. The later uses of letters, derived from musical sources and subsequent theoretical writings, in particular from Prosdocimus de Beldemandis, are shown in fig.61. There seems to be no theoretical or practical justification for the widespread modern teaching that undesignated semibreves in senaria imperfecta are to be read with the longest note last (in the bar or in each half of it); if anything other than the French way was wanted, it was specified by stems.

Minims were present only in the French divisions and in the third division or beyond of the Italian manner. They did not technically halve the value of a semibreve, although two minims were equal to one minor semibreve, because they were themselves a kind of semibreve. Semiminims, on the other hand, which were mentioned in Ars nova but not by the Italian theorists, came into use in later musical sources to divide the minim in half. They had a loop to the right or left of the minim stem. Triplets – three minims in the time of two – were shown by a loop in whichever was the opposite direction (as in fig.59c).

Other innovations of the later sources included the dragma – a semibreve with upward and downward stem (fig.62a) – with a fixed value of two minims. This was often used to represent three minor semibreves in the time of two major semibreves. The same effect could also be achieved by void coloration, which could give three notes in the time of two or four in the time of three. A note augmented by half was represented as shown in fig.62b. A dot could not be used because of its function as marking the division.

See also Sources, MS, §VIII.

Notation, §III, 3: Polyphonic mensural notation, c1260–1500

(v) Late 14th-century notation.

Towards the end of the century, in the music of Landini’s generation, many French features had entered Italian notation. The Italian division signs, although Prosdocimus’s formulation of them was even later, were increasingly superseded by actual or implicit French mensuration signs. Dots of division, downward stems and variable rests gradually disappeared. Breves were imperfected, and dots of addition replaced the other special signs. The notational unrest of this stage was reflected in many pieces combining French and Italian characteristics, and in the existence of more than one notated version of some pieces, an otherwise rare phenomenon (Fischer, 1959). The eventual absorption of Italian notation by French was the result of a final exploitation of the inherent possibilities of both systems. Extreme rhythmic complexities were indulged in by composers of both nationalities, largely in the orbit of the schismatic papal court at Avignon and of Gaston Fébus, Count of Foix.

The principal technique used was syncopation. The existing means of fixing the values of notes that were to act as syncopating agents were greatly expanded by the use of a variety of stems, hooks, dashes and loops whose precise meaning varied from piece to piece and sometimes within a single piece, as well as by the use of displaced dots of division. Specialized colorations were also used. These sometimes fixed note values and were thus additional means of achieving syncopation, and sometimes they expressed a proportional relationship of one passage to another (see §vii below). The main manuscripts containing this sophisticated and short-lived repertory are I-MOe α.5.24, F-Pn it.568 and CH 564 (for further discussion see Stone, 1994).

See also Ars Subtilior and Sources, MS, §VIII.

Notation, §III, 3: Polyphonic mensural notation, c1260–1500

(vi) English 14th-century notation.

Robert de Handlo, in 1326, gave clear indications that the English continued to pursue the notational individuality they had shown in their pre-Franconian notation (see §III, 2 above) into the 14th century, and musical sources confirm this. Handlo’s treatise is an expanded and glossed version of Franco; his other chief authorities were Petrus de Cruce and a certain ‘Johannes de Garlandia’ (for discussion of the identity of the theorist see Johannes de Garlandia). Here if anywhere there is justification for crediting Petrus de Cruce with an important stage in notational development; however, Handlo’s account does not permit the ascription to him of any advance on Franco that was not more exhaustively dealt with by Johannes de Garlandia. All three follow Franco in accepting only a ternary division of the breve. (Other than an apparent reference to duple time in the problematic dicta of Petrus le Viser (CoussemakerS, i, 388; see also edn of Robert de Handlo by Lefferts), there is no theoretical support for duple time in England until the late 14th-century treatise of Hanboys, though a few compositions at an earlier date require duple interpretation.)

The basic ternary division of the breve was into three ‘minor’ semibreves. If two semibreves took the place of a breve, one of them became major and was distinguished by a downward stem. Some evidence, more musical than theoretical, points to pairs of semibreves without stems and separated by dots often being performed trochaically (see (ii) above). Evidence for trochaic performance of undesignated pairs of breves in 13th-century English music is strong (Sanders, 1962): this may support the 14th-century case, but the grounds are musical rather than notational, because Franco’s long-breve relationship was not applied at the level of the semibreve (i.e. like Italy, unlike France).

Each of the three minor semibreves was subject to a further subdivision into three. Each minor semibreve’s-worth might be marked off by a small circle, or signum rotundum, which was quite distinct from the dot of division used to mark off tempus. If only two semibreves fell within one such division they were to be read unequally as 1–2 (minima–minorata) unless the reverse was indicated by a downward stem on the first of the pair. As in Italy, the French concepts of imperfection and alteration were entirely absent and cannot thus be used to justify iambic interpretation of strings of semibreve pairs. The system of circles reflected an English reluctance to use stems where a note could be evaluated by convention, although not many occur in surviving musical sources. If four was considered the basic Italian division of the breve and six the French, the English was nine, which necessitated some additional clarification by stems or circles.

Later in the century, after the period of French influence discussed below, Hanboys (?c1370) distinguished within imperfect time between curta and longa mensura, the former having four minims to the breve, the latter eight (as in GB-Lbl Sloane 1210 and DRc 11).

Rests were inconsistently notated early in the century; by the latter half, despite the allegation by several English theorists, including Hanboys, that rests could be altered or imperfected, the forms of rests followed French practice: semibreve hanging from a staff-line, minim placed on a line. There is one important exception: a rest intersecting a line, in effect a semibreve plus a minim rest, was often used for the perfect semibreve. Even in a major-prolation piece an imperfect semibreve rest was often shown by the normal semibreve rest, whereas in French notation it would be shown by two minim rests (as it sometimes was in England, too).

Other English peculiarities, mostly with theoretical and musical documentation, included the brevis erecta (fig.63a) to indicate chromatic alteration, the swallow-tailed note (fig.63b) to indicate rhythmic alteration (also serving to elongate the first of a pair of semibreves – it appears to be a successor to the downward-stemmed semibreve), and the use of the stepwise descending form of the semibreve–semibreve ligature (fig.63c) to indicate rhythmic alteration of the second note.

It is clear from the variety of notational practice in musical sources, as well as from the treatise of Hanboys, that at this period there was no single English notation but, rather, that there were diverse English notations. Hanboys cited some individual notational practices of which he disapproved. One of these accords with a surviving musical composition which is adjacent in its source to an example of approved practice.

French influence was not felt until some time after the middle of the century. It is clearly present in the pro-Vitrian treatise Quatuor principalia (completed in 1351), as well as in some imported French motets, all of which are in imperfect time and major prolation. The dot of addition makes no appearance in England (nor is there any substitute for it, as in Italy) until the very end of the century when the French influence was most fully assimilated, just before the Old Hall manuscript (GB-Lbl Add.57950) was compiled. Quatuor principalia condemned some uses of the more notably eccentric auxiliary signs in England, but at the same time achieved some startling fusions of English and French practice. Imperfect breves started to appear in English sources around that time, often in trochaic alternation with semibreves. Quatuor principalia declared the major semibreve (presumably of the English tradition) to have the same value as an imperfect breve and to be written like it. Thus it is not known whether these English breves were thought of as imperfected breves or major semibreves (evidence of parallel passages favours semibreves). Minims, with upward stems, began to appear around that time, occasionally in combination with unstemmed minims and in conjunction with signa rotunda which are in fact made redundant by the stems and did not long survive them.

Notation, §III, 3: Polyphonic mensural notation, c1260–1500

(vii) 15th-century notation.

In England about 1400 there existed notational practices as complex as those in southern France; these can be seen in the Old Hall repertory. There are canonic and isorhythmic pieces that involve advanced notational features, and virtuoso essays in syncopation and complex proportional usage. The full resources of continental coloration were available: that is, in addition to normal black-full notes there were black-void, red-full and red-void; and two pieces in the Old Hall repertory use blue-full notes. The normal coding of colour for proportions in English pieces was black-void 2:1, red-full 3:2, red-void 3:1. These colorations could be further modified by the use of numerals and signatures. They made it possible to conceive of rhythmic patterns that could otherwise have been notated in only the most clumsy or inadequate way. It was this, rather than innate conservatism, that led the English to retain some use of black-full notation, alongside black-void, after most continental scribes had abandoned black-full about 1430.

Coloration was used also to express imperfection: to prevent alteration and perfection in notes that might otherwise be subject to them, rather than to bring about a reduction in all note values. When the notation was principally black-full, the coloration was red or black-void; when black-void, the coloration was normally black-full. The indication of imperfection remained the most common function of coloration throughout the 15th century and into the 16th. Fig.64 shows black-void coloration being used to bring about imperfection and to prevent alteration (see also Woodley, 1993).

The earliest examples of black-void notation date from about 1400 and are mostly English. The reason for the change is obscure but may perhaps best be accounted for by the change in writing habits associated with the general move from parchment to paper as the main writing surface. It is also true that the greater simplicity of style that dawned with the 15th century did not, except in the continuing English tradition, require the availability of so many colorations for proportions. For the change was much more than a simple reversal of black-full and black-void: as black-void superseded black-full, so the latter came largely to replace red-full and thus red notation came to be abandoned (as in fig.65 – see bars 8–9). Continental compositions using proportions (e.g. those in GB-Ob Can.misc.213, from the late 1430s) inclined much more to the use of numerical proportion signs and mensuration signs with graphic or numerical modifications.

The reason for proportional notation lay in what may be called minim equivalence: that is, in French notation, where a change of mensuration occurred, the relationship between the two mensurations was that of minim = minim (this is clearly established at this time by pieces in which mensuration changes in the different parts occur at different points in the composition – it applies in fig.65 between bar 16 and bar 17). Proportional notation was simply a way of overriding that equivalence, and thus of extending the possibilities of the mensural system. It did so for shorter or longer passages by expressing a different note relationship to a preceding passage or to other voices in the composition.

If the relationship was expressed numerically, the number of new units would be placed above the equivalent number of old units in the form of a fraction. The unit referred to in such a fraction was normally the minim, though it could be the semibreve of the same kind. Thus the ‘3’ in fig.65, which implies 3 over 2, indicates the occurrence of three minims in the time of the previous two. The half-circle with vertical bar (often called ‘cut C’ by modern writers: fig.66a) indicated what was known as ‘diminution’: that is, the performance of a passage faster than normal, by a specified ratio. Sometimes diminution occurred in the exact ratio of 2:1, in which case it was called dimidietas. In other cases it did not or could not; a slight acceleration may be denoted by Tinctoris’s acceleratio mensurae. Anonymus 12 (CoussemakerS, iii, 484) reported that with the circle with vertical bar (‘cut O’: fig.66b) one third of all values was taken away. Later in the century these ‘cut’ mensuration signs were sometimes used as a conventional signal for imprecise diminution which enabled longer note values to be written, and sometimes they were used with no apparent mensural significance or as general-purpose signs (Wegman, 1992; Bent, 1996). This was a way of avoiding an otherwise inevitable flood of short note values, with their less easily legible stems. The reversed half-circle (fig.66c) sometimes carried the function of duple diminution when placed after a passage governed by the half-circle. However, when it occurred after a passage with a triple dimension to its mensuration (circle or half-circle with dot) it indicated a proportion of 4 : 3 (see Hamm, 1964; see also Proportional notations). The principle of equating notes of different denominations by means of a stated ratio became a well-established practice in the music of Ockeghem’s generation, when numerically modified mensuration signs could shift the basic set of relationships in the way shown in fig.67.

But apart from the cultivation of proportions in a few works by a small number of composers, the trend of the late 15th century was towards notational simplification. It is significant that, at just the same time, the late 15th century and the early 16th, cases arose of a simplified notation using only one note shape and repeating it at the same pitch to make up any note of greater value, or using only a short vertical stroke in the same way. Such a notation was presumably designed for singers who could not cope with the complexities of the mensural system, especially with imperfection and alteration. It was in the early 16th century that note values in mensural notation came to be precisely determined by their appearance regardless of context, rather than by their denomination as long, breve, semibreve or minim in a given context (the step that Franco had achieved) – at least, that became true of the essential working of notation, for imprecision and considerations of context in practice continue to feature in notation right up to the present day. However, in about 1500 musicians increasingly often placed a dot after a note that was to be perfect, even where earlier practice would not have required one. The practice of alteration gradually decayed. An intermediate stage before notators felt free to place an imperfect breve before a perfect one was the use of the coloured (black-full) breve where previously an altered semibreve would have been used.

See also Sources, ms, §IX, 2–11.

Notation, §III, 3: Polyphonic mensural notation, c1260–1500

BIBLIOGRAPHY

theoretical sources

listed alphabetically as items largely undatable

Amerus: Practica artis musice, ed. J. Kromolicki: Die Practica artis musicae des Amerus und ihre Stellung in der Musiktheorie des Mittelalters (Berlin, 1909); ed. C. Ruini, CSM, xxv (1977)

Anonymous [John of Tewkesbury]: Quatuor principalia, CoussemakerS, iv, 200–98

Anonymous [St Emmeram anonymus], ed. H. Sowa: Ein anonymer glossierter Mensuraltraktat 1279 (Kassel, 1930)

Anonymus 5 [CoussemakerS, iii]: Ars cantus mensurabilis, CoussemakerS, iii, 379–98

Anonymus 12 [CoussemakerS, iii]: Tractatus de musica; Compendium cantus figurati; De discantu,CoussemakerS, iii, 475–95

Anselmi, Giorgio: De musica, ed. G. Massera: Georgii Anselmi Parmensis ‘De musica’ (Florence, 1961)

Dietricus: Regule super discantum, ed. H. Müller: Eine Abhandlung über Mensuralmusik (Leipzig, 1886)

Franco of Cologne: Ars cantus mensurabilis,CoussemakerS, i, 117–36; GerbertS, iii, 1–16; ed. F. Gennrich (ed. G. Reaney and A. Gilles, CSM, xviii (1974)

Gaffurius, Franchinus: Practica musicae (Milan, 1496, 2/1497), ed. and trans., C.A. Miller, MSD, xx (1968); Eng. trans., I. Young: The Practica musicae of Franchinus Gafurius (Madison, WI, 1969)

Guido frater: Ars musice mensurate, ed. F.A. Gallo: Mensurabilis musicae tractatuli, AntMI, Scriptores, i/1 (1966), 17–40

Hanboys, John: Summa, CoussemakerS, i, 403–48; ed. and trans. P.M. Lefferts (Lincoln, NY, 1991)

Jacobus of Liège: Speculum musice,CoussemakerS, ii, 193–433 [attrib. Johanes de Muris]; ed. R. Bragard, CSM, iii (1955–73)

Johannes de Garlandia (attrib.): De mensurabili musica, CoussemakerS, i, 175–82; ed. E. Reimer (Wiesbaden, 1972); Eng. trans., S. Birnbaum (Colorado Springs, CO, 1978); later version as De musica mensurabili positio, CoussemakerS, i, 97–117

Lambertus [Pseudo-Aristoteles]: Tractatus de musica, CoussemakerS, i, 251–81; CSM (forthcoming)

Marchetto da Padova: Pomerium, GerbertS, iii, 121–87; ed. G. Vecchi, CSM, vi (1961)

Marchetto da Padova: Lucidarium, GerbertS, iii, 64–121; ed. R. Monterosso, Studi medievali, 3rd ser., vii (1966), 914–31; ed. and trans. J. Herlinger (Chicago, 1985)

Muris, Johannes de: Notitia artis musice,GerbertS, iii, 312, 256–7, 311–15 [book 1]; 292–301 [book 2]; ed. U. Michels, CSM, xvii (1972), 47–107; partial Eng. trans. in StrunkSR2, ii, 152–9

Muris, Johannes de: Compendium musice practice, GerbertS, iii, 301–7; ed. U. Michels, CSM, xvii (1972), 119–46

Muris, Johannes de: Libellus cantus mensurabilis, CoussemakerS, iii, 46–8; ed. D. Katz, The Earliest Sources for the ‘Libellus cantus mensurabilis secundum Johannem de Muris’ (diss., Duke U., 1989), 266–88

Odington, Walter: Summa de speculatione musice, CoussemakerS, i, 182–250; ed. F.F. Hammond, CSM, xiv (1970); Eng. trans. of pt.vi, J.A. Huff, MSD, xxxi (1973)

Petrus de Cruce: Tractatus de tonis,CoussemakerS, i, 282–92; ed. D. Harbinson, CSM, xxix (1976)

Prosdocimus de Beldemandis: Tractatus practice cantus mensurabilis ad modum Ytalicorum, CoussemakerS, iii, 228–48; ed. C. Sartori as La notazione italiana del Trecento (Florence, 1938); Eng. trans., J.A. Huff, MSD, xxix (1972)

Robert de Handlo: Regule, CoussemakerS, i, 383–403; Eng. trans., L.A. Dittmer (Brooklyn, NY, 1959); ed. and trans. P.M. Lefferts (Lincoln, NY, 1991)

Vitry, Philippe de (attrib.): Ars nova,CoussemakerS, iii, 13–22; ed. G. Reaney, A. Gilles and J. Maillard, CSM, viii (1964); Eng. trans., L. Plantinga, JMT, v (1961), 204–23

polyphony c1260–1500: studies

H. Bellermann: Die Mensuralnoten und Taktzeichen des 15. und 16. Jahrhunderts (Berlin, 1858, 2/1906, enlarged 4/1963, ed. H. Husmann)

J. Wolf: Geschichte der Mensural-Notation von 1250–1460 nach den theoretischen und praktischen Quellen (Leipzig, 1904/R) [see also review by F. Ludwig, SIMG, vi (1904–5), 597–641]

E. Kurth: ‘Kritische Bemerkungen zum V. Kapitel der “Ars cantus mensurabilis” des Franko von Köln’, KJb, xxi (1908), 39–47

J. Wolf: ‘Ein anonymer Musiktraktat aus der ersten Zeit der Ars nova’, KJb, xxi (1908), 33–8

J. Wolf: Handbuch der Notationskunde, i (Leipzig, 1913/R), pts.iii, iv

J. Wolf: Musikalische Schrifttafeln (Leipzig, 1922–3)

J. Wolf: Die Tonschriften (Breslau, 1924)

H. Birtner: ‘Die Probleme der spätmittelalterlichen Mensuralnotation und ihrer Übertragung’, ZMw, xi (1928–9), 534–48

A.M. Michalitschke: ‘Studien zur Entstehung und Frühentwicklung der Mensuralnotation’, ZMw, xii (1929–30), 257–79

A. Tirabassi: Grammaire de la notation proportionelle et sa transcription moderne (Brussels, 1930)

J. Wolf: ‘L’arte del biscanto misurato secondo el maestro Jacopo de Bologna’, Theodor Kroyer: Festschrift zum sechzigsten Geburtstag, ed. H. Zenck, H. Schultz and W. Gerstenberg (Regensburg, 1933), 17–39

W. Apel: ‘The Partial Signatures in the Sources up to 1450’, AcM, x (1938), 1–13 [see also Postscript, AcM, xi (1939), 40–42]

C. Sartori: La notazione italiana del Trecento (Florence, 1938)

W. Apel: The Notation of Polyphonic Music, 900–1600 (Cambridge, MA, 1942, 5/1961; Ger. trans., rev., 1970), pt.ii, pt.iii chaps.5–9

G. De Van: ‘La prolation mineure chez Guillaume de Machaut’, Sources, i (Paris, 1943), 24–35

F. Gennrich: Abriss der frankonischen Mensuralnotation, Musikwissenschaftliche Studien-Bibliothek, i–ii (Nieder-Modau, 1946, 2/1956)

H. Anglès: ‘La notación musical española de la segunda mitad del siglo XV’, AnM, ii (1947), 151–73

F. Gennrich: Abriss der Mensuralnotation des XIV. Jahrhunderts und der ersten Hälfte des XV. Jahrhunderts, Musikwissenschaftliche Studien-Bibliothek, iii–iv (Nieder-Modau, 1948, 2/1965)

W. Apel: Introduction to French Secular Music of the Late Fourteenth Century (Cambridge, MA, 1950)

M.F. Bukofzer: Studies in Medieval & Renaissance Music (New York, 1950)

A. Carapetyan: ‘A Fourteenth-Century Florentine Treatise in the Vernacular’, MD, iv (1950), 81–92

L.A. Dittmer: ‘The Ligatures of the Montpellier Manuscript’, MD, ix (1955), 35–51

R.H. Hoppin: ‘A Musical Rotulus of the Fourteenth Century’, RBM, ix (1955), 131–42

N. Pirrotta: ‘Marchettus de Padua and the Italian Ars Nova’, MD, ix (1955), 57–71

H. Anglès: ‘Die alte spanische Mensuralnotation’, Musikwissenschaftlicher Kongress: Vienna 1956, 7–17

K. von Fischer: Studien zur italienischen Musik des Trecento und frühen Quattrocento (Berne, 1956)

K. von Fischer: ‘Zu Johannes Wolfs Übertragung des Squarcialupi-Codex’, Mf, ix (1956), 77–89

R.H. Hoppin: ‘Conflicting Signatures Reviewed’, JAMS, ix (1956), 97–117

G. Massera: ‘Un sistema teorico di notazione mensurale nella esercitazione di un musico del '400’, Quadrivium, i (1956), 273–300

G. Reaney: ‘The “Ars Nova” of Philippe de Vitry’, MD, x (1956), 5–33

G. Vecchi: ‘Su la composizione del Pomerium di Marchetto da Padova e la Brevis compilatio’, Quadrivium, i (1956), 153–205

L.A. Dittmer: ‘The Dating and the Notation of the Worcester Fragments’, MD, xi (1957), 5–11

H. Hewitt: ‘A Study in Proportions’, Essays on Music in Honor of Archibald Thompson Davison (Cambridge, MA, 1957), 69–81

A. Kellner: Ein Mensuraltraktat aus der Zeit um 1400 (Vienna, 1957), 72

C. Parrish: The Notation of Medieval Music (New York, 1957, 2/1959/R), chaps.5–7

H. Anglès: ‘De cantu organico: tratado de un autor catalán del siglo XIV’, AnM, xiii (1958), 1–24

K. von Fischer: ‘Trecento – Trecentoprobleme’, AcM, xxx (1958), 179–99

A. Gilles and G. Reaney: ‘A New Source for the Ars nova of Philippe de Vitry’, MD, xii (1958), 59–66

K. von Fischer: ‘Zur Entwicklung der italienischen Trecento-Notation’, AMw, xvi (1959), 87–99

U. Günther: ‘Der Gebrauch des tempus perfectum diminutum in der Handschrift Chantilly 1047’, AMw, xvii (1960), 277–97

U. Günther: ‘Die Anwendung der Diminution in der Handschrift Chantilly 1047’, AMw, xvii (1960), 1–21

R.H. Hoppin: ‘Notational Licences of Guillaume de Machaut’, MD, xiv (1960), 13–27

R. Federhofer-Königs: ‘Ein anonymer Mensuraltraktat aus der 2. Hälfte des 14. Jahrhunderts in der Stiftsbibliothek Michaelbeuren/Salzburg’, KJb, xlvi (1962), 43–60

A. Geering: ‘Eine tütsche Musica des figurirten Gesangs 1491’, Festschrift Karl Gustav Fellerer zum sechszigsten Geburtstag, ed. H. Hüschen (Regensburg, 1962), 178–81

U. Günther: ‘Die Mensuralnotation des Ars nova in Theorie und Praxis’, AMw, xix–xx (1962–3), 9–28

C. Hamm: ‘Manuscript Structure in the Dufay Era’, AcM, xxxiv (1962), 166–84

F.J. León Tello: Estudios de historia de la teoría musical (Madrid, 1962, 2/1991)

E.H. Sanders: ‘Duple Rhythm and the Alternate Third Mode in the 13th Century’, JAMS, xv (1962), 249–91

R. Bockholdt: ‘Semibrevis minima und Prolatio temporis’, Mf, xvi (1963), 3–21

K. von Fischer: ‘Neue Quellen zur Musik des 13., 14. und 15. Jahrhunderts’, AcM, xxxvi (1964), 79–97

S. Gullo: Das Tempo in der Musik des XIII. und XIV. Jahrhunderts (Berne, 1964)

C. Hamm: A Chronology of the Works of Guillaume Dufay based on a Study of Mensural Practice (Princeton, NJ, 1964)

A. Hughes: ‘Mensuration and Proportion in Early Fifteenth Century English Music’, AcM, xxxvii (1965), 48–59

R. Mužíková: ‘Pauli Paulirini de Praga musica mensuralis’, Acta Universitatis Carolinae: philosophica et historica, ii (Prague, 1965), 57–87 [with Ger. summary p.87]

F.A. Gallo: ‘Citazioni da un trattato di Dufay’, CHM, iv (1966), 149–52

F.A. Gallo: La teoria della notazione in Italia dalla fine del XIII all’inizio del XV secolo (Bologna, 1966)

T. Göllner: ‘Notationsfragmente aus einer Organistenwerkstatt des 15. Jahrhunderts’, AMw, xxiv (1967), 170–77

A. Hughes: ‘The Old Hall Manuscript: a Re-appraisal’, MD, xxi (1967), 97–129

A. Hughes and M. Bent: ‘The Old Hall Manuscript: an Inventory’, MD, xxi (1967), 130–47

R. Strohm: ‘Ein Zeugnis früher Mehrstimmigkeit in Italien’, Festschrift Bruno Stäblein, ed. M. Ruhnke (Kassel, 1967), 239–49

M. Bent: ‘New and Little-Known Fragments of English Medieval Polyphony’, JAMS, xxi (1968), 137–56

F.A. Gallo: ‘Alcune fonti poco note di musica teorica e practica’, L’ars nova italiana del trecento: convegni di studi 1961–1967, ed. F.A. Gallo (Certaldo, 1968), 49–76

C.A. Miller: ‘Gaffurius’s Practica musicae: Origin and Contents’, MD, xxii (1968), 105–28

G. Vecchi: ‘Primo annuncio del sistema proporzionale di Marchetto in un passo del “Lucidarium”’, Quadrivium, ix (1968), 83–6

M. Bent: The Old Hall Manuscript: a Paleographical Study (diss., U. of Cambridge, 1969)

R. Federhofer-Königs: ‘Ein Beitrag zur Proportionslehre in der zweiten Hälfte des 15. Jahrhunderts’, SM, xi (1969), 145–57

F.A. Gallo: ‘Tra Giovanni de Garlandia e Filippo da Vitry: note sulla tradizione di alcuni testi teorici’, MD, xxiii (1969), 13–20

U. Michels: ‘Der Musiktraktat des Anonymus OP: ein frühes Theoretiker-Zeugnis der Ars nova’, AMw, xxvi (1969), 49–62

G. Vecchi: ‘Anonimi Rubrice breves’, Quadrivium, x/1 (1969), 125–34

E.C. Fellin: A Study of Superius Variants in the Sources of Italian Trecento Music: Madrigals and Cacce (diss., U. of Wisconsin, 1970)

W. Frobenius: ‘Zur Datierung von Francos Ars cantus mensurabilis’, AMw, xxvii (1970), 122–7

N.S. Josephson: ‘Vier Beispiele der Ars Subtilior’, AMw, xxvii (1970), 41–58

U. Michels: Die Musiktraktate des Johannes de Muris (Wiesbaden, 1970)

C. Wolff: ‘Arten der Mensuralnotation im 15. Jahrhundert und die Anfänge der Orgeltabulatur’, GfMKB: Bonn 1970, 609–13

N. Böker-Heil: ‘Weisse Mensuralnotation als Computer-Input und -Output’, AcM, xliii (1971), 21

R. Bockholdt: ‘Französische und niederländische Musik des 14. und 15. Jahrhunderts’, Musikalische Edition im Wandel des historischen Bewusstseins, ed. T.G. Georgiades (Kassel, 1971), 149–73

C. Dahlhaus: ‘Die Mensurzeichen als Problem der Editionstechnik’, Musikalische Edition im Wandel des historischen Bewusstseins, ed. T.G. Georgiades (Kassel, 1971), 174–88

W. Frobenius: ‘Minima’, ‘Semibrevis’, ‘Tactus’ (1971), HMT

F.A. Gallo: ‘Due trattatelli sulla notazione del primo Trecento’, Quadrivium, xii/1 (1971), 119–30

N.S. Josephson: ‘Rodericus, Angelorum psalat’, MD, xxv (1971), 113–26

M.L. Martinez-Göllner: ‘Musik des Trecento’, Musikalische Edition im Wandel des historischen Bewusstseins, ed. T.G. Georgiades (Kassel, 1971), 134–48

H. Schoop: Entstehung und Verwendung der Handschrift Oxford Bodleian Library, Canonici misc. 213 (Berne, 1971)

W. Arlt: ‘Der Tractatus figurarum: ein Beitrag zur Musiklehre der “Ars Subtilior”’, Schweizer Beiträge zur Musikwissenschaft, i (1972), 35–53

J.A. Bank: Tactus, Tempo and Notation in Mensural Music from the 13th to the 17th Century (Amsterdam, 1972)

W. Frobenius: ‘Prolatio’, ‘Semiminim’ (1972), HMT

H. Besseler and P. Gülke: Schriftbild der mehrstimmigen Musik, Musikgeschichte in Bildern, iii/5 (Leipzig, 1973)

W. Frobenius: ‘Longa – Brevis’, ‘Perfectio’ (1973), HMT

F.A. Gallo: ‘Figura and Regula: Notation and Theory in the Tradition of Musica mensurabilis’, Studien zur Tradition in der Musik: Kurt von Fischer zum 60. Geburtstag, ed. H.H. Eggebrecht and M. Lütolf (Munich, 1973), 43

W. Frobenius: ‘Modus (Rhythmuslehre)’, ‘Proprietas (Notationslehre)’ (1974), HMT

P. Gossett: ‘The Mensural System and the Choralis Constantinus’, Studies in Renaissance and Baroque Music in Honor of Arthur Mendel, ed. R. Marshall (Kassel and Hackensack, NJ, 1974), 71–107

K.-J. Sachs: ‘Punctus’ (1974), HMT

M. Bent: ‘A Preliminary Assessment of the Independence of English Trecento Notations’, La musica al tempo del Boccaccio e i suoi rapporti con la letteratura: Siena and Certaldo 1975 [L’Ars Nova italiana del Trecento, iv (Certaldo, 1978)], 65–82

L. Treitler: ‘Regarding Meter and Rhythm in the Ars Antiqua’, MQ, xlv (1979), 524–58

M.P. Long: Musical Tastes in Fourteenth-Century Italy: Notational Styles, Scholarly Traditions, and Historical Circumstances (diss., Princeton U., 1981)

A.E. Planchart: ‘The Relative Speed of Tempora in the Period of Dufay’, RMARC, no.17 (1981), 33–51

E. Schroeder: ‘The Stroke Comes Full Circle: and C in Writings on Music, ca. 1450–1540’, MD, xxxvi (1982), 119–66

F.A. Gallo: ‘Die Notationslehre im 14. und 15. Jahrhunderts’, Die mittelalterliche Lehre von der Mehrstimmigkeit, Geschichte der Musiktheorie, ed. F. Zaminer, v (Darmstadt, 1984), 257–356

W. Arlt: ‘A propos des notations pragmatiques: le cas du codex Las Huelgas: remarques générales et observations particulières’, RdMc, xiii (1990), 401–19

A.M. Busse Berger: ‘The Myth of diminutio per tertiam partem’, JM, viii (1990), 405–10

E. Roesner, F. Avril and N.F. Regalado: Introduction to Le Roman de Fauvel in the Edition of Messire Chaillou de Pesstain (New York, 1990)

B.J. Blackburn, E.E. Lowinsky and C.A. Miller, eds.: A Correspondence of Renaissance Musicians (Oxford, 1991)

R.C. Wegman: ‘What is “acceleratio mensurae”?’, ML, lxxiii (1992), 515–23

A.M. Busse Berger: Mensuration and Proportion Signs: Origins and Evolution (Oxford, 1993)

R. Woodley: John Tucke: a Case Study in Early Tudor Music Theory (Oxford, 1993)

A. Stone: Writing Rhythm in Late Medieval Italy: Notation and Musical Style in the Manuscript Modena, Biblioteca Estense, Alpha.M.5.24 (diss., Harvard U., 1994)

M. Bent: ‘The Use of Cut Signatures in Sacred Music by Binchois’, Binchois Studies: New York 1995

A. Blachly: Mensuration and Tempo in 15th-Century Music: Cut Signatures in Theory and Practice (diss., Columbia U., 1995)

M. Bent: ‘The Early Use of the Sign ’, EMc, xxiv (1996), 199–225

M. Bent: ‘The Use of Cut Signatures in Sacred Music by Ockeghem and his Contemporaries’, Johannes Ockeghem: Tours 1997, 641–680

B.J. Blackburn: ‘Did Ockeghem Listen to Tinctoris?’, Johannes Ockeghem: Tours 1997, 597–640

A.M. Busse Berger: ‘Cut Signs in Fifteenth-Century Musical Practice’, Music in Renaissance Cities and Courts: Studies in Honor of Lewis Lockwood, ed. J.A. Owens and A.M. Cummings (Warren, MI, 1997), 101–12

(ii) Notes: shapes, colours, abbreviations.

4. Mensural notation from 1500.

(i) General.

(iii) The division of time.

(iv) The joining and separation of notes.

(v) Clefs, staves, leger lines.

(vi) Accidentals, key signatures.

(vii) Dynamics.

(viii) Scores; harmonic and descriptive notations.

(i) General.

The simplified void notation of the late 15th century and the 16th, used throughout Europe for the international polyphonic repertory, was, like the medieval systems from which it developed, a singer’s notation. It was not well suited to notating more than a single melodic line, especially when associated with printing by movable type. In succeeding centuries, however, especially after the rise of the thoroughbass, theory and teaching were increasingly controlled by instrumentalists such as keyboard players, and the staff notation used for the bulk of the repertory was influenced by instrumental requirements, adopting many features that permitted it to express increasingly complex information. Conversely, keyboard tablature began to decline. The instrumental features adopted included, in the 16th and 17th centuries, the bar-line, beam and slur, permitting the clear grouping of notes for rhythmic and other purposes; the standardization of clefs, facilitating the sight-reading of even fairly complex textures; and the reintroduction of the score, which had been dropped in French notation in the 13th century. In the 16th, 17th and 18th centuries, the demisemiquaver and the hemidemisemiquaver were added to the range of note values; keyboard notation adopted, when necessary for the sake of clarity, a score layout with more than two staves to the system, not previously used except in the partitura. In the 19th century, the vocabulary of signs for dynamics, accents and articulation was greatly extended; some novel features, which became basic to 20th-century practice, were introduced by Beethoven, Schumann and Liszt.

Thus notation continued to develop after the 16th century. Yet a rift gradually developed between notational theory and notational practice; professional musicians often came to treat theory as elementary and in consequence to expound it merely within the sphere of musical rudiments or incidentally in treatises on performance. This situation began to change only in the second half of the 19th century. Meanwhile, however, proposals for reform had been made, from the 17th century onwards, by those seeking a universal musical notation. Even though most proposed reforms were impracticable and were adopted by no-one but their inventors, as a whole they strikingly illustrate the desire of Western notators for a notation independent of any single musical style. Even a system as economical and adequate as Tonic Sol-fa was not adopted for the bulk of diatonic music: its limitation in practice to a single style was felt as a fatal flaw, as similar limitations had never been present in medieval notational systems. That did not prevent its use for the benefit of the musically uneducated: and Tonic Sol-fa merely exemplifies the numerous novel notational systems for vocal music devised from the 16th century onwards for this purpose. These systems are often unconcerned with theoretical abstractions, and thus resemble instrumental tablatures. Most of them were based on popular solmization practice, and many provide the same information in more than one way.

A turning-point in notational practice seems to have occurred in the second half of the 19th century in consequence of the harmonic and rhythmic theory of the period (Moritz Hauptmann, Hugo Riemann and Mathis Lussy). The notational principles outlined, to some extent en passant, by these theorists were popularized in Germany, France and Britain and may have laid the foundations for a number of details of modern notational theory and practice. In particular, the rules for orthography in accidentals and in rhythmic notation (with slurs and beams) came under close scrutiny, with attempts to abolish the less theoretically justifiable aspects of notation in the 18th century and the early 19th. The heavily edited versions of Classical works produced by Riemann and others may well represent attempts at transcription into a new notational language, rather than arbitrary suppression of the composer’s wishes in favour of the editor’s; perhaps for that reason, some scholars opposed the concept of the Urtext edition, holding that the careless adoption of obsolete and hence misleading notational conventions was indefensible.

The notation evolved by Riemann and Lussy, precise as it is in rhythmic detail, well deserves the title of ‘orthochronic’ notation (an equivalent term was coined by Chailley, 1950): note shapes uniquely fix durational relationships between notes, and there are no subdivisions of notes other than duple unless specially indicated. However, the extension of this term to all notation since the 16th century seems arbitrary, since no account is then taken of the numerous conventions whereby rhythms intended in performance were not explicitly indicated in the score. These conventions, including the occasional anomalous triple subdivision of note values, were widespread until the last third of the 19th century, and may be found in much music (though not the bulk of the repertory) even later than that. The term ‘orthochronic’ is, accordingly, avoided here in favour of the more comprehensive term ‘mensural’, which may legitimately be used wherever note shapes are directly related – even if only vaguely or notionally – to the durations of notes in performance; in other words, to almost all notation in the mainstream repertory, classical or popular, except tablature, from Franco of Cologne to the present.

In the 20th century proposals for notational reform by professional notators and experiments in notation by composers greatly increased. Where these are not simply arbitrary, they represent to some extent further developments of the notation of the late 19th century, with further extensions of the capacity of mensural notation to carry large quantities of information; they may be seen as new departures reflecting the new ideas underlying the music. With the rise of historical musicology and ethnomusicology, notation has been faced with new problems in the attempt to use it to represent material originally designed for another, or no, notational system. In ethnomusicology, notation has become for almost the first time on any large scale descriptive rather than prescriptive. Since most musical works notated in the 20th century were tonal and traditional in style, whether editions of old music or new compositions, only certain universally useful devices, such as the representation of durations proportionally by the spacing and alignment of notes, gained universal currency.

The fullest discussion of the history of Western notation, copiously illustrated, is to be found in the two volumes of Wolf’s Handbuch der Notationskunde (1913–19/R), to which the reader is referred for more detailed information; a shorter survey is Rastall’s The Notation of Western Music (1983, rev. 2/1998). Apel’s Notation of Polyphonic Music, 900–1600 (1942, rev. 5/1961) is also valuable for medieval and Renaissance notations. For information on recent notational usage the volumes by Read (1964 and 1978), Karkoschka (Schriftbild, 1966) and Risatti (1975) may be found helpful.

(ii) Notes: shapes, colours, abbreviations.

Void (‘white’) notation (see §3(vii) above), with duple relationships for the most part between note values, and dots (when used for rhythmic purposes) only as dots of addition, was generally (though not universally) adopted by the early 16th century in both vocal and instrumental music, tablatures apart. It was generally adopted by printers from Petrucci onwards, since it was readily adaptable to printing from movable type; in some music, such as popular metrical psalters, this notation survived virtually unchanged for centuries (as in fig.68, a 19th-century metrical psalter). Even when the appearance of the notation changed, the representation of primary (uninflected) pitches by their position on the staff, in the manner established in the Middle Ages, remained unchanged in succeeding centuries except in occasional instances where staff notation was treated as a tablature. The latter may be seen in the modern notation of harmonics on string instruments by finger position rather than by sound, and more strikingly still from the 17th century in Scordatura notation, where the written notes or chords represent finger positions and, since the instrument is abnormally tuned, do not correspond with the sounds. For the notation of accidentals, see §(vi) below.

After 1600 black-full notation (i.e. where the note heads of minims and higher values are black) was never again of great importance, despite the advocacy of such a notation by Lacassagne (1766). It was used for symbolic reasons in some works of the 15th, 16th and 17th centuries, such as Ockeghem’s Missa ‘mi-mi’, with black-full notes at the word ‘mortuorum’, and J.C. Kerll’s Missa nigra (see Eye music). The opposition of void and full notes was used also in various 20th-century reform proposals, for distinguishing pitches rather than durations (e.g. in Equitone, where full notes are a semitone higher than the equivalent void notes, and in Klavarskribo, where void and full notes correspond with white and black notes on the modern keyboard – see fig.79).

Red notes were still in occasional use at the beginning of the 16th century for distinguishing rhythmic proportions (as in GB-Llp 1, probably dating from the reign of Henry VIII), but dropped out of general use as rhythmic style became simpler; their use would, moreover, have entailed unnecessary expense in music printing. They continued, however, to be described by theorists such as Morley (A Plaine and Easie Introduction, 1597; ed. Harman, pp.114ff), and red and other colours have remained in occasional use to the present day in one of their oldest and simplest uses: to distinguish individual strands of the notation from one another. Red, green and black notes are used for this purpose in the 16th-century manuscript D-Bsb Mus.ms.theor.57, and red and black notes on a single staff in the 18th-century manuscript Bsb Mus.ms.40296. Red is used to distinguish the main melody in 16th-century Spanish lute tablatures (here with red numerals rather than red notes); and the same principle appears in a few late 19th-century editions (fig.69). Dallapiccola used square red notes for a canon whose resolution is printed in normal notation, in the ‘Andantino amoroso e contrapunctus tertius’ from the Quaderno musicale di Annalibera (1952). Other uses of colour include yellow or red for notes subject to chromatic alteration (G.M. Trabaci).

Coloration in a more general sense – full notes used in opposition to void notes for rhythmic purposes – survived in the 16th and 17th centuries especially for expressing hemiola rhythms in 3/2 time, three full semibreves or equivalent replacing two normal void dotted semibreves. The derivation of these full semibreves from 14th- and 15th-century imperfect semibreves is clear, even though redundant dots had been placed after perfect semibreves generally from about 1500; the continuing influence of 15th-century principles may be seen in the omission of dots after ‘perfect’ void semibreves in even so late a source as Caccini’s Euridice of 1600 (fig.70).

Soon after 1600, coloration was used for entire movements in mensural notation, such as courantes, whether or not hemiola rhythms were intended (fig.71a, from Frescobaldi, 1626, where the rests show that the ‘crotchets’ are coloured minims). This practice, derived from tablature notation, may have contributed to the increasing use of the crotchet as the beat; in G.B. Fontana’s practice (1641, fig.71b) crotchet rests are used to correspond to coloured minims, and the semibreve rest is used for a bar’s rest (Riemann, 1910, pp.140ff).

Smaller note values (fusa and semifusa) were increasingly used in the 16th century, owing to, or resulting in, the slowing down of note values in general (see §(iii) below). In the late Middle Ages, a semiminim could be written as a coloured note (red in black notation, black in void notation) with a stem but without a flag, or as a non-coloured note with both stem and flag; this generated a series of smaller note values with alternative forms, the non-coloured forms bearing one more flag than the coloured. These alternative forms remained theoretically available, although the coloured forms (as in modern practice, where a crotchet is the coloured form of the minim) have been generally preferred. This meant, paradoxically, that as small note values were increasingly used, and especially as the semiminim came to represent the beat at the end of the 16th century, ‘void’ notation (i.e. notation in which the minim and larger values were written with white note heads) consisted more and more of black notes.

The non-coloured forms of the semiminim and below, which in the 16th century often occur in sections in fast triple time where the time unit was the semibreve rather than the minim, survived until the 18th century (fig.72, from Couperin). By the time of Couperin almost all the shorter note values used today may be found, mostly in written-out ornamentation; both small and large note values, with corresponding exceptional time signatures, occur for symbolic reasons in Telemann’s Getreuer Music-Meister of 1728 (see Eye music, fig.1). Beethoven used small note values and rests particularly lavishly (fig.73, from the Fantasia op.77). For the grouping of smaller note values by means of beams, and for the continuing use of ligatures, see §(iv) below.

Standard small melodic formulae, mostly of short notes (ornaments), had been abbreviated with special signs in keyboard tablatures from the late Middle Ages onwards, and in medieval vocal music some abbreviations are also found to indicate repeated material (for an example see Isorhythm). The double bar with two (or four) dots to indicate repetition is already found in essence in 15th-century polyphony. A large vocabulary of signs indicating abbreviations of ornaments, not generally precise before the 17th century, was developed in the 18th century, especially in French keyboard and lute music (see Ornaments, §7). Some notators, such as Bach, often preferred to write ornaments out in full, a tendency increasingly evident in the 19th century as improvised ornamentation declined (see Improvisation, §II, 3(iv)). A parallel phenomenon was the increasing reluctance of notators during the 19th century to abbreviate at the repetitions of short phrases, for example in Alberti basses. (For details of special notations for abbreviating repeated notes and figures see Abbreviations.)

The lozenge-shaped notes of many 15th-century sources continued to be used in much printing from movable type (see fig.68 above) and in carefully written manuscripts throughout the 16th century. Rounded note shapes came increasingly to replace them from as early as the 15th century (fig.74, with pear-shaped notes, from I-PEc G.20); no adequate reason seems yet to have been given for this change. Etienne Briard jettisoned the lozenge-shaped notes in favour of oval ones in French printing as early as about 1530, but in England the change did not occur in printing until Carr’s Vinculum societatis (1687; fig.75).

Notes of a smaller than normal size occur in early 19th-century English songs, printed as keyboard music (i.e. with the vocal part and accompaniment notated on two staves rather than three: see §(v) below). The main melody is notated normally, whereas the accompaniment on the upper staff is distinguished by small notes (fig.76). The use of small notes to distinguish ornamentation, alternative versions of passages or other subsidiary material became normal in 19th-century piano music (fig.77, from Chopin’s Prelude op.28 no.8, published in 1839; the proportion of small notes to large is particularly high). The small notes often did not count towards the value of the full bar; sometimes they refer to notes intended to be played very rapidly. (For the use of small notes to represent music without a regular pattern of beats, see §(iii) below.)

Unconventional note shapes, like some coloured notes, have occasionally been used within the normal mensural system for special purposes (see fig.78, with reversed note shapes representing one strand of a complex texture). The problem of differentiating such strands was solved by Schoenberg, on the other hand, by the use of squared slurs joined to the capital letters H (Hauptstimme, principal voice) or N (Nebenstimme, subordinate voice).

Since the reintroduction of the score, and particularly in the 20th century, duration has frequently been related to the horizontal distance between notes, though aesthetic considerations have often led notators to place notes symmetrically between bar-lines, so that arguments about simultaneity cannot usually be settled conclusively by considering alignment. Thus the staff has been treated as the axis of a graph; and, as far as this is true, the indication of duration by note shapes is redundant. Reformers have sometimes attempted to eliminate the redundancy: Hans Wagner (Vereinfachte Notenschrift, 1888) proposed the abolition of all note shapes but the semibreve. The Equitone and Klavarskribo systems have attempted the same: duration is related to the distance between notes, and note shapes are used to represent pitch (fig.79).

Other proposals for changing or abolishing the mensural note shapes, up to the late 19th century, have generally been of little practical significance. Examples are the 15th-century proposals of Giorgio Anselmi to distinguish durations by ascending and descending stems variously applied to a void breve shape (Gaffurius, Practica musice, 1496, ii, chap.4) and, as one of the first efforts to devise a thoroughly reformed notation, J. van der Elst’s series of somewhat complex note shapes (fig.80, from Notae Augustinianae, 1657; see also his Den ouden ende nieuwen grondt van de musijcke, 1662) for both vocal and instrumental notation. Another unsuccessful reform, that of Sauveur (Système général des intervalles des sons, 1701), attempted to give each pitch a distinctive note shape, and may thus be seen as a forerunner of the 19th-century shape-note system (see §5(iv) below; the shape-notes were taken up and used in a different sense by Cowell: see §(iii) below). (For details of other reforms, see Wolf, 1919, 335ff; for novel note shapes representing various durations, see Risatti, 1975, pp.1ff.)

For chords including several adjacent semitones, notated on a single staff, traditional mensural notation is inadequate, allowing as it does only for two vertical groups of notes a 3rd apart, either side of the stem. From the early 20th century such chords were notated with supplementary diagonal stems branching from the common stem, by means of which the chords could include three vertical groups of notes. The extension of such chords into clusters suggested the adoption of abbreviated signs, notably those of Henry Cowell (fig.81), which have been adapted also to represent sustained clusters (see fig.82 and Risatti, 1975, pp.26–7, 36).

(iii) The division of time.

Vestiges of the system of proportional mensuration signs persisted to the 18th century in some places. After 1500 the more complex proportions are found only in theoretical works, and in a few 16th-century polyphonic works to illustrate the text (e.g. the pieces by Renaldi and Striggio quoted by Morley, 1597). Nevertheless proportional signatures, in the form of fractions like those of the 15th century and, as then, cancelled by the reciprocals of the fractions, were used in the 17th and the early 18th centuries in Italy and Germany for pieces with short sections in different metres (e.g. 12/8 is cancelled by 8/12, 6/4 by 4/6). Apel’s suggestion (Notation of Polyphonic Music, 5/1961, pp.163, 442) that these mensuration changes might have carried connotations of tempo change seems only speculative. Examples of this notation occur in Frescobaldi (fig.83), Corelli’s op.5, Georg Muffat (Apparatus musico-organisticus, 1690), F.X. Murschhauser (Prototypon longo-breve organicum, 1707) and the manuscript CS-KRa II/133. On the more complicated question of C and C as proportional signatures, see below.

A fundamental change in tactus notation occurred, however, from the 17th century; it eroded the significance of proportional signatures for tempo, and makes unambiguous determination of tempo very difficult in a good deal of later music. In medieval notation there was a progressive slowing down of note values (see §3 above), and this continued during the 16th century, partly no doubt owing to the proliferation of short note values. By the second half of the century the minim had become the normal beat in polyphony. But this slowing down did not continue uniformly throughout the polyphonic repertory: even though the crotchet became the main time unit for much music in the 17th century, the minim continued to be the normal beat in much music produced for popular consumption, such as the metrical psalters and hymnals, and in church music in the stile antico. Indeed it still survives as the normal beat in hymn tunes and Anglican chants; the crotchet has only recently taken its place in some hymn tunes, and then usually only when settings are complex or connotations of a modern style are sought.

The change, then, lies largely in the increasing readiness of notators arbitrarily to adopt different note lengths as the main beat in different contexts (for an example of this seeMadrigal, fig.2). This variety in tactus notation presumably had its roots in the 15th-century notation of augmentation and diminution, which continued to be expounded as the basis for theoretical distinctions such as those between C and C. By the time of Beethoven any note value between the semiquaver and the dotted minim was capable of functioning as the main beat (compare parts of the Arietta of the Sonata op.111, fig.89 below, with his scherzos: that of the Ninth Symphony includes specific recognition of the dotted minim as the beat – ‘ritmo di tre battute’, etc.).

With this increasing variety of augmentation and diminution, especially from the 18th century, any note value could theoretically function as the beat, independent of considerations of tempo, through a novel explanation of fractional time signature (found at least as early as G.M. Bononcini’s Musico prattico, 1673). Here, as in modern theory, the denominator of the fraction representing the time signature indicates the note value on which the metre is based (usually the beat, with the figure 1 for the semibreve, 2 for the minim, 4 for the crotchet etc.), and the numerator indicates the number of such note values to the bar.

Parallel with the partial emancipation of the time signature from tempo, there were two developments tending to make the determination of tempo and time easier: the increased use of bar-lines and of verbal specifications of tempo. Vertical lines had been used through staves in medieval score notation, not in their modern sense as bar-lines but to divide sections from one another; but some 15th- and 16th-century keyboard and lute sources include the visual separation of units of one or more bars, either by a space left between them or by a bar-line. Such bar-lines are used with varying degrees of consistency and frequency (for bar-lines marking off single beats, see Apel, 1942, p.67). The bar-line was used in vocal music also (mainly in scores) from the late 16th century, but was not adopted generally in mensural notation until the 18th century. Even later than that some notation lacked it, as do some 19th- and 20th-century editions of old music. In 20th-century music dotted bar-lines were used to clarify the subdivisions of larger bars, as in Debussy’s Les sons et les parfums tournent dans l’air du soir (from Préludes, i, 1910). (For the use of conflicting bar-lines, see below.)

The increasing unreliability of time signatures as indicators of tempo is also reflected in the adoption of Italian (and later German, English and other) terms for this purpose. These tempo indications (in Donington’s terminology, ‘time-words’: see Interpretation of Early Music, 3/1974, pp.386ff), like bar-lines, seem to have appeared first in polyphonic music for soloists, perhaps because of the complexity of this music from the individual performer’s point of view when compared with vocal music. Tempo indications occur in Luis de Milán’s El maestro (1536) but were not generally adopted before the 17th century: the terms adagio, allegro, grave, largo, lento and presto are attested between 1596 and 1619, with others during the 17th century. These tempo indications have not always carried their present connotations, nor has their significance always been precise. From the early 19th century (Beethoven) they were supplemented still further by metronome indications, and in the 20th century (Bartók) by precise indications of the duration of a piece in minutes and seconds (see Tempo and expression marks and Metronome (i)).

Despite these developments, time signatures never completely lost their associations with tempo, although the associations of numerical (fractional) time signatures, taken in isolation, are seldom unambiguous. No consistency exists in the music of the last three centuries even in the relationship between the note values chosen to function as beats and tempo.

With and C, the circular and semicircular signatures inherited from the Middle Ages, practice was even more confused. Theorists continued to expound the significance of vertical bars in time signatures (as in C), and of the reversal of symbols (e.g. in ) as signifying diminution; but even when distinctions can be drawn between C meaning 4/4 and (‘alla breve’) meaning 2/2 or 4/2 (the latter, for example, in the Credo of Bach’s B minor Mass), it is by no means clear that the tempos of the beats were intended to be equivalent. In the 16th century the sign C became uncommon, the basic duple metre of most polyphony being signified by C; precisely the reverse convention became common at the beginning of the 17th century, and the reason for the change is obscure, for no change in meaning seems necessarily to have been intended. This change occurred in English music printing quite suddenly about 1594 in madrigal partbooks and about 1621 in psalm books: see fig.84. These signs may enclose a dot without changing in meaning. Similarly, is sometimes used as a synonym for , C 3, C 3/2, C 3/2, C 3/2, 3, 3/1 and so on, for quick triple time; from the 17th century and seem to have been dropped until was later revived with a new meaning (see below). These time signatures were used without total consistency well into the 19th century at least; Schubert often used C adagio movements in 4/4 and C for fast movements, whereas Bruckner used C for fast 4/4 movements and C for slow movements. (In the first movement of Bruckner’s Seventh Symphony, moreover, it is hard to see a real tempo difference being intended between the allegro moderato C of the opening and the ruhig C at bar 51.) Even books of rudiments may imply that C and C are synonyms (Dibdin, Music Epitomized, 1808 edn., p.37).

The most that can be said is that vertical bars in time signatures, and reversed (‘retorted’) signs, indicate relatively fast tempos, but not always reliably; this is particularly likely when C is used for music in the stile antico, or when the time signature changes during the course of a piece. (For relevant passages from a wide variety of theorists, see Donington, Interpretation of Early Music, 3/1974, pp.405ff.) There has been no thorough investigation of time signatures used since the 16th century; the degree of ambiguity at different times and places can scarcely be assessed, and the reasons for it are unknown.

Signs sometimes used in the 18th and 19th centuries as equivalents of 4/2 (‘great alla breve’) rather than C (2/2 or 4/4) include 2/1, , revived in a new sense (e.g. Bach, Gigue from Partita no.6, bwv830), CC (Rossini), C C and C C (Schubert, Impromptu d899 no.3, altered to C by Schubert’s publisher). was sometimes written as C | (i.e. with its elements spaced out).

Even when the tempo implied by a time signature is clear, divisions of the time within individual bars are not always literally those written, even apart from considerations of agogics, in terms of which most notators intended the written note values to be interpreted with some degree of rhythmic freedom. Unwritten rhythmic conventions cannot generally be guessed in European music before the 16th century. At that period Tomás de Santa María wrote of pairs of notes written equal but intended to be played unequally (Arte de tañer fantasia, 1565); this may have been widespread, and a similar practice is well attested in 17th- and 18th-century France (see Notes inégales). In some cases of unequal performance of note pairs, the first note of each pair was to be lengthened; in others it was the second note, though this was generally indicated in some other way. Even written-out ornaments must have been subject to some rhythmic alteration in practice: some trills written as successions of even rapid notes were intended to begin slowly and then speed up. Such practice was in certain contexts so much a matter of course that notational devices were used to indicate the absence of inequality: either a verbal direction (e.g. ‘notes égales’) or dots written over individual notes (Marin Marais). A comparable unwritten rhythmic convention, attested in some 19th-century keyboard music, is the introduction of unwritten rhetorical pauses (see Franklin Taylor’s preface to his Clementi edition, concerning the Didone abbandonata Sonata), though Lussy (1874) sought to restrict this practice to salon pieces (Eng. trans., pp.207–8).

Discrepancies between written and intended rhythms are particularly likely when different strands of the texture are notated in different time signatures; these multiple time signatures (in Read’s terminology, ‘polymeters’) occur fairly frequently in the 18th century (as in Bach and Mozart). In such cases it is usually at least possible that the conflicting rhythms which result are to be accommodated to one another (for exceptions, see below). Dotted-note figures with duple subdivisions against triplets are cases in point: particularly in late Baroque music it often seems likely that dotted rhythms are to be relaxed into triplet rhythms: the use of a crotchet and quaver under the numeral 3 (and often slurred), for the more accurate notation of triplet rhythms in cases such as these, is attested in the mid-18th century (Arne, 1756; see fig.85, where it is immediately adjacent to the older convention) but not generally used before the 19th. In some 19th-century notation, for example chorus parts in Verdi operas, the accommodation of dotted rhythms to triplets also seems highly probable. There is even some evidence in the 19th century of duplets in a melody and triplets in an accompaniment being accommodated to each other (Bochsa, New and Improved Method of Instruction for the Harp, c1818–19, p.60); although theorists explain triplets as three notes in the time of two, they do not always state that all the notes involved are equal in length. Some piano notation, with polyphonic figuration and notes occurring in more than one polyphonic voice (fig.86), absolutely requires accommodation of the rhythms, though its evidence ought not, perhaps, to be pressed into proving rhythmic accommodation elsewhere. The correct practice in Schubert’s music, where dotted and triplet rhythms often appear simultaneously, is particularly difficult to establish (see MT, civ (1963), 626, 713, 797, 873).

On the other hand, even an apparently straightforward case of dotted notes against triplets in Paisiello was cited as early as 1806 by Callcott (fig.87, from A Musical Grammar, p.236, repeated in many subsequent editions) as an ambiguous case: ‘There is some doubt whether this Melody should be played as written, or as if it were compound; that is, one dotted Crotchet, one Crotchet, and one Quaver, in the first Measure’. The possibility of maintaining conflicting rhythms in certain contexts had been raised by some in the second half of the 18th century (Quantz, Eng. trans., 1966, p.82; Türk, 1789). A general tendency in cases of conflict to accommodate all rhythms to the most relaxed within a texture ultimately lacks logic, and a cautious approach combined with aesthetic judgment seems advisable in the present lack of detailed studies based on a large cross-section of notational evidence.

A distinction between intended and written rhythms, literally interpreted, is likely, on the grounds of the category to which a piece belongs, until the 19th century at least and even later in popular music. Double-dotting, though attested in Marais as early as 1701, is, like the precise notation of triplets, uncommon in mensural notation before the 19th century; yet the French overture is a well-known example of a category with a well-defined tradition of tempo and double-dotting in performance, which was required but not normally spelt out in the notation. There were conventions concerning the tempo and rhythmic features of various categories, particularly dances, such as the minuet, gavotte, chaconne and pastorale; these conventions varied to some extent according to period and country, and were sometimes ambiguous even to contemporaries. Nevertheless the notation used for them might for the sake of convenience vary in literal detail from the intended effect, if there was no danger of misunderstanding at the time – for example in the choice of C as the time signature of a gigue, with quick triple time intended throughout (see Ferguson, 1975, pp.92–3).

The tradition-bound approach to notation implicit in practice such as this led some to retain traditional ‘category’ notation even when the notation was no longer suitable to the category. Chopin, for example, retained the 3/4 time signature of the scherzo (descended from the 18th-century minuet) even though the tempo had so greatly increased by his time that the bar contains only one beat, and single phrases frequently contain notes tied over three or four bars, as well as rests of two bars or more (fig.88). According to later 19th-century rhythmic theory, this traditional notation seemed inadequate (for criticisms of category notation based ultimately on this theory, see S. Macpherson, 1908, rev. 1915, pp.39ff, and 1911, rev. 1932, p.17). Nevertheless, category (or rather style) notation remained alive in 20th-century popular music notation: notated almost universally in C, it very often requires to be interpreted on grounds of style as if notated with unequal pairs of notes closer to 12/8; moreover, certain other rhythmic characteristics (syncopation etc.) are frequently required by the style though not spelt out in the notation.

In addition to these complexities, there are many contexts in 18th-century music where triple subdivisions of notes are extensively tolerated. The lack of theoretical provision for such practice at times renders passages difficult to read: a notable example is the Arietta of Beethoven’s sonata op.111 (fig.89) where the demisemiquavers are to be taken as ‘perfect’ in the medieval sense unless followed by a hemidemisemiquaver and thus rendered ‘imperfect’ (this detail of Beethoven’s notation survives in modern editions of the sonatas).

The confusion in the use of time signatures and subdivision of beats, especially in relation to tempo, was recognized by Riemann (Musikalische Dynamik und Agogik, 1884). He recognized that the choice of note length for the beat was often arbitrary, particularly since 6/8, for example, could represent either two or six beats to the bar. Accordingly, and to facilitate the representation of beats with triple subdivisions, he proposed a system of time signatures based on the beat, ignoring differences that had long been artificial, such as that between 2/4 and 2/8. In his reformed system, time signatures were to comprise simple integers (e.g. 2, for two beats to the bar, whatever their nominal value), integers separated by dots (e.g. 2.3, meaning six beats in two groups of three each) or fractions (e.g. 2/3, meaning two beats with triple subdivisions, or 3.2/3 meaning six beats with triple subdivisions in three groups of two). However soundly based and economical, this ingenious system did not win general acceptance, though the use of the simple integer (found with a more restricted meaning earlier in the French Baroque), omitting the denominator of the conventional fractional time signature, is fairly widespread in 20th-century mensural notation.

Another abortive attempt to increase the variety of the subdivisions of the beat, in this case well beyond the capacity even of 14th-century Ars Subtilior notation though not matching the theoretical potential of 15th-century proportional notation, was the system proposed by Henry Cowell. He sought to supplement the traditional vocabulary of note lengths with ‘two-third notes’, ‘four-fifth notes’, ‘four-seventh notes’ (i.e. as fractions of a semibreve) and further submultiples of the semibreve, which were to be represented with void notes of various shapes without stems (triangles, squares, lozenges etc.). Some of these shapes were borrowed from traditional American shape-note notation (see §5(iv) below). These notes would then generate others by the addition of stems and flags, in the same way as the semibreve: with a stem, for example, ‘third-notes’, ‘two-fifth notes’, ‘two-seventh notes’ and so forth. The system is exemplified in Cowell’s Fabric of 1917, published in 1922 (fig.90: see also Read, 1964, 2/1969, pp.76–7; Stone, 1963, p.19). A further system of durational proportions, based on ratios and not requiring novel note shapes – and thus more flexible than Cowell’s system – has been adopted by Stockhausen (Klavierstück I).

Multiple time signatures occasionally occur from the 18th century in pieces where there is clearly no question of accommodating the rhythms in one part to those in another: Fux’s Concentus musico-instrumentalis (DTÖ, xlvii, Jg.xxiii/2) has a movement with a simultaneous ‘Aria italiana’ in 6/8 and an ‘Aire française’ in C; and the ‘Fanfare’ from La triomphante in Couperin’s tenth ordre (fig.91) has conflicting signatures, with the explanatory note ‘Quoy que les valeurs du dessus ne semblent pas se raporter avec celles de la basse; il est d’usage de le marquer ainsi’. In some 20th-century music and editions of older music, both conflicting signatures and conflicting bar-lines may be found (figs.92 and 93: examples from Bartók, String Quartet no.3, 1929, and an edition of Monteverdi madrigals by Leichtentritt).

Time signatures representing additive metres (those in which the beats within a bar cannot be subdivided into groups of equal size) are found in the 18th century: Handel included a few orchestral bars in 5/8 in Orlando (1733) to represent madness; Burney (History) termed this ‘a division of time which can only be borne in such a situation’. (The principle of additive rhythm occurs much earlier than this in vers mesurés à l’antique.) Additive time signatures were used by Reicha (‘3/8 et 2/8’), Chopin, Tchaikovsky, Bartók (3 + 3 + 2 over 8) and others, but Moritz Hauptmann’s rhythmic theory regarded them as ‘inorganic’ and thus to be condemned (1853, Eng. trans., 1888, pp.196ff). A list of 20th-century works with additive and other unusual signatures may be found in Read, 1964, 2/1969, pp.159ff; some are based (not necessarily consistently) on small rapid note values, rather than beats, as the unit for the numerator of the fraction. A variant of this occurs in Stockhausen’s Klavierstück I, with the smallest note value, not necessarily directly represented in the changing time signatures, regarded as the basic time division. As changes of time signature within a piece became increasingly common in the 20th century, various notational details were simplified: the double bar previously usual before a change was often reduced to an ordinary single bar-line, time signatures were enlarged and written between the staves, or above the staff (Debussy).

For music partly or entirely outside a system of regular beats, notational practice has varied. The oldest sign representing an indefinite prolonging of a note’s duration is the pause sign or fermata (a semicircle over a dot), inherited from the Middle Ages and still universally used in Western notation (in the 20th century it was sometimes modified to provide various degrees of extra length, or inverted to signify shortening rather than lengthening). Relatively lengthy passages of music without a regular metric beat occur from the 17th century onwards in recitative; Italian recitative was normally divided arbitrarily into bars of four beats, with C as a time signature, whereas French recitative was notated with frequent changes of time signature more closely reflecting the declamation of the text. (The arbitrary use of a time signature in Italian recitative is paralleled by the occasional 16th- and 17th-century practice of notating pieces in duple metre even though their musical sense is triple: see Apel, Notation, pp.66–7.) An experimental notation is found in some French harpsichord pieces of the last quarter of the 17th century and the early 18th century, where conventional time divisions are quite abandoned and the music notated either entirely in ‘semibreves’ grouped with slurs, or in a mixture of ‘semibreves’ joined with slurs and ‘short note values’ joined with beams (fig.94; for details of this notation and its interpretation see Prélude non mesuré, and Moroney, 1976).

Various methods were used from the 18th century to notate irregular expressive melodies in free rhythm in instrumental music as for example in written-out cadenzas or in keyboard fantasias (Mozart, Beethoven). They may be notated, like Italian recitative, by using a regular time signature and bar-lines and by dividing the passage arbitrarily into beats, as in Beethoven’s Ninth Symphony (fourth movement) or in his Piano Sonata op.31 no.2 (first movement). This notation has been maintained by later composers, including Wagner, for the shepherd’s piping in Act 3 scene i of Tristan und Isolde. Alternatively the passages may be written without a time signature, either in notes of conventional size, or in small notes, or a mixture of the two, grouped with beams as required to clarify the accentuation, and with any bar-lines irregularly placed as an auxiliary means of grouping: this method was used by Mozart and many later composers (fig.95).

In notation of this sort the note values carry only imprecise connotations of duration. A more systematic use of imprecise durations was required in some 20th-century works: notes of indeterminate length were notated in various novel ways, sometimes with imprecise distinctions between longer and shorter notes (see Risatti, 1975, pp.1ff). In some 20th-century music, great rhythmic variety within the texture had to be represented without the aid of regular beats in any strand, and increased precision was sought in the notation of accelerandos and decelerandos, previously indicated only with verbal directions in the score. This was sometimes achieved through the modification of aspects of notation not formerly used to represent the division of time: converging and diverging multiple beams used for groups of short note values notated in an otherwise traditional fashion may denote increasing and decreasing tempos; or staves may be slanted upwards from the horizontal to denote an increase in tempo and downwards to denote a decrease in tempo (Bussotti). Other devices include the multiplication of metronome indications at short intervals, the use of ‘+’ and ‘−’ signs for (imprecise) tempo changes and so on (see Risatti, 1975, pp.21ff). Rhythmic proportions more complex than those available with the traditional numerals (3 = three in the time of two, 5 = five in the time of four, etc.) have been represented by a precise spacing of notes to a specific scale (e.g. one second to 2·5 cm of score); this notation may be supplemented with auxiliary signs specifying the duration of individual ‘bars’ (short subdivisions) within the music, resembling the specifications of precise lengths in an architectural scale-drawing. In 20th-century music generally, whatever the style, vertical alignment of different parts of the texture became a generally reliable indication of the order in which notes are to be sounded, and whether or not notes are simultaneous; and spacing of notes tends generally to be proportional to their durations.

(iv) The joining and separation of notes.

15th-century ligature theory was fully expounded by Morley (1597), and still appears in 17th-century didactic material; but it was not always thoroughly understood, even by theorists, and the only ligature to remain in fairly common use was that ‘with opposite propriety’ signifying two semibreves. Even this ligature was confined mostly to music in the stile antico. The ligature system was unsuited to printing by movable type, and since it applied only to long note values it was relatively useless after the minim had become the basic beat in polyphony. The two-semibreve ligature survived in Austria as late as the first half of the 18th century (Fux).

Ligatures had always been relatively uncommon in keyboard and other instrumental notation, but a comparable device had been the beam, found in some but not all early keyboard sources to join together groups of small note values (e.g. in the Buxheimer Orgelbuch, D-Mbs Cim.352b; see fig.130 below) and in some sources to join groups of rhythm signs together in a characteristic grid pattern. In these sources the primary sense of the beam is rhythmic, since the first of any group of notes joined together is stressed; this continued to be the meaning of the beam in instrumental music even after it had been transferred to vocal music. Another device comparable to the ligature was the slur or tie; the latter occurs in 16th-century keyboard sources such as Cavazzoni’s Recerchari, motetti, canzoni (1523) and Buus’s Intabolatura d’organo (1549; fig.96). Both the beam and the slur came to be used in vocal music for a purpose originally served by the ligature: to join together the notes to be sung to a single syllable, the slur for long note values, and both the beam and the slur for short ones. Praetorius (Syntagma musicum, iii, 2/1619) recommended the slur in place of all ligatures save that ‘with opposite propriety’; both the slur and the beam are used to join notes to be sung to a single syllable in Gabriel Bataille’s Airs de différents autheurs (1608; fig.97), and occur generally, though not always consistently, in 17th-century printed collections and manuscripts of vocal music from Italy and southern Germany. They occur for a similar purpose in English printed music first in the Vinculum societatis of J. Carr (1687; see fig.75 above); it is not clear which (perhaps both) of these notational innovations is intended by the ‘vinculum’ of the title.

This 17th-century convention still survives in most vocal music, though some notators have begun to adopt a notation more closely resembling instrumental notation, since syllabic vocal music is often difficult to read if small note values are at all numerous. 20th-century additions to it in scholarly editions of old music included square slurs to represent notes originally grouped as ligatures, and dotted, hairline or slashed slurs to differentiate editorial from original ones. Even Lussy in the 19th century, despite his concern to use the beam in the service of rhythmic theory, made a specific exception in favour of traditional vocal notation (Eng. trans., p.29).

In instrumental music the beam continued to be used for joining together small notes, in groups generally corresponding to a single beat or to simple multiples and submultiples of beats. An extension of its use occurred in the breaking of secondary beams (generally all but the first beam) within a group to clarify the subdivisions of the group, a practice not apparently found in Beethoven but attested at least as early as Liszt (fig.98, from his Fantaisie romantique sur deux mélodies suisses, 1837 edn) and adopted by many later notators, including Reger. This notation was recommended by Lussy since it clarified accentuation within groups, and is now part of standard notational practice (Read, 1964, 2/1969, pp.83–4).

Certain simple standard formulae involving syncopation had been notated since the Middle Ages contrary to the principle that a note or rest symbol should always occur on each beat, the note being tied to the last note of the previous beat if necessary. The chief examples of these exceptions were patterns involving a note value between two of the next shorter note value (e.g. quaver-crotchet-quaver) and dotted notes; and until the 18th century at least, it was possible to write a void note with a bar-line passing through it, or a note in one bar and its dot in the next (the latter device occurs occasionally even in Brahms’s practice). Other unorthodox groupings of notes, uncommon up to the 18th century, were used more frequently from the early 19th; they were condemned in terms of later 19th-century rhythmic theory.

Some 19th-century unorthodox rhythmic groupings of notes were undertaken purely for considerations of simplicity, for example Clementi’s use in Gradus ad Parnassum of a minim (meaning a dotted crotchet tied to a quaver) in 9/8 time (fig.99). Some, however, represent the first examples of beaming across beats and across bar-lines in order to clarify cross-rhythms. This latter practice, whose introduction is often erroneously attributed to early 20th-century composers, is found occasionally in Beethoven’s notation, notably in the Rondo of his Piano Sonata op.10 no.3, 1793 (fig.100), though it is exceptional as early as this. It occurs in Schumann’s notation of his characteristic staggered rhythmic groups as early as his ‘Abegg’ Variations op.1 (1830) and more extensively in later works such as Carnaval (1834–5: fig.101). The practice is important in the notation of 20th-century composers such as Stravinsky, Bartók and Prokofiev. Some 19th-century notators, including Brahms, sometimes used slurs across bar-lines to achieve the same effect. The use of beams over rests, again in the interest of clarifying rhythm, is also attested in the first half of the 19th century though it is often attributed to 20th-century notators.

Further 20th-century developments involving beams included beams broken by notes or rests but visually continuing through them (Debussy, as in fig.102, from Danseuses de Delphes, from Préludes, i, 1910, and later composers), rests connected to beams with stems (Stockhausen, as in fig.103, from Klavierstück IV; any distinctions intended by the various ways of connecting the rests and beams seem obscure), and notes written as single notes (with flags) but joined together with beams (Boulez, Le marteau sans maître, 1953–5 (fig.104) and others; this symbol has been used in conflicting senses). (For the use of beams to group together relatively fast notes of imprecise value, and to indicate duration in other ways, see Risatti, 1975, pp.7ff.)

Since the 16th century, slurs have come to be used for various other purposes; all of these imply joining together two or more notes. For example, slurs in instrumental music might by the 17th century refer to bowing, breathing or tonguing units (see fig.105) and hence, sometimes, phrasing (see Donington, Interpretation, 3/1974, pp.473–4), sometimes denoting that the first note under the slur was to be accented, or, with quavers slurred in pairs in the French Baroque style, that a rhythmic inequality was intended (see Notes inégales). (For further details on early conventions for notating bowing, see Wolf, 1919, 240–41; for further on phrasing slurs, see below.) In keyboard music, from the 18th century at the latest, rapid slurred white-note scales implied a glissando, single or double, as in Bach’s Concerto in C for two harpsichordsbwv1061, and Beethoven’s Piano Sonata in C op.53, last movement; the glissando (here termed ‘sdrucciolato’) and other special effects are illustrated in a didactic ‘Lesson … of Different Touches’ in Pasquali’s Art of Fingering (?1760; fig.106). Vertical slurs beside chords in 18th- and 19th-century keyboard music indicated, like the short angled line through the chord, and wavy lines (at first an alternative form) that have now superseded both, that the chords were to be broken or ‘sprinkled’.

Despite the early use of the slur for phrasing, consistency in the use of the legato slur was apparently not generally achieved until the middle of the 19th century. Slurs imply in a general way that the music is to be performed legato, and the notes at the beginnings and ends of the slurs are usually not intended to be given any special treatment (for Berlioz’s practice, which may not have been peculiar to him, see Temperley, ‘Berlioz and the Slur’, ML, 1, 1969, p.388–92). The desire of notators to represent phrasing more precisely seems likely to have developed from the rhythmic theory of the second half of the 19th century. Lussy deplored the lax practice of earlier notators (Eng. trans., p.44) and proposed that in keyboard notation the slur should represent phrasing by being equated with physical action: ‘All the notes … covered by a slur … should be played … with a single movement of the wrist for the first note, and the other notes must be articulated by the fingers alone, the hand merely gliding to right or left without any further movement of the wrist’. (The practice of placing a dot under the last note of a slurred group at this period, presumably indicating staccato detachment of that note, was deplored by Lussy on the grounds that it misled performers into accenting these notes.) Later writers who distinguished between traditional notation and accurate phrasing notation include Tobias Matthay (The Slur or Couplet of Notes, London, 1928) and Stewart Macpherson, who devoted considerable space to an attack on traditional notation and an exposition of the ‘correct uses of notational signs’ (Studies in Phrasing and Form, rev. 1932, pt.i), requiring editors to adopt consistent phrasing notation rather than reproduce the original ‘with an almost touching fidelity’. Riemann (Musik-Lexikon, 1882) sought still further precision, because of the ambiguity of the slur: he proposed the use of squared slurs or commas in order to avoid confusion with the legato slur, but from 1900 used both squared and conventional slurs for phrasing. For an example of the complexity of Riemann’s phrasing notation as evolved for his special ‘phrasing editions’ of various classical works, see fig.107. The comma was frequently used in 20th-century notation, as in Riemann’s, in order to notate articulation in a melody (see also Rhythm).

Debussy seems to have broken new ground with ties and slurs, particularly in indicating their beginnings and endings separately (La fille aux cheveux de lin), and, later, in notating chords sustained over two or more bars by a series of small ties across the bar-line, without repetition of the chords themselves. He also used ties to indicate, without theoretical accuracy, that notes within a broken chord were to be sustained until, and beyond, the end of a bar (fig.108, from Les fées sont d’exquises danseuses, from Préludes, ii, 1913).

Signs indicating the separation of notes, motifs and phrases rather than their conjunction are found in the early 17th century: Cavalieri used a signum at the ends of lines of text in vocal parts, perhaps, as Schering suggested, indicating breathing marks (fig.109, from Rappresentatione di Anima, et di Corpo, 1600: GMB, p.183; see Signum concordantiae and Fermata). This usage may be seen in chorales of Bach’s time and Bach himself used a fermata on the last note of the phrase of a cantus firmus in chorale preludes, even though the accompanying figuration allows no pause. Staccato signs (dots or vertical dashes) are found in the Baroque period; for the sake of illustration Pasquali (1758; fig.106) distinguished several different degrees of articulation, but distinctions between dots, dashes and other symbols became generally consistent only in the 19th century. Some of these symbols, including dots, seem also to have meant accents; it is not always clear in Chopin’s music, for example, whether bass notes with dots over or under them are to be detached or accented. In the late 19th and the 20th centuries, notably in the music of Reger, Debussy and Schoenberg, an elaborate hierarchy of some dozen different combinations of signs has sometimes been used to cover the range from strong accents to lightly detached notes, and numerals have sometimes been substituted for these (e.g. Read, 1964, chap.15). Many new symbols were introduced in the 20th century to denote related matters such as attack and playing technique on specific instruments.

(v) Clefs, staves, leger lines.

The F and C clefs, positioned so as to avoid leger lines, were supplemented from the 14th century with the G clef and a bass G or gamma clef (fixing bass G), in order to allow further exploration of the treble and bass registers without the necessity for leger lines. From the 15th century standard combinations of clefs became increasingly common in vocal music: three-part songs were often notated with a C clef on the first line for the upper voice and C clefs on the fourth line for tenor and contratenor. Later, standard combinations of three different clefs came to be used in four-part songs. In 16th-century polyphony, after Petrucci’s publications, combinations of four different clefs became more common and the combination of soprano, alto, tenor and bass clefs – that is, C clefs on the first, third and fourth lines and an F clef on the fourth line – first became standard, together with the combinations of transposed clefs, used to avoid leger lines (and obsolete by the 17th century), known as Chiavette.

From the 17th century the G clef was increasingly used, especially in instrumental notation. It occurs on the first line for violins and recorders (Lully): this practice was largely French but also occurred in Germany (Bach used it mainly for the Violino piccolo). But increasingly it came to appear on the second line, as in modern practice, for all instruments of treble range. It occurs in 17th- and 18th-century English vocal and keyboard music, for example, in the upper staves of songs notated as keyboard music (melody line and bass, without a separate staff for the keyboard right hand; for a later example of this usage, see fig.76 above). Purcell used it in vocal ensemble music for the treble line, with C clefs for alto and tenor lines. The form of the G clef found in Vinculum societatis of 1687 (see fig.75 above) occurs throughout the 18th century in English notation.

C clefs were retained in Italian 17th- and 18th-century vocal music, and in German, both scores and parts, for soprano, alto and tenor lines; they still appear in the notation of Wagner, Brahms and Schoenberg and are not wholly obsolete even today. In vocal scores both in Germany and elsewhere, however, modern practice is found as early as the beginning of the 19th century, with G clefs for soprano and alto and a G clef with octave transposition for the tenor (this notation was not however universal at that time, even in England). The C clef on the first line remained normal in German keyboard music until a remarkably late date; Mozart sometimes used it, and although Haydn and Schubert favoured the G clef, the C appears in isolated cases much later (as in fig.110, from an edition of Brahms’s organ music, where the alto clef appears occasionally so that leger lines may be avoided).

Diversity of clefs has seemed increasingly arbitrary since the 17th century, and notational reform, whether formulated theoretically or not, has generally tended to reduce the number of clefs and in consequence to be increasingly tolerant of leger lines. A single clef with octave transpositions was advocated by Juan Caramuel (Ars nova musicae, 1645–6) and Thomas Salmon (Essay to the Advancement of Musick, 1672), but these proposals did not come from the musical profession, and Salmon’s were ridiculed by Matthew Locke (fig.111, from The Present Practice of Musick Vindicated, 1673; see Baldwin and Wilson, 1970). Other unsuccessful proposals for clef reform were made by Montéclair (Principes de musique, 1736) and Lacassagne (‘Réflexions sur l’usage des clefs’ in Traité général des élémens du chant, 1766; L’uni-cléfier musical, 1768). In anticipation of modern practice, Grétry sought to eliminate all but the G and F clefs, transposing where necessary (Mémoires, ou Essais sur la musique, 1789).

In practice, notational reform has tended to abolish the C clefs, substituting G clefs with octave transpositions where necessary (mainly for the tenor voice and some wind instruments) but retaining the F clef, as in keyboard music. In the 20th century several modified forms of the G clef were introduced in order to specify transposition unambiguously where appropriate. Examples are a doubled G clef (used already by Grétry for a similar purpose), a G clef with a vestigial tenor (C) clef added to it, and a G clef with a figure 8 attached underneath. The latter version seems now to have become standard, and the 8 has been analogously added above or below both G and F clefs to signify transposition up or down an octave. (The addition of other figures for transposing instruments has been proposed, e.g. a 5 below the G clef for an english horn.) Traditional C clefs remain standard for music for the viola and trombone, and for the high registers of the cello and bassoon.

Five-line staves, used in the Middle Ages except in Italy for vocal polyphony, were used for keyboard music with C clefs by Attaingnant (1529–30), but did not become standard until the 17th century. In 16th- and 17th-century English keyboard music, pairs of six-line staves (expanded to seven or eight if the range required) remained normal; the six-line staff was not replaced by the five-line one in English keyboard music until around 1700. In The Second Book of the Harpsicord Master, 1700, six-line staves are used; in The Third Book, 1702, the pieces are ‘now plac’d on five lines, it being now the Generall way of Practice’. Modern practice generally adheres to the use of the treble and bass clefs on the upper and lower of a pair of staves; with this standardization, and with the extension during the 19th century of the range of the piano, leger lines have become increasingly common; they appear as early as 1523 in Cavazzoni’s Recerchari, motetti, canzoni. (For examples of 16th-century leger lines, see fig.119, and Leger line.) In practice more than five leger lines are seldom found, notators preferring to transpose very high or very low passages one or two octaves towards the central range and to use abbreviations such as ‘8va’ or ‘8va bassa’, except in orchestral parts. Some keyboard music since the 18th century has, however, occasionally been written on three or more staves (see §(viii) below).

The standardization of clefs since the 19th century, and their consequent predictability, has allowed notators unusual licence. Some 20th-century notation, for example, includes the simultaneous use of treble and bass clefs on a single five-line staff for notating widely-spaced strands of the texture, when there is no possibility of misunderstanding (see fig.112, from Debussy’s Voiles, from Préludes, i, 1910). Simple horizontal wedge-shapes represent the treble clef when next to the second line and the bass when next to the fourth (for further details of these and other notational licence, see Read, 1964, 2/1969, pp.59ff).

A number of notational reforms proposed since the 19th century have concerned the staff. Of these the most radical is the Klavarskribo system (fig.79), in which the staves run vertically rather than horizontally in order that the appearance of the music may more closely resemble the layout of the piano keyboard, on which the system is based; accordingly, bar-lines are horizontal. Another staff reform based on the keyboard is that of W. Steffens (1961). Other reforms have often necessitated a change in the number of lines in the staff; Equitone (fig.79) uses two lines to the octave, with notes in five possible positions relative to them: with the lines running through the notes, or tangential to them, or with the notes (touching neither of the lines) closer to one or other of the lines, or midway between them. The use of full and void notes in these positions yields 12 different possibilities to the octave, for the 12 semitones of the equal-tempered system. The Notagraph system (fig.113b) of Constance Virtue uses a seven-line staff, with the space between staves divided proportionately to permit further representation of intervals for the most part without leger lines; the staff covers an octave, the step from a line to the adjacent space representing a semitone, and different octaves are distinguished with special clefs (V, O and inverted V, variously placed).

For the use of curved staves and other devices for representing tempo fluctuations, see §(iii) above.

See also Clef and Staff.

(vi) Accidentals, key signatures.

The sharp and flat signs, inherited from medieval notation, were supplemented from the late 15th century by the natural sign; this had at an earlier period been an alternative form of b quadratum and like the sharp and flat was derived from a version of the letter ‘b’. In medieval notation, as still during and perhaps after the 16th century (particularly in vocal music), these signs signified that the notes to which they applied were to be solmized using the syllable fa (for the flat) or mi (for the sharp). Some of these accidentals are ‘cautionary signs’, warnings that a rule of musica ficta was for the occasion to be suspended. When a distinction was drawn between sharp and natural and three signs were used, however, there may have been a change in the significance of the accidental: it then came to signify the raising or lowering of pitch (see Musica ficta, §2(iv)). The use of all three signs did not become general until the 18th century. Any lowering of pitch was generally indicated by a flat and any raising by a sharp; the notator’s intention was usually clear (at least to contemporaries) until remote chromatic chords became part of the normal musical language and until ‘orthography’ in accidentals became a concern (see below). The older notation lacking the natural may be found until the end of the Baroque period and, in isolated cases (e.g. fig.114, dating from c1841) even later; it survives strongly in a modified form (the sharp and flat being replaced by ‘+’ and ‘−’ signs respectively) in 20th-century jazz and popular music notation (see §(viii) below).

For a similar reason, and because bar-lines were not used in the modern way until a late date, absolute consistency in the notation of accidentals – with a rule that accidentals are required only as shown, and that they hold good until the end of the bar – is not generally found before the 18th century or even the 19th. An accidental before the late 18th century generally applies only to the note next to which it is written or to notes in its immediate vicinity (see Donington, Interpretation, 3/1974, pp.131ff). Even as late as the early 19th century, for example in keyboard music printed in London, accidentals may be provided for only one note of an octave, with the performer expected to supply the second. Here as in other aspects of the notation simplicity was thought more desirable than precision.

Initial flat signatures (indicating transposition down a 5th once with one flat and twice with two) had been usual in the Middle Ages; signatures with sharps appeared (apart from isolated examples as early as the Middle Ages) in the 17th century, and like flat signatures at this date are to be regarded as key signatures in the strict sense. Nevertheless, Baroque composers often wrote the accidentals of key signatures in more than one octave, contrary to modern practice: this may represent an archaism (medieval signatures may be presumed to refer only to notes at the pitch specified, with octave transpositions remaining unaffected in the absence of any indication to the contrary). Baroque key signatures often contain one flat or (more rarely) sharp fewer than would be included in modern practice, particularly in minor keys, perhaps (as Donington suggested) because G minor, for example, was thought of as the Dorian mode in which the E was theoretically natural, or perhaps because a piece in G minor might have E naturals at least as often as E flats.

The double sharp and double flat, like sharp key signatures, were mainly products of the tonal system in the 17th century. Donington provides tables showing different forms used for writing the natural, sharp, flat, double sharp and double flat in the 17th and 18th centuries (3/1974, p.127). Since that time, there has never been total consistency about the method of cancelling double accidentals: a natural alone, a sharp or flat alone, or (most commonly) a natural with a sharp or flat have all been used.

From the Middle Ages various signs were invented for representing intervals supposed to be those of the enharmonic and chromatic genera of the ancient Greeks. Besides those of Marchetto da Padova, the use by Nicola Vicentino (L’antica musica ridotta alla moderna prattica, 1555) of dots over notes to raise them by a diesis (see Diesis (ii)) and the special signs (see fig.115) of Lusitano (Introdutione facilissima, 1553, 2/1558) may be mentioned. Microtonal intervals have also been represented with special signs (see below).

Until the 19th century accidentals were often notated without theoretical accuracy, for the sake of convenience: for example, in the Buxheimer Orgelbuch, where E is notated as the form for Dis (D), A analogously as G etc., regardless of the incongruity of the notation from a theoretical point of view. Similar considerations, no doubt, led some 17th- and 18th-century notators to write enharmonic equivalents of double sharps or double flats (e.g. G for F double sharp), and sharps for ascending chromatic semitones and flats for descending, as a rule of thumb not based on theoretical considerations. With the appearance in the 19th century of theories of harmony supposedly based scientifically on acoustical laws, ‘orthography’ – the notation of accidentals according to harmonic grammar – seemed important enough to some to outweigh considerations of practical convenience. According to Lussy, for example, ‘every chromatic note, or note foreign to the key or mode in which a melody is constructed, is accented’ in certain circumstances (Eng. trans., p.142), and thus the presence of an accidental has rhythmic and accentual implications. Accordingly, the traditional lax notation was misleading for expressive purposes; Lussy (p.151) criticized Beethoven’s notation in op.26 (fig.116), submitting that B should be substituted for C in the first chord of the example. (For a more detailed investigation of Beethoven’s ‘unorthographic’ notation in his piano sonatas and string quartets, see Van der Linde, ‘Die unorthographische Notation in Beethovens Klaviersonaten und Streichquartetten’, Beethoven-Studien: Festgabe, ed. E. Schenk, Vienna, 1970, pp.271–325.)

For a similar reason Lussy called for ‘correctness’ of notation in key signatures, since an incorrect key signature would misrepresent the accentuation:

In the overture to ‘Zampa’, which starts in D with two sharps, the Prayer is introduced in the key of B. The composer, by retaining the signature of D for these sixteen bars, is forced to use about a hundred flats and naturals … In such cases as this the chords preceded by accidentals do not require forcing.

Despite the general avoidance since the late 19th century of gross incongruity in the notation of accidentals, ‘convenience’ notation of accidentals, primarily according to the manner of playing the notes, is still required in special notations (such as that of harp music, because the instrument, with a natural scale in C, is easier to play in flat keys: in fig.117 the harp and piano parts largely correspond, but the notation of accidentals is different).

Since the late 19th century notational practice with accidentals has changed chiefly in music where conventional major-minor tonality has been weakened or jettisoned. The simultaneous use of different key signatures is occasionally found, as in Bartók’s Mikrokosmos or Britten’s Peter Grimes. Sharps and flats in signatures may be placed at unconventional pitches, indicating a return to the medieval conception of the signature affecting only one pitch, not octave transpositions (for example in Mikrokosmos). In works not in the major-minor or any other diatonic system, where key signatures have naturally been abandoned, it has often been found convenient to return to the convention that an accidental applies only to the note to which it is joined; this renders the natural sign redundant, as is stipulated in Busoni’s Sonatina seconda, 1912: ‘die Versetzungszeichen gelten nur für die Note, vor der sie stehen, sodass Auflösungszeichen nicht zur Anwendung kommen’. In some music of the 1960s and 70s, every note is preceded by a sharp, flat or natural sign.

Microtonal intervals have been the subject of speculation in European music for centuries (see Microtone). For much of the 20th century, composers concentrated on divisions of the equal-tempered semitone, with such intervals as the quarter-tone and the sixth-tone being notated by various altered forms of the sharp and flat signs (see Read, 1964, 2/1969, p.145, and Risatti, 1975, pp.16–17). Fig.118, an example from Hába, one of the earliest 20th-century experimenters, illustrates one such system. With later work on divisions of the octave in which the notes do not always coincide with the 12-note scale (the 20- and 31-note scales, which fall into this category, are both in use, as are many others), this type of notation is not always convenient. Some composers have used up- and down-arrows and/or ‘+’ and ‘−’ in conjunction with signs based on the sharp and flat; such symbols are also found in transcriptions by ethnomusicologists. An alternative is to use a numerical system, in which fractions or cent values make obvious series within the octave; and some composers have used a mixture of numerical and symbolic signs, the latter still based on the sharp and flat (see Darreg, 1975, and 1979; Blackwood, 1991).

Notation of accidentals with signs other than the traditional medieval ones still in normal use is occasionally encountered in keyboard mensural notation, or the mensurally notated sections of Old German organ tablature. In the Buxheimer Orgelbuch, for example, downward stems from notes are to be understood as accidentals rather than indications that notes are lengthened. In some early 16th-century keyboard sources, dots above or below notes are also used for this purpose: examples are Cavazzoni, Recerchari, motetti, canzoni (1523), the volumes of keyboard music printed by Attaingnant, and the anonymous Intabolatura nova di varie sorte de balli da sonare (1551; fig.119; this volume uses both this notation and conventional accidentals).

See alsoAccidental

(vii) Dynamics.

Indications of dynamics are rare before 1600. The rubric ‘tocca pian piano’ occurs in Vincenzo Capirola’s lutebook (c1517; fig.120), but seems to be an isolated example until the polychoral and echo effects of the late 16th and early 17th centuries suggested the exploitation of dynamics; specific indications occur in the Sonata pian e forte (1597) by Giovanni Gabrieli and other works of the period. Mazzocchi (Madrigali, 1638) used abbreviations for forte, piano and so on and for crescendo and diminuendo effects; otherwise diminuendo effects in the 17th and early 18th centuries are generally indicated by a series of dynamic markings (e.g. ‘lowd–soft–softer’ in Matthew Locke’s music for The Tempest, 1674; and ‘forte–piano–pianissimo’ in the pastorale from Corelli’s Christmas Concerto op.6 no.8, posthumously published in 1714). Later in the 18th century these were supplemented with the modern ‘hairpin’ symbols for crescendos and diminuendos (Geminiani, Prime sonate, 1739, a revision of his op.1, 1716). These ‘hairpins’ are in early 19th-century music often combined into a characteristic lozenge shape (fig.121), indicating a crescendo immediately followed by a diminuendo, but this sign is invariably divided into two separate signs in modern editions. (It should also be noted that it is frequently difficult to distinguish between diminuendo signs and wedge-shaped accents in the notation of such composers as Berlioz and Schubert.)

In 19th-century practice the superlatives of loudness and softness (fff, ppp) were extended, with composers prescribing down to pppppp and up to ffff (Verdi, Tchaikovsky), and a scale of 12 or more imprecise degrees of loudness was constructed. These degrees were specified with great care in some early 20th-century works, where almost every note has its own dynamic marking; in some later 20th-century practice, dynamic markings were graded numerically for greater precision. Other 20th-century devices to make dynamic indications more precise or to give them greater visual impact include the use of progressively fuller note heads on a scale where a void note is inaudible and a full note fff (Schäffer), the use of signs (unfortunately resembling accents) to represent various increases in loudness (Stockhausen, Klavierstück XI), and the relative size of note heads (see Risatti, 1975, pp.29ff); the last device was proposed in 1903 by Abdy Williams (p.212).

See also Tempo and expression marks.

(viii) Scores; harmonic and descriptive notations.

Although score notation had been abandoned in polyphony with the adoption of Franconian notation in the 13th century, it lingered in certain peripheral areas of medieval notation until the 15th and 16th centuries (see §3 above). Instrumental notation may be considered a particular case of score notation, in both its tablature form and its purely mensural score form, such as the Faenza Codex (see Sources of keyboard music to 1660, §2(i)). Instrumental notation of the late Middle Ages, like later scores, frequently includes the visual separation of ‘bars’ or other metric units by bar-lines or spaces.

Early 16th-century score notation, apart from that in tablatures, some keyboard music (e.g. Cavazzoni, Attaingnant) and surviving medieval repertories in Bohemia, is mostly didactic and intended for inexperienced musicians, as in Agricola’s Musica instrumentalis deudsch (1529), which illustrates how to put music into tablature. From this period to the second half of the 18th century at least, there is evidence of the use of the tabula compositoria, a device with staff-lines and vertical bar-lines, on which polyphony could be written in score to facilitate copying or composition and then erased to permit re-use. Bermudo (1555) claimed that organists played, according to their ability, in descending order of competence, from choirbooks, tablatures and scores.

The first complete surviving scores proper are the Musica de diversi autori … partite in caselle (2/1577¹¹) and Tutti i madrigali di Cipriano di Rore a 4 voci (1577); printed scores are attested not much later outside Italy (M. Gomołka, Melodie na psalterz polski uczynione, Kraków, 1580, in score without bar-lines, fig.122; Balet comique de la Royne, Paris, 1582). Some of these were intended for keyboard and other instrumental performance, and were compiled after the parts had been completed. The same is true of less comprehensive organ parts, supporting the lowest-sounding voice throughout vocal and instrumental pieces, which are attested from 1587, in a 40-part motet by Alessandro Striggio (i). Such an organ part was often termed a Partitura (or spartitura), another respect in which it resembles a score.

In the early 17th century Thoroughbass notation developed from these organ parts and it too was early associated with the score. It became almost universal in every type of polyphony except that for solo instruments in the 17th and early 18th centuries, whether in score or parts, after which time it declined in secular polyphony. In essence it represents an abbreviated notation for chords, associated with a single bass line in ordinary mensural notation. The symbols used, as with those of musica ficta, are often warnings against adopting a particular course of action. The abbreviations are in the form of numerals representing the intervals to be played above the bass line, often supplemented with accidentals. Such accidentals are occasionally found in a partitura comprising the outer voices, as in Banchieri’s Concerti ecclesiastici (1595) where, as in later practice, they distinguish major and minor chords; numerals as well as accidentals appeared around 1600 in the thoroughbasses of the earliest operas, which were printed in score (Peri, Caccini: see fig.70). Unlike later thoroughbass notation, the early operas often contain numerals in excess of 9, and they thus specify the octave for the elaboration of the bass (in Caccini the numerals extend to 15 and in Cavalieri even beyond that; see fig.109). Not all early thoroughbass sources include numerals and accidentals, partly because of the difficulties of setting them in type.

The placing of the accidentals in early thoroughbass notation is not always consistent; they may appear in almost any position fairly near to the numerals they qualify. As in the ordinary staff notation of the period, sharps and flats refer respectively to any raising or lowering of a note. A stroke through the numeral 6 instead of a sharp next to it, signifying that it is to be raised a semitone, was introduced by Scheidt (1622) but not generally adopted until the second half of the 17th century (e.g. by Rosenmüller, 1652), when it was supplemented by a 6 with a flat sign through it as a direction to lower the 6th by a semitone. This practice was extended to other numerals (4, 5 etc.) in some of Roger’s editions of Corelli, and became general in Italian and Italian-derived practice of the 18th century (fig.123). In the second half of the 18th century a diagonal stroke was introduced (Kirnberger, 1781, p.74, referring to Graun’s practice; this sign is also cited by C.P.E. Bach, together with alternatives, Versuch, ii, 1762, Eng. trans., 1949, p.196) to be placed under appoggiaturas in the bass to signify that the following bass note was to be harmonized in advance; but this practice is not often attested. For tasto solo (i.e. a direction to leave the bass line unharmonized), practice varied in 18th-century thoroughbass notation: some notators used a verbal direction, some staccato dashes (perhaps equivalent to the figure 1), some the figure 0 and so on.

Thoroughbass was popularized in Germany especially through the diffusion of Viadana’s Centum concerti ecclesiastici (first published 1602); in England the practice appeared in publications from the 1630s and in France from the 1650s. French thoroughbass used horizontal lines at an early date to indicate the retention of previous harmony, a device used internationally in the 18th century. By the end of the 17th century French thoroughbass notation had developed a good number of distinctive and inconsistent traits, such as inconsistent notation of sharps or the use of strokes through numerals to signify, variously, both diminished and augmented intervals. Many of these traits were tabulated by Rameau (Dissertation sur les différentes méthodes d’accompagnement pour le clavecin, ou pour l’orgue, 1732). Some French notational characteristics are occasionally found in German figured basses from about 1750.

While thoroughbass was still mainly a practical, rather than a didactic or theoretical, device, occasional abortive attempts were made to reform its notation. Rameau (1732) proposed a system based on his harmonic theories (see Wolf, ii, 327) but later dropped it; Telemann (preface to Musicalisches Lob Gottes, 1744) proposed a system of numerals supplemented with horizontal, diagonal and curved strokes, in order to achieve a ‘happy mean’ between basses with too few figures and those ‘resembling an arithmetic book’.

During the 17th century, score notation was used in other areas of the polyphonic repertory, such as solo songs and cantatas. Some of these scores were intended to facilitate conducting, though until the 19th century (and in some areas later) conducting scores might contain little more than a first violin part, or a figured bass supplemented with cues, recitatives in full and so on; the latter type, when intended for a conductor, might be labelled ‘M[aestro] D[i] C[appella]’. The keyboard score also spread beyond Italy in the 17th century (M. Rodrigues Coelho, Flores de musica, 1620; Scheidt, Tabulatura nova, 1624). In 17th-century scores, bar-lines became usual, though not always consistent, at a relatively early date. In early scores they extend only through a single staff; they were extended throughout each system by Bach and others in the 18th century, but the practice was not standardized until the 19th. Similarly, the order in which the parts are set out varies until well into the 19th century (see Score). For clef reform in score notation, see §(v) above.

Keyboard score notation developed characteristics of its own, some deriving from tablature, from the 17th century onwards. As early as the 17th century some notators avoided pedantic accuracy in the notation of polyphonic textures, omitting rests and simplifying note lengths especially in inner parts, but Bach sometimes maintained the older practice of using precise note lengths even within a complex polyphonic texture. A thorough-going adoption of the simpler practice is found in Liszt’s notation, with the abandonment of rests or precise note values where these were unnecessary to the performer. Other devices used by Liszt to clarify complex textures include the broken subsidiary beaming of short note values (see §(iv) above), and the use of the direction of note stems to distinguish strands of the texture or the notes to be played by the right or left hands (see fig.124, from his Rhapsodie espagnole). Other composers used comparable devices such as the extensive use of small notes (see §(ii) above).

The use of more than two staves in keyboard scores other than partituras, again in the interests of clarity in complex textures, is occasional before the 19th century, usually to distinguish lines for separate manuals, separate instruments or (for the organ) pedals. One of the earliest examples of modern keyboard notation in which three staves are intended to be played by a single performer on a single manual of a keyboard instrument is found in G.J. Vogler’s ‘Marlborough’ variations (fig.125: the clef forms are typical of Austrian and south German usage at this period). This practice too was adopted and extended by Liszt, with piano music written on three or four staves, and appears in the piano notation of Debussy and Rachmaninoff.

The specialization of keyboard score notation is reflected also in the adoption of fingering indications, found regularly from the 19th century but quite often before that, especially in tablatures; it is also occasionally found from the 16th century in other instrumental music. 19th-century piano music had two distinct fingering conventions: the ‘continental’, with numerals from 1 to 5 for the thumb and fingers; and the ‘English’, with a ‘+’ sign for the thumb and numerals from 1 to 4 for the fingers. The latter system, now superseded by the former, was still used well into the 20th century. Pedalling has been shown in piano music since the early 19th century by a number of special signs. Comparable instructions for physical actions, to produce special effects of many kinds, have multiplied since the 19th century in instrumental music: these include signs for playing harmonics and for special methods of attack in string and harp music, bowing in string music and percussive key-clicks in woodwind music (see Karkoschka, Schriftbild, 1966; Read, 1964, 2/1969; and Risatti, 1975).

Specialist notations of other kinds have been used in scores to assist the abstract study of music. Descriptive notation for analytical purposes had been part of the European tradition since the Renaissance but had not required material modifications to normal notation: thus Kircher presented a (spurious) ‘Pindaric’ melody in normal notation (fig.126, from Musurgia universalis, 1650) and Hebrew melodies, in which he had been preceded by Johannes Reuchlin (De accentibus et orthographia linguae hebraicae, 1518) among others. The great increase from the second half of the 18th century in historical and analytical musicology, and the broadening interests of scholars, prompted notational modifications. Early examples of specialized descriptive notations and formats include the miniature score (an early example is a 19th-century edition of Haydn quartets by Pleyel). Both performing and study scores came to be provided with bar numbers or letters for easy reference, though the numbering of bars, every 50, is found as early as 1688 (William Nott, A Collection of Simphonies).

Specialist score notations for presenting the results of analysis were also developed from the early years of the 19th century (e.g. Momigny, 1803–6). In the 20th century, analytical notation was developed into systems of great subtlety, for example by Schenker (see Analysis, §II, 4). Non-Western music was presented for European readers in a kind of score comprising the original notation in parallel with a transcription by F.J. Sulzer (fig.127, from Geschichte des transalpinen Daciens, 1781–3); this represents one of the earliest ethnomusicological notations. The preparation in the 19th and 20th centuries of the great historical editions of early music (see Editions, historical) has made standard many novel practices, such as the use of a squared slur to link notes joined in ligatures in the original, or the use of small notes or parentheses to distinguish editorial additions. Ethnomusicological notation has adopted many novel signs to express, for example, intervals outside the European system. For attempts to devise machines to notate melodies, and the notations adapted to them, see §6(i) below.

In the 19th century thoroughbass notation lent itself to adaptation for analytical and other didactic purposes: by this time it was no longer extensively used in practical music-making. The modifications made to it in the 19th century tended mainly to improve it as a theoretical harmonic notation; Honoré Langlé, for instance, proposed a system of nomenclature that would be primarily chordal rather than intervallic; major, minor, diminished and augmented chords, and the various 7th chords, were consistently distinguished, and the relationships between inversions and root positions were shown, with a modified thoroughbass notation including symbols such as ‘+’, ‘−’, ‘=’, circumflexes, inverted circumflexes and dots (Nouvelle méthode pour chiffrer les accords, 1801). The figured bass survived in its older traditional form well into the 20th century, however, both as a shorthand harmonic notation and (as in Prout, Harmony: its Theory and Practice, 1889 and later editions) as a device for teaching harmony by the advance identification of chords in harmony exercises (see fig.128, from an Oxford DMus examination paper of the early 20th century).

Other types of chordal notation, using letters or numerals for the chords and supplementary symbols to distinguish different types of chord, developed from the early 19th century. The degrees of the scale and the chords based on them were denoted by Roman numerals as early as 1800 (G.J. Vogler, Choral-System); H.C. Koch (Musikalisches Lexikon, 1802, ‘Klangstufe’) wrote of indicating ‘each note of those of a key, arranged in a scale, by means of a number associated with it’. In Versuch einer geordneten Theorie der Tonsetzkunst (1817, 3/1830–32), Gottfried Weber distinguished major and minor chords and keys by the use of upper- and lower-case letters (i.e. as in modern German practice) with superscript numerals to denote diminished chords, 7ths and so on. His proposals were widely adopted and extended (e.g. with the symbol ‘+’ to distinguish an augmented triad, and with distinctions drawn between the inversions of chords, by E.F.E. Richter, Lehrbuch der Harmonie, 1853, and Otto Tiersch, Kurze praktische Generalbass-, Harmonie- und Modulationslehre, 1876). In accordance with Moritz Hauptmann’s view of minor chords as inversions of major chords (see Harmony, §4), Arthur von Oettingen used letters of the alphabet with a superscript ‘+’ sign for major chords and a superscript zero for minor chords; in minor chords the ‘root’ is reckoned as the top note of the triad (e.g. G in a C minor triad) (Harmoniesystem in dualer Entwickelung, 1866). Hauptmann and Oettingen also distinguished between notes (for acoustical reasons, depending on the way they were theoretically generated) by using upper- and lower-case letters.

Later in the century Hugo Riemann invented a system of chordal notation which he termed ‘Klangschlüssel’ (Skizze einer neuen Methode der Harmonielehre, 1880; Musik-Lexikon, 1882, ‘Klangschlüssel’). Intervals were shown by numerals, those of major chords by Arabic ones, as in thoroughbass but always reckoned from the root of the chord upwards, and those of minor chords by Roman, reckoned from the root (in Hauptmann’s and Oettingen’s sense) downwards. The roots of the chords were identified alphabetically. Intervals shown by simple numerals were perfect or major, except for the minor 7th; major and minor triads were distinguished, when necessary, with Oettingen’s symbols. Horizontal strokes above and below the numerals denoted that the note in question was in the bass or in an upper part; the notation, unlike thoroughbass, was in principle independent of a mensurally notated bass line. The sharpening or flattening of notes was shown by wedge shapes, resembling accents in ordinary mensural notation, either in normal form or reversed. In later works Riemann went on to develop a system of ‘functional notation’ or ‘Funktionsbezeichnung’ (Vereinfachte Harmonielehre, 1893), where he abandoned letters representing pitches in favour of the letters T, D and S, representing tonic, dominant and subdominant functions, qualified as Tp, Dp or Sp as necessary, the p (Parallelklang) indicating that the 5th above or below the root of the chord had been replaced by a 6th.

Similar systems have been the stock-in-trade of most harmony textbooks since the late 19th century; some of the more influential ones were those of Sechter, Grabner, Prout, Macpherson and Schoenberg. Possibly through their influence some popular music of the 20th century also adopted chordal notations for guitar, keyboard and other ‘continuo’ instruments, which generally resemble Gottfried Weber’s system. This notation has yet to be studied historically. Chords are commonly identified by a letter for the root, qualified with ‘mi’ for a minor chord or a superscript zero or ‘+’ sign for a diminished or augmented chord; the letter alone represents a major chord. Superscript numerals and accidentals are used as in thoroughbass notation (i.e. the numerals are reckoned as diatonic intervals from the note named, and qualified by accidentals) and, also as in thoroughbass notation, the rhythmic realization is left to the performer to supply from his knowledge of the appropriate style. Common alternatives for accidentals are ‘+’ and ‘−’ signs, used in the same way as sharp and flat signs in the 17th century – to signify any raising or lowering. A tabulation of various types of sign, made in an attempt to introduce uniformity of practice among professional copyists, may be found in Roemer (1973, p.137; see also Read, 1964, 2/1969, pp.410–11, and Brandt and Roemer, 1975). For an example of simple chordal notation of this type, see fig.129. For the notation of pitch (including distinctions between different octave repetitions of the same pitch) seePitch nomenclature.

For bibliography see end of §6.

(ii) Tablatures for plucked string instruments.

5. Alphabetical, numerical and solmization notations.

The most important type of notation to be considered here is Tablature, which is fully discussed in its practical aspects under its own heading. For more detailed information the reader is referred to Wolf’s Handbuch der Notationskunde (1913–19), Apel’s Notation of Polyphonic Music, 900–1600 (1942, rev. 5/1961) and Rastall's Notation of Western Music (1983 rev. 2/1998).

(i) Keyboard tablatures.

(iii) Tablatures for other instruments.

(iv) Vocal notations.

Notation, §III, 5: Alphabetical, numerical and solmization notations

(i) Keyboard tablatures.

Wolf suggested that a passage in the treatise of Anonymus 4 (c1275) implies the existence of instrumental notation in the 13th century (Wolf, 1919, 5, referring to the passage in Reckow’s edition, Der Musiktraktat des Anonymus 4, 1967, i, 40, ll.24ff). No known example survives from that date, but the earliest known keyboard sources are nearly all in tablature, which is a distinctive instrumental notation. The term ‘tablature’ generally signifies a notational system using letters of the alphabet or other symbols not found in ordinary staff notation, and which generally specifies the physical action required to produce the music from a specific instrument, rather than an abstract representation of the music itself. The latter qualification, though perhaps the primary one, does not apply to the German organ tablatures of the late Middle Ages and later: in these, letters are used to identify pitches rather than finger positions.

Most surviving keyboard sources up to the early 16th century are notated in the so-called old German organ tablature. This term is used even though the earliest source of all, the 14th-century Robertsbridge Codex (GB-Lbl Add.28550), is of unknown origin and has features of 14th-century Italian mensural notation (see Tablature, fig.1). 15th-century German tablatures include those of Adam Ileborgh (1448, in a private collection; Tablature, fig.2) and Conrad Paumann (1452, Fürstliche Stolberg’sche Bibliothek, Wernigerode, Zb 14), and the Buxheimer Orgelbuch (D-Mbs Cim.352b; fig.130). Virdung’s Musica getutscht (1511) and Schlick’s Tabulaturen etlicher lobgesang und lidlein (1512) are the earliest known printed keyboard music and there are several early 16th-century manuscript tablatures from the regions of Switzerland and Germany near the Rhine (e.g. fig.131) and from Poland (the tablature of Jan z Lublina): for further details see Sources of keyboard music to 1660. Each of these early sources generally displays notational idiosyncrasies, but in all of them the top voice is notated in a void or full mensural staff notation and the other voices in alphabetical notation, the letters corresponding with the names of the notes. In both parts of the notation accidentals are specified; in the mensurally notated voice, this may be with unusual signs such as downward stems with slashes. As in most later tablatures special rhythm signs above the letters specify the durations of the notes; they were sometimes joined with beams, as in the 15th-century Buxheimer Orgelbuch.

The number and variety of keyboard sources increase rapidly for the period after 1500. In Italy and France there are printed keyboard sources, using mensural notation throughout, as in the earlier Faenza Codex (see Sources of keyboard music to 1660, fig.1). Examples are Cavazzoni’s Recerchari, motetti, canzoni (1523) and the series of keyboard collections published in France by Attaingnant from the 1530s (fig.132). This keyboard mensural notation is closer in a number of respects to 19th- and 20th-century mensural notation than to contemporary vocal notation, for example in the use of bar-lines, but complex score notation was not very well suited to movable-type printing and came into its own only after the introduction of music engraving. Nevertheless score notation remained normal in French and Italian keyboard music, as it was later in English keyboard sources (see Sources of keyboard music to 1660, §2(vi)); it was cultivated either in the modern two-staff form or as the partitura (see §4(viii) above).

From about 1570 the old German organ tablature was superseded in German-speaking areas by a new German organ tablature, in which letters were used as in the earlier system but now for the highest voice as well as the others (fig.133). This alphabetical notation was supplemented by a uniform system of rhythm signs, derived from those of Italian lute notation. The change may have been due in part to the difficulty and cost of printing the mensurally notated top voice. This system became widely diffused in northern Germany in the 17th century and survived into the 18th, latterly mostly in manuscripts written by organists, including J.S. Bach, for their own use (see Bach, §III, 7 and fig.7). It was used by Buxtehude for vocal and single-line instrumental as well as keyboard music (for illustration, see Buxtehude, Dieterich, and Winternitz, 1955, ii, pl.7). A curious mixture of this system, used only for the pedal line, with ordinary mensural notation occurs in the Tabulatuur-boeck van psalmen en fantasyen of Anthoni van Noordt (1659; facs. in Wolf, ii, 263); fig.134 shows another curious and in several respects anomalous alphabetical (?) keyboard notation from early 17th-century France.

The only other major keyboard tradition to use tablature was that of Spain. In Bermudo’s Declaración de instrumentos musicales (1555) various systems are mentioned, using numerals to represent the keys of the keyboard. The latter may be numbered consecutively throughout, or the white keys may be numbered consecutively and the others provided by supplementary accidentals; or the white keys within each octave may be numbered from 1 to 7, with accidentals and octaves distinguished by diacritical marks. Rhythm signs are placed above the music, defining the durations in the fastest-moving part (see Tablature, fig.3). Such systems are also found in Italy, in the Spanish-influenced Intavolatura de cimbalo of Antonio Valente (1576), and they persisted into the 17th century. There is also slight evidence of the use of comparable tablatures with letters or numerals for psaltery music.

Notation, §III, 5: Alphabetical, numerical and solmization notations

(ii) Tablatures for plucked string instruments.

Petrucci’s early 16th-century publications include four books in so-called Italian lute tablature (1507–8), of which the second gives rules for playing from the tablature, evidently for the benefit of performers without knowledge of musical theory or notation. The printing of Italian tablatures continued until 1616; manuscript Italian lute tablatures are attested until the mid-17th century. The principles on which Petrucci’s tablatures rest remained fundamental to Italian lute tablature: six lines of a ‘staff’ represent the six courses of the lute, with the course lowest in pitch at the top. Numerals placed on the lines then indicate the fret to be stopped on the relevant course, zero being used for open strings, and rhythm signs placed above the ‘staff’ indicate the durations of the shortest notes within the texture at any point (see Tablature, fig.5). These rhythm signs no doubt derive from mensural note shapes but lack the note heads; they were joined with beams as early as the first half of the 16th century. The rhythm signs appear in Petrucci’s prints above each note or chord, but even in the early 16th century the notation is sometimes simplified by omitting rhythm signs unless there is a change in note value. The system of rhythm signs normally precludes the specification of simultaneous notes of different durations, but some tablatures employ a cross or sharp-like symbol after numerals to indicate that the note in question is to be prolonged beyond the next note or chord (e.g. fig.135, from Antonio Rotta, Intabolatura de lauto, 1546); this device also occurs in German tablature (e.g. Judenkünig, 1523). Normally these Italian tablatures are accommodated on a single ‘staff’; a vocal part, if included, is usually but not invariably notated mensurally on a separate staff. Spinacino occasionally placed even the upper voice of a lute piece on a separate staff for the sake of convenience. (For another example of Italian lute tablature, see fig.120).

A similar tablature notation was used in Spain for the vihuela. In the earliest surviving example, Luis de Milán’s El maestro (1536; see Tablature, fig.6), and according to Bermudo in other 16th-century Spanish vihuela music the sequence of courses is reversed, so that the highest-sounding course is represented by the top line. Normally, however, Spanish practice and Italian correspond in this respect. Milán and others used complete note shapes for rhythm signs, in a manner otherwise similar to Italian practice; vocal lines are occasionally included in the tablature staff and distinguished from the instrumental accompaniment by being notated in red (fig.136), or (Esteban Daza, 1576, the latest known source) with dots above the numerals for alignment.

The series of printed French lute tablatures, like the Italian, has as one of its earliest examples a publication giving instructions for beginners in playing from tablature: Attaingnant’s Très briefve et familière introduction (1529: see Sources of lute music, fig.3), published only a few months after his Dixhuit basses dances, is the earliest surviving source. The ‘three short rules’ of the Introduction establish the principles found in later French tablatures. The chief differences from Italian lute tablature lie in the use of five rather than six lines in the staff, even though there are already six courses, the sixth being given a ‘leger line’ when necessary; the arrangement of the lines with the highest-sounding course represented by the top rather than the bottom line; and the use of an alphabetical sequence of letters, rather than numerals, for the frets, with ‘a’ for open strings. Rhythm signs generally correspond with those of Italian lute tablature; fingering is indicated by dots (see fig.137), later by numerals. Other later developments in French lute tablature include the adoption of a six-line staff; this is used in isolation in an Attaingnant publication of 1530, but not generally adopted until after the publication of the Pratum musicum of Emanuel Adriaenssen in 1584, and then used almost without exception. Various expedients were adopted to notate up to two extra bass courses before the end of the century, and further bass courses introduced during the 17th century and played as open strings (see Tablature, fig.7; Sources of lute music, fig.8). For details of other subsidiary signs in 17th-century French lute tablatures see Lute, §6.

French lute tablature declined in popularity in France from the early 18th century but had spread to England, the Netherlands, Germany and elsewhere, and it persisted especially in Germany, where French tablatures continued to be printed until 1771 and to be produced in manuscript until the 1790s. Music for other string instruments such as cittern, bandora, mandore, mandolin, colascione and angélique, was notated in tablatures of this kind, though sometimes with fewer lines if the instrument had fewer courses than the lute.

Before the introduction of French lute tablature to Germany, lutenists there had used a German tablature, said by Agricola to have been invented by the blind 15th-century organist Conrad Paumann. The first surviving printed sources of this tablature are in Virdung’s Musica getutscht (1511; see Tablature, fig.4) and Schlick’s Tabulaturen (1512), and German tablature persisted for about a century, when it was finally superseded by the French tablature, which had first appeared in German prints during the 1590s. German lute tablature is based on a five-course lute, but early sources are for six-course instruments: the frets of the top five strings are designated by letters of the alphabet, supplemented with a few other symbols, reading across the first frets of all five courses, then across the second frets and so on rather than by a series of symbols repeated for each course. Thus each fret on the instrument has a unique symbol; the necessity for a staff in the French or Italian manner is eliminated, at the cost of increased complexity in the notation. The lowest course, presumably added after the establishment of the notation, is assigned a series of letters independent of the rest of the notation. Open strings are shown by numerals for each course (fig.138; see Sources of lute music, fig.2).

Guitar music from around 1550 is notated in either Italian or French lute tablature; as in tablatures for other instruments, the number of staff-lines varies according to the number of courses. 17th-century guitar tablatures developed features of their own, no doubt because the constant repetition of chords prompted an abbreviated notation. Of the two principal methods the Italian, attested from 1606, uses capital letters to represent single chords (see Tablature, fig.8), and the Spanish, attested from 1626, uses numerals for the same purpose (fig.139). These abbreviated systems were used at times in combination with the earlier lute notation (for further details see Wolf, ii, §I, chap.3). Tablatures for guitar remained in use until the late 18th century, when they yielded to ordinary mensural notation on a single staff, written an octave higher than sounding (fig.140).

For much of the 20th century tablatures of a new type were in use for the guitar and ukelele in popular music, with a grid of six vertical and four horizontal lines (guitar) or four vertical and four horizontal (ukelele), providing a schematic picture of the fingerboard; dots represent the positions of the fingers (fig.141). This tablature chord notation, like the abbreviated representation of chords by capital letters (an alternative to it: see §4(viii) above), lacks any indication of rhythm within the duration of each chord, which is to be supplied by the performer from his knowledge of the style. Some 20th-century guitar music, mostly of a popular nature in the so-called ‘finger-picking’ styles, uses another type of tablature notation, closer to the lute tablatures of the Renaissance. Many publications of the 1960s and 70s reflect this notation. A six-line staff is used, corresponding to the strings of the instrument; as in French lute tablature the top line represents the string of highest pitch, and as in Spanish vihuela tablature numerals are the basis of the notation. Time signatures, bar-lines and so on are as in staff notation; the letters ‘TAB’, written vertically, often replace a clef, presumably for ready identification of the tablature when both staff and tablature notation appear in the same book. Otherwise there is no standard practice: the numerals in some tablatures represent the frets, in others the fingering, the notes being identified in some other way (e.g. by capital letters for chords). Rhythm signs are freely used: a vertical or diagonal dash for a crotchet, and stems (without note heads) with flags and beams as in staff notation for quavers, semiquavers and so on. Part-writing may be specified far more precisely in this tablature than in any Renaissance one (see fig.142). Special signs are used for ornaments and other effects.

Harp tablatures are also attested from the late Middle Ages, and Spanish vihuela tablature was intended also for the harp. Irish manuscripts have various notational systems, perhaps for harp music; one from the Elizabethan period has various combinations of acute and grave accents, circumflexes and rhythm signs; another has a series of symbols, in part resembling those of Greek notation, representing successive notes in a diatonic series. 17th-century Welsh manuscripts, including that copied by Robert ap Huw (GB-Lbl Add.14905), contain another tablature for the harp, which like German organ tablatures uses the letter-names of the notes. It is closer than the Irish sources to other contemporary notation, being written in score with bar-lines and rhythm signs like those of other tablatures of the period (fig.143). Extravagant claims of antiquity have been made for both the Welsh and Irish tablatures and their repertories, but without firm evidence.

French and German harp music appears to have been notated in various ways: alphabetical tablature (Agricola, Musica instrumentalis deudsch, 1529, f.XXXII); normal mensural notation; with numerals corresponding to the strings (Mersenne, Harmonie universelle, ii, 1637, bk.3, p.171); or by lute tablature. These possibilities are not represented by surviving examples.

Notation, §III, 5: Alphabetical, numerical and solmization notations

(iii) Tablatures for other instruments.

Viol music has normally been notated in ordinary mensural notation, but tablature is occasionally encountered, mostly in didactic works. The earliest sources are German (Virdung, Musica getutscht, 1511; Agricola, Musica instrumentalis deudsch, 1529; Gerle, Musica teusch, 1532) and are notated in German lute tablature or other alphabetical notation (fig.144, from Agricola). In Italy viol tablature is found first in Ganassi dal Fontego’s Regola rubertina (1542), corresponding in essence to the Italian lute tablature though with modification because of the greater number of frets required (in both types of tablature single symbols, rather than numerals, were used for numbers greater than 9, in order to avoid ambiguity) and for precision of fingering. In France, in the few instances where mensural notation was not used, French lute tablature was used for viol music (fig.145), sometimes with ancillary signs for special effects, and also for music for other related instruments such as the viola bastarda. French lute tablature was also used for the English lyra viol repertory.

Modified lute tablatures of various national types were occasionally used also for violin music, but with only four staff-lines, corresponding to the strings of the instrument. In the absence of frets, the series of numerals or letters used were not bound to correspond to semitone steps: Italian violin tablatures, from Gasparo Zanetti’s Scolaro … per imparar a suonare di violino, et altri stromenti (1645; fig.146), use numerals to specify diatonic steps, with accidentals added for the semitones as in mensural notation. This notation persisted for more than a century and is still attested in Pablo Minguet y Yrol’s Academia musical (1752); comparable modifications of French lute tablature were also made, with the letters representing diatonic steps. The older lute notation based on semitone steps also continued to be used for violin music.

Wind music has nearly always been notated mensurally, but tablatures are occasionally attested, based on the positions of the fingers. A recorder tablature is found in Virdung (1511), using numerals and diacritical marks. Thomas Greeting in his Pleasant Companion (1682 edition) used a six-line staff for the six holes of the flageolet with vertical lines for covered holes, crosses for half-covered holes and commas for ornaments (fig.147); Pablo Minguet y Yrol (Academia musical, 1752) used an eight-line staff, with the spaces representing the seven holes, and full, void and half-void circles representing covered, open and half-covered holes. Other tablatures were devised for wind instruments such as the musette in 17th-century France, and tablatures have been attested for brass fanfares; numerical tablatures were used in the 19th century for the accordion and other popular instruments.

Notation, §III, 5: Alphabetical, numerical and solmization notations

(iv) Vocal notations.

Since the 16th century, periodic attempts have been made to construct simple systems of vocal notation, often based on the practice of Solmization, for the benefit of the musically uneducated. Many of these indicate pitch redundantly in two different ways: by conventional mensural notation supplemented by some alternative means of identifying the pitches, either with the letter-names of the notes or with solmization syllables; or with distinctive note shapes or numerals representing the solmization syllables. These systems multiplied from the 18th century, mainly where rapidly acquired musical literacy was sought, or in pioneering or mission areas, and are associated mainly with popular music (hymns, psalms, ballads etc.).

An attempt to develop a simplified solmization notation with numerals was made by Pierre Davantes (Pseaumes de David, … avec Nouvelle et facile methode pour chanter chacun couplet des pseaumes sans recour au premier, Geneva, 1560; see fig.148). Numerals from 1 to 9, supplemented by the letters A and B, represent the notes in an ascending sequence beginning on E, C or B (the latter either B or B depending on the hexachord); the numbers are reckoned as in the natural hexachord if written without dots, in the hard hexachord if followed by a dot and in the soft hexachord if preceded by a dot. Vertical dashes are used for rhythm signs. A simpler solmization notation was adopted in a number of psalm books published by John Day in the 1570s, with abbreviations of the solmization syllables joined redundantly to conventional notes on staves (Error! Hyperlink reference not valid.; see Krummel, 1975, pp.71ff).

Specific solmization notation was uncommon in England. The Fasola solmization system, later known as ‘Lancashire sol-fa’, used a reduced series of solmization syllables; it was expounded in popular publications from the early 17th century until the late 19th, as in John Playford’s Breefe Introduction to the Skill of Musick (1654), and was normally a sight-singing system applied to music in ordinary mensural notation. In America, however, it gave rise to a number of distinctive notational systems for hymn and psalm books, beginning with that of John Tufts (An Introduction to the Singing of Psalm-Tunes, 1721; earliest extant edn., 5/1726), in which the letters M, F, S and L (for the solmization syllables Mi, Fa, Sol and La) are placed on a conventional staff, with dots for rhythm signs (two dots for a breve, one for a semibreve and none for a minim; fig.150). Comparable systems multiplied in the 19th century. In the south and mid-west USA, a number contained distinctive ‘shape-notes’ (i.e. notes of four different shapes, each representing one of the four fasola syllables); these may have first appeared in Little and Smith’s The Easy Instructor (1801), whose system eventually prevailed over other early 19th-century systems (fig.151). Such systems are known also as ‘patent’, ‘buckwheat’ or ‘figured’ notes, and the shape-notes have survived into the 20th century. (See Shape-note hymnody; also §4(iii) above.)

From the 17th century many numerical notational systems have been proposed as alternatives to or replacements for conventional mensural notation. One of the earliest was that of William Braythwaite (Siren coelestis, 1638; see Krummel, 1975, pp.100ff, including facsimiles), comprising numerals for notes and various different types of comma for rests; other early numerical systems are those of Kircher (Musurgia universalis, 1650, ii, 46ff) and Giovanni d’Avella (Regole di musica, 1657). Such systems in the 17th century and later relied mainly on numerals, with or without letters of the alphabet, and some used conventional rhythm signs to fix the durations of notes; most used the numerals to count diatonic intervals arithmetically from a given note or notes. An exception is Mersenne’s proposal (Harmonicorum libri XII, vii, 1648, pp.148ff) to represent notes by inverse intervallic ratio as calculated by the length of string required to produce the note, rather than by frequency; the basis was c', taken as an arbitrary 3600.

Rousseau, in his Projet concernant de nouveaux signes pour la musique (1742/R) and elsewhere, used the numerals 1 to 7 for the diatonic scale of C major, placed on, above or below lines to distinguish between different octaves; this notation was designed for complex pieces. A second system, for simple melodies, dispensed with lines, using dots over or under numerals to indicate a move to a higher or lower octave (shown with only the first note in the new register). Simple integers were used for time signatures, rather than conventional fractional signatures; subdivisions of a bar, if unequal, were indicated by commas and by horizontal lines over or under groups of notes, functioning like beams in mensural notation. Rhythm signs in the usual sense were thus dispensed with, as in the most influential 19th-century solmization and alphabetical notational systems. Rousseau’s notational proposals, though not widely adopted at the time, were taken up on a relatively large scale in the 19th century in France in the Galin-Paris-Chevé method, whose influence extended to other European countries (Germany, the Netherlands, Denmark and Russia).

In the English-speaking world notational systems were developed in the 19th century based on seven-syllable solmization systems, which had been advocated from the 18th century as theoretically superior to fasola. The most important of these systems was the Tonic Sol-fa system, perfected by John Curwen from a method of sight-singing. Like some of the 18th- and 19th-century American notational systems described in Marrocco (1964), Tonic Sol-fa jettisoned the staff and conventional note shapes, using instead letters as abbreviations of the syllables representing the degrees of the major scale, with changes of vowels for accidentals. The necessity for rhythm signs, found in most earlier notational systems in which conventional note shapes were abandoned, and even for time signatures, was obviated by the expedient of making the distance between symbols proportional to the duration of the notes, with dots and colons used to separate beats. The notation is supplemented in teaching with hand signs and a device known as a Modulator (see Modulator (ii)).

This economical and ingenious system was well suited to relatively uncomplicated vocal music. Associated in England at first largely with nonconformity, it was adapted for use in Germany and Poland; it was widely diffused through Christian missionary work and popular ballads (in printed popular ballads it sometimes supplements ordinary staff notation: see fig.141 above). Tonic Sol-fa has become independent of white musicians in various parts of the world; it is widely used by African musicians, for example, for vocal music, often without the precise spacing and distinctions between different octaves of 19th-century Tonic Sol-fa (fig.152). A derived notation, using the numerals from 1 to 7 (and 0 for rests) instead of the sol-fa symbols from d to t, was developed in Japan and is widely used in 20th-century printed music in China and Japan (see L.E.R. Pickens, NOHM, i, 1957, 83–104, esp. 101); bar-lines are used as in sol-fa, but bars and double bars underneath the numerals, rather than punctuation marks, show the subdivision of the bars (for a related example see fig.153).

Although Tonic Sol-fa is used by those without musical education, it should not be regarded as a simple rule-of-thumb notation like some other alphabetical notations. Helmholtz, for example, considered it superior to staff notation for theoretical reasons, believing that it was a better means of producing correct intonation from singers (see Die Lehre von den Tonempfindungen, Eng. trans., 1875, appx 18). Fig.154 shows Tonic Sol-fa as applied to a fairly complex tonal piece; most of the notational features are self-explanatory.

Since the late 19th century the limitations of Tonic Sol-fa have become more apparent because of its clumsiness when the music modulates rapidly and its inapplicability to non-tonal music. Notators accordingly have often preferred conventional mensural notation, which has ousted Tonic Sol-fa even from areas in which it had been well-established, such as English choral music. On the other hand, attempts to construct notational systems based on solmization with more than seven syllables to the octave have had no general success. Such systems include the Eitz method, the systems of J.L. Acheson (Douzave System of Music Notation, 1936) and of L. Benke (1967).

For the syllabic notation employed by Scottish pipers to record pipe music (‘canntaireachd’) see Scotland, §II, 6(i).

For bibliography see end of §6.

6. Non-mensural and specialist notations.

(i) 20th-century non-mensural notation.

Although the mensural notational system proved adaptable to the requirements of 20th-century music, there are some areas where it proved less effective. This occurred where the music makes relatively little use of notes of definite pitch or definite duration, or of traditional temperament systems. It occurred also in prescriptive notation for indeterminate music, when precise specification is at a minimum; and, perhaps paradoxically, also in descriptive notation at the other end of the spectrum of precision, when scientific accuracy of notation is required – as, for example, in ethnomusicological notations.

A move away from mensural notation occurred with so-called action notation: expansions of the verbal directions found in earlier notation, or symbols replacing them (e.g. the abbreviations for pedalling, fingering etc.) at the expense of the mensural aspects of the notation. From this, perhaps, developed the graphic notations particularly associated with indeterminacy (graphics, implicative graphics), which were used at least as early as 1950–51 (Morton Feldman, Projections). This notation is generally designed to evoke a musical response from the performer by non-specific analogy rather than by direct instruction; thus any two performances should be quite different. According to Karkoschka (Schriftbild, 1966, Eng. trans., 1972, p.77), graphic notation strives to ‘stimulate without constricting the imagination’. Theoretically, any type of visual pattern may be used, though a certain degree of influence of conventional notation often seems evident, particularly in the choice of shapes associated with articulation and dynamics, and in the idea that a score represents a graph with a pitch range as its vertical axis and a time-scale as its horizontal axis. Graphic notation may be combined with conventional notation within a single score, as in figs.155 and 156. In some cases, such as in the works of Logothetis and Cardew, particular emphasis is placed on developing the aesthetic aspects of graphic notation. The use of abstract patterns as graphics is paralleled by the use of verbal texts not as instructions but as a ‘notation’ intended to evoke a musical response (as in the Concert for Orchestra by George Brecht, whose score comprises the single word ‘exchanging’). An intermediate position between graphic and conventional notation is occupied by the so-called ‘frame’ notation, in which relatively free interpretation is permitted within certain prescribed boundaries; sections of scores in this notation may literally be notated within frames (fig.157).

Notation has sometimes been used for electronic music, although when such music is composed on tape the necessity for notation is not always present. Some pieces have been notated in order that the composer may be protected by copyright; or to provide a study score; or to provide a cue-sheet for performers when electronic music is combined with live performers. Scores of electronic music may thus be either prescriptive or descriptive, and may not always contain representations of every aspect of the music. The notation used may draw on the resources of conventional mensural notation, in so far as these are usable for the purpose, and on those of graphic notation. Proposals have been made for notational reform and notational standardization in electronic music (Fennelly, 1968).

Another area in which mensural notation is clearly inadequate is the precise recording of musical data, particularly those of non-Western music and folk music. Attempts to record music as it is being performed have been made since the mid-18th century, for example by attaching recording machines to keyboard instruments; these were termed ‘melographs’ at least from 1828, and it was hoped to record improvisations on them. One such instrument, from 1780, survives at the Deutsches Museum, Munich (inventory no.43872). Shorthand notations for recording music at speed were also devised (see §6(ii) below). No wholly satisfactory method was available until the invention of machines to record sound, and even then transcription into visual notation was seldom sufficiently precise for ethnomusicological material, even though efforts were made from the 1920s to divorce ethnomusicological transcriptions from Western mensural notation. But in the 1950s an improved Melograph (see illustrations in that article) was developed by Charles Seeger. This machine now provides immediate transcriptions of music in threefold graphic form; one section of the ‘melogram’ represents a pitch-time graph, another an amplitude-time graph and the third a timbre-time graph. The resemblance of this notation to the graphic notation described above is clear.

Unprecedented precision has also been required of notation adapted to the digital computer. If notation is to be converted into a computer programme, ambiguity and redundancy must be eliminated; such programmes have been used for the stylistic analysis, along statistical lines, of various repertories. Accordingly attempts have been made to construct methods of notation adapted to computers which lend themselves readily to transcription between mensural or other notation and a computer programme (see for example Symposium II in Brook, 1970, with details of some of the problems and proposals for solving them; see also Cole, 1974, pp.117ff).

(ii) Musical shorthand.

Before the invention of sound recording, a musical equivalent of shorthand was required. The first attempts to devise one were made in France in the early 18th century (e.g. Joseph Sauveur, Principes d’acoustique, 1701), though the earliest systems are scarcely shorthand in a practical sense since they either are alphabetical systems or draw heavily on the resources of conventional notation. As late as 1805, P.J. de La Salette claimed as a shorthand system one that required letters of the alphabet, horizontal and vertical strokes for rhythm signs and simplified signs for accidentals (Sténographie musicale).

Démotz de la Salle in the 1720s proposed signs more suitable to a shorthand system, which were capable of being rotated and reversed (Méthode de musique selon un nouveau système); they were derived from mensural notation, but later systems used simpler geometrical signs (e.g. J.L. Riom’s Sténographie musicale, 1833), dots, curved lines and so on. All the early systems used separate signs for each note, but Hippolyte Prévost attempted to overcome this drawback by a system in which complete bars could be written as single multiple signs; the system required the use of a five-line staff with two auxiliary dotted lines above and two below. A similar notation was devised to record accompanying harmonies (fig.158, from Sténographie musicale, 1833).

(iii) Notation for the blind.

Like musical shorthand, musical notation for the blind first developed in the 18th century and the first attempts at it were hampered by too close an adherence to the conventional mensural system. Rameau (Code de musique pratique, 1760), Tans’ur (Elements of Musick, 1772) and others envisaged, broadly speaking, a conventional notation placed in relief so that it could be read by touch, with note shapes somewhat altered to facilitate their recognition by touch. Several other notations for the blind were devised in the late 18th and early 19th centuries, but the most important was that devised by Louis Braille (Anaglyptographie, 1829), which departed entirely from the conventional signs. Embossed dots were arranged in two adjacent vertical rows of three each, with the upper four dots referring to pitch and the lowest two to duration (for further details of this system, see Braille notation). This has superseded all other notations for the blind; revisions of it have not all been adopted universally, and different forms are used in different places.

(iv) Cryptography.

From the 17th century at least, musical notation has occasionally been used as a secret code for conveying messages. Even earlier than that, the association of notes with solmization syllables had occasionally suggested their use as a pun, as for example in the use of an interpolated B (= fa) replacing the syllable ‘fa’ in Du Fay’s name (GB-Ob Can.misc.213); this too is a type of cryptography, and has many later parallels. Many musical codes equate single notes and note shapes arbitrarily with individual letters of the alphabet; there are German examples from the 17th century and later (e.g. Kircher, Gaspar Schott, J.B. Friderici, Michael Haydn), which are comparable to the system described in John Wilkins’s Mercury, or the Secret and Swift Messenger (1641; see fig.159 and Krummel, 1975, p.128).

Another type of cryptography is represented by the use of motifs comprising notes whose letter-names (or letters derived from them, e.g. E = Ger. Es = S) spell words (for example Bach’s and other composers’ use of the motif B–A–C–H, that is B–A–C–B in German terminology; Schumann’s ‘Abegg’ Variations, 1830; Ligeti’s Fragment, 1961). These examples belong to the history of composition, however, rather than to that of notation.

An ambitious ‘universal’ musical language was essayed by Jean-François Sudre (Langue universelle, 1867), which was intended to express definite extra-musical ideas in a manner intelligible to all, of whatever nationality. Motifs were associated with ideas (fig.160) and were communicable through performance, notation, cheironomy and in other ways. Although the system achieved surprisingly wide acclaim in France at the time, it soon sank into oblivion.

See also Cryptography, musical.