(Lat.: ‘false, feigned or contrived music’; synonymous with falsa mutatio, coniuncta).
These terms were used by theorists from the late 12th century to the 16th, at first in opposition to musica recta or musica vera, to designate ‘feigned’ extensions of the hexachord system contained in the so-called Guidonian hand. Most scholars accept that notated polyphony of this period required performers to interpret under-prescriptive notation in accordance with their training (by contrapuntal and melodic criteria about which scholars disagree), ensuring the perfection of consonances, and approaching cadences correctly. These requirements could often be met within the recta system, but musica ficta was used ‘where necessary’ – in modern terms only, by ‘adding accidentals’; in medieval terms, by ‘operating musica ficta’.
In modern usage, the term musica ficta is often loosely applied to all unnotated inflections inferred from the context, for editorial or ‘performers'’ accidentals rather than notated ones (whether properly recta or ficta). Editors usually place accidentals that they have supplied, on behalf of performers, above the affected note or in brackets or small type, to distinguish them from those having manuscript authority. (On the placing of editorial accidentals, see especially Anglès, 1954; Hewitt, 1942; Jeppesen, 1927; Lowinsky, 1964 and 1967; J. Caldwell, Editing Early Music, Oxford, 1985.)
4. Rules for inflection and adjustment.
MARGARET BENT (1–4, bibliography), ALEXANDER SILBIGER (5)
The hexachords of musica recta built on G, c and f (and their upper octaves, g, c', f', g') comprise the ‘white’ notes of the modern diatonic scale from G to e'' with the addition of b, and b'; each letter name has tagged to it the solmization syllables of its recta hexachords, which define the default interval arrangement of the gamut, the ‘normal’ relationships of syllables to letters (see Solmization, §I, Table 2). The internal arrangement of each hexachord was identical (tone–tone–semitone–tone–tone, identified by the syllables ut–re–mi–fa–sol–la). These were the hexachords of musica vera or recta (La Fage, 1864, Anonymus 1) and their constituent pitches those of musica vera or recta (see Solmization, §I, 2) in the system attributed to Guido of Arezzo (1025–6 or 1028–32). Mi–fa or fa–mi was always a diatonic semitone, and a semitone was always either mi–fa or fa–mi. The singer moved up and down the overlapping hexachords as the music required, making transitions (mutations or coniuncte) on notes common to two hexachords, in order to get into position to solmize the next semitone step as mi–fa or fa–mi, without mutating between its boundary notes. These transitions were practical and local means of negotiating and teaching semitone locations, but they have no prescriptive status; the singer must know where he wishes to place the semitone before selecting a hexachord; it is functional, a vocal analogy to fingering. The purpose of the system was to contextualize and demonstrate the position of semitones deemed necessary. Solmization was the practical language in which intervals were expressed; it was originally devised as a pedagogical tool for melodic chant, providing the vocabulary for interval specification.
The system was extended to cope with the growing demands of polyphony, where simultaneities often needed correction at the expense of line, by accommodating the extra notes thus required. Semitone steps other than B–C, E–F, A–B were provided from ficta hexachords beginning in ‘unusual’ places, on notes other than G, C and F; these were sometimes conceived as the transposition of recta hexachords to alien pitches. The F needed for an approach to G, for example, is contrived by a ‘fictitious’ D hexachord, making the F–G semitone mi–fa; the E to make a perfect 5th below a B might be fa in a B hexachord. In such cases not only the F and the E had ficta status but also the G fa and the D mi, since the hexachordal status affected context, not just individual pitches. The hexachord beginning on low F, and therefore B, had ficta status. The close relationship of ficta to solmization is confirmed by the synonym falsa mutatio.
The range of available ficta hexachords was increased and rationalized until, in the 1430s, Ugolino of Orvieto (Declaratio musice discipline) recognized a complete system including recta and ficta hexachords whose sole purpose was to accommodate the pitches needed for interval correction in polyphony, and to give them a place within the extended solmization system. When melodic integrity had to yield to the higher priority of simultaneous consonance, legitimate progressions in polyphony could no longer be confined to intervals acceptable in chant. Solmization is essential to understanding what the theorists say about interval correction, but does not itself provide solutions or determine what the sounds should be, since any melodic progression, even one illegal in chant, could be solmized by an extension to the system. A few theorists allow disjunct hexachordal change, for an awkward interval without a common note on which to mutate, by means of the disiuncta. Until the late 15th century, when keyboard-influenced attempts at reconciling the separate systems were made, Johannes Boen (Musica, 1357) was virtually alone in attempting to conflate the monochord and the gamut in a single exposition, as distinct from the normal practice of using independent letters to label the monochord, and separately tagging hexachord syllables to the letter names of notes in the gamut. Boen resorted to some unusual vocabulary in so doing, such as mansio (perhaps as in lunar mansion), and extorquere, for the removal of sounds from those proper places.
Some earlier scholars took for granted that modes were an a priori assumption for polyphony (Apel, Accidentien und Tonalität, 1937, tailored accidentals to fit the mode; Aldrich, 1969); more recent work has rejected modal interval species as binding for ficta, in favour of more neutral and flexible tonal typings. But Christian Berger has argued (1992) that 14th-century composition has an a priori modal basis closely linked to Allaire's controversial theory of hexachords (1972), even overriding many notated accidentals (challenged by Fuller, 1998). Both modes and solmization were originally designed for the classification and teaching of plainchant, which require little use of extraneous notes except for the correction of melodic tritones. Before it was stretched by the extra demands of polyphony, the recta gamut as devised for plainchant was also not incompatible with modal interval species, but the introduction of fictive adjustments led most theorists from the 13th century onwards (e.g. Johannes de Grocheio) to repudiate the application of modes to polyphony. Isolated brief mentions before the 16th century link them; but the Berkeley Manuscript treatise (c1375; US-BE 744) and Tinctoris in the 1470s, and even 16th-century successors such as Aaron and Glarean, confine their classifications to the tenor, and these classifications are apparently not undermined by the need for tenor inflections. (See Mode, §III.)
Musica ficta has often been defined in terms of ‘chromatic’ notes that by modern standards are non-diatonic. But ‘chromatic’ properly refers only to melodic progressions involving the chromatic semitone (Haar, 1977). F–G–A are two adjacent diatonic semitones; F–F is a chromatic semitone. The word was used in Greek theory and transmitted to the Latin West only to designate one of the tuning systems that could be applied to a standard arrangement of tetrachords, and indeed many 16th-century debates about chromaticism were dominated by considerations of tuning (see Berger, 1980). Zarlino (Le istitutioni harmoniche, 1558) characterized individual fictive notes as borrowed from the chromatic genus; he preferred a classicizing explanation over the medieval hexachord system.
Each tetrachord or hexachord is a diatonic entity, containing one diatonic semitone; but the tight overlapping of hexachordal segments – some as small as an isolated coniuncta – to produce successive or closely adjacent semitones did not necessarily compromise their diatonic status. The tenor of Willaert's so-called chromatic duo is entirely diatonic in its progressions (Bent, 1984), as are Lowinsky's examples of ‘secret chromatic art’ (Lowinsky, 1946) and indeed almost the entire repertory. True chromatic progressions (e.g. F–F–G) are occasionally allowed in theory (Marchetto, GerbertS, iii, 82–3) and prescribed in manuscript sources. Except where a melodic chromatic interval is introduced in the interests of vertical perfection (e.g. Old Hall, no.101; see ex.2d), musica ficta is by nature diatonic.
Even music liberally provided with notated sharps is not necessarily chromatic; this has been called ‘accidentalism’. Increasingly explicit use of accidentals and explicit degree-inflection culminates in the madrigals of Marenzio and Gesualdo, which are remote from medieval traditions of unspecified inflection, and co-exists in the 16th century both with older hexachordal practices and with occasional true melodic chromaticism. It is the small number of chromatic intervals in Lassus's Sibylline Prophecies (Carmina chromatica), for example, that determine its chromatic status, not the large number of sharps that give it ‘chromatic’ colouring according to looser modern usage.
Vicentino (L'antica musica ridotta alla moderna prattica, 1555) employed chromatic and enharmonic tone systems for composition, and tuning in imitation of the ancient genera. Such experiments, as well as those originating in a fresh use of chordal chromaticism of a colouristic type, are less indebted to the tradition of musica ficta. In one of the most remarkable experiments of the century, Guillaume Costeley's extraordinary chromatic chanson Seigneur Dieu (Levy, 1955; Dahlhaus, 1963), hexachordal solmization ( = fa) co-exists with non-hexachordal degree inflection.
(i) Antecedents, 9th–12th centuries.
The Enchiriadis treatises of about 900 give the earliest explicit and extensive theoretical account of the additional semitones that we would call chromatic alteration. The anonymous author of the Scolica enchiriadis defined absonia (elsewhere dissonantia) as the lowering or raising of a note from its normal pitch. The word vitium, used in this context, seems to imply no more than a disturbance of the normal scale, the force being very similar to that of the later falsa (indeed, the term falsus sonus appears in this treatise; GerbertS, i, 177). The absonia arises from faulty intonation (a ‘vice’ of the human voice to which instruments are less subject) or, more important, from the nature of the music, where it has the effect of transplanting or restoring the mode. A fusion of the Greek Greater and Lesser Perfect Systems (see Greece, §I, 6(iii) and Table 1) allowed for two different positions for the note B through the former's disjunct diezeugmenōn tetrachord (providing B) and the conjunct synēmmenōn tetrachord of the latter (providing B). This rationalization of the two positions of B is applied by Hucbald in De harmonica institutione (c900; GerbertS, i, and trans. in Palisca, 1978, pp.29–31) to specific chant formulae.
Using dasian signs the author of the Scolica set up tetrachords (disjunctly, with a central semitone flanked by two tones) yielding the remarkable scale G–A–B–c–d–e–f–g–a–b–c'–d'–e'–f'–g'–a'–b'–c'' (Spitta, 1889; Jacobsthal, 1897; Spiess, 1959). This is proposed in addition to the more normal scale as specially suited to organum at the 5th: the early use of such extreme alterations seems to be occasioned by polyphony. For plainchant the author was more conservative but no less ingenious. He evolved a system of pentachords involving recta forms as well as the absonia. The pitches of e and f are introduced by changing the dasian name on one note – in effect a mutation. By extending the tetrachord system to cover the legitimate transpositions of the pentachords with absonie, Jacobsthal further advanced the possibility that the Enchiriadis treatises also allow for c, g, d and A. Thus B was recognized even by some early theorists as part of the regular (recta) system of available notes, with further allowance for alterations other than the alternative inflections of B, although the terms musica ficta or falsa were not yet used.
The usual reason given for melodic alterations to chant is avoidance of the melodic tritone. The anonymous author of the 10th-century Dialogus de musica (Huglo, 1969, 1971) referred to the ‘vice’ of additional semitones outside the ‘prefixed rule’ (GerbertS, i, 272) and cited chants in which b, e, c and f were required, but he no longer explained them by tetrachords. The accommodation of such notes by modal transposition (see Mode, §II, 1(i)) is clearly specified by some 11th-century theorists. Guido of Arezzo discussed the Affinitas or relationship between a modal final and the note a 5th above, whereby a shared configuration of tones and semitones for each pair of pitches makes it possible for either pitch to begin or end the same piece (Pesce, 1987; see also Proprietas, Hexachord and Mode, §II, 3(ii) (b)). Berno of Reichenau recognized transposition of f and f and e and e to the theoretically acceptable double position on b and b, where they become recta locations for chromatic notes found elsewhere in untransposed chant (GerbertS, ii, 75). Johannes Cotto gave more detail and accepted transpositions up a 5th for some modes (GerbertS, ii, 248; ed. J. Smits van Waesberghe, 1950, p.101; for Guido and Johannes see Palisca, 1978). Johannes also provided for a process of ‘emendation’ in a few places where the notes can be neither notated at original pitch nor transposed. The author of the Dialogus allowed ‘emendation’ where necessary – that is, where the piece could not be sung in another mode. Such prescriptions already anticipate later warnings against using ficta when the situation could be corrected by other means. The development of a system of modal transpositions coincided with the rise of a clearer pitch notation which, however, had very little capacity as yet to cope with the additional notes required for the necessary perfection of simultaneous intervals in polyphony: f and c appear besides B and B to permit perfect intervals in parallel organum at the 5th. Notes outside the system are recognized, usually as undesirable distortions in chant, and hence false, but useful for modal transposition.
The tetrachordal mapping developed in these early treatises allowed alternative diatonic routes but no direct access from one kind of B to the other. By the 12th century, most theorists extended tetrachords to overlapping hexachords in the system atttributed to Guido, with the same function of defining and containing the semitone step. The status of B was much debated, sometimes described as ‘added’ (adiunctum) or irregular (even by Guido), although B and B were given equal status by several early writers, from Hucbald (c900) to the author of the Summa musice (c1200; ed. Page, 1991, pp.89, 171).
Although there is as yet no use of the term musica ficta, there is a direct terminological link. The synēmmenōn was translated into Latin as coniuncta, which came to be a commonly given synonym for falsa mutatio or musica ficta.
The earliest known use of the term musica falsa is in a late 12th-century didactic poem, describing variable hexachord steps (I-Rvat pal.lat.1346; an unpublished edition by Smits van Waesberghe is cited in Sydow-Saak, 1990). 13th-century theorists at first continued the negative definition of musica falsa as a contamination of the chant; Elias Salomo refers to the false bellowing (‘mugiens’) of a false musician (GerbertS, iii, 19, 42–3, 61ff). Falsity implied transpositions associated with irregular intervals; the melodic tritone was to be avoided, a vice analogous to a false proposition in logic (Summa, c1200; ed. Page, 1991, p.122, and GerbertS, iii, 238a). At this time it was often the fault, not its remedy, that was considered ‘false’. Theorists qualified and excused the negative term and definition, before shifting from denoting the fault to be cured to the means of correcting it.
Opinions were divided about the use of falsa or ficta to avoid melodic tritones in plainchant, but all who declared themselves on the subject recognized its essential role in correcting simultaneities in polyphony. Jacobus of Liège asserted its importance in plainchant (CSM, vi/lxvi); Hieronymus de Moravia, however, allowed it in polyphony but excluded it from plainchant (CoussemakerS, i, 86). Johannes de Garlandia, in his treatise on plainchant and measured music, specified that much was necessary on instruments, especially in polyphony (or organs: ‘organis’; CoussemakerS, i, 166). Hieronymus's addition to Garlandia gives priority to the correction of concords over maintaining melodic integrity (ed. Reimer, 1972, i, 95). The St Emmeram Anonymus (1279) also affirmed the role of musica falsa (equated with ficta) in polyphony as a helping hand for the essential correction of consonance (De musica mensurata, ed. J. Yudkin, Bloomington, IN, 1990, pp.274–5). Lambertus likewise expressed dissatisfaction with designating as falsa something necessary for achieving good consonance (CoussemakerS, i, 258); ‘it is not so much false as unusual [inusitata]’ (Anonymus [after Lambertus], ed. Gilles, 1989, p.48). Modern scholars' misreadings of this word as ‘mutata’ derive from a mistranscription by Coussemaker and have no basis in the manuscripts (e.g. Russo and Bonge, 1999). Anonymus 2 may be the earliest to distinguish the two often-cited reasons for using musica falsa: necessity (causa necessitatis), for correcting consonances, and beauty (causa pulchritudinis), apparently for melodic reasons (CoussemakerS, i, 312; ed. Seay, 1978, p.28; see also Vatican organum treatise, ed. in CSM, ix, 47).
Hieronymus de Moravia equated musica falsa with the synēmmenōn (coniuncta) and accordingly based his exposition not on hexachords but on tetrachords. Walter Odington wrote of ‘movable solmization names’ (CoussemakerS, i, 216, and CSM, xiv, 1970), Lambertus and Anonymus 2 of ‘false mutation, or falsa musica’ (CoussemakerS, i, 258a, 310; Anonymus 2 also in Seay, 1978). The idea of false mutation came to be applied to hexachords with a term originally derived from tetrachords, and by the later Middle Ages developed into a full-blown system of infinitely transposable places. Johannes de Garlandia, Anonymus 2, Lambertus and many others defined musica falsa as ‘when we make a tone of a semitone or vice versa’ (CoussemakerS, i, 166, 258, 310; Anonymus 2 also in Seay, 1978), a widely used definition also for musica ficta and the coniuncta.
Increasing acknowledgment of its necessity in the growing art of polyphony prompted a change to the less pejorative term musica ficta (‘not false but true and necessary, because no motet or rondellus could be sung without it’: Vitry, Ars nova, 23) or the even more neutral coniuncta (Berkeley MS, c1375, ed. Ellsworth, 1984). This theorist defined the problem in terms of ‘imaginary transposition’ of hexachords and, explicitly dealing with plainchant and specific categories of polyphony, exemplified the coniuncta from chant, contrary to some 13th-century usage. The mid-15th-century Anonymus 11 (CoussemakerS, iii, 429) said that coniuncte were necessary in both plainchant and polyphony.
The transition from 13th-century discant to 14th-century counterpoint teaching laid greater stress on contrary motion and the controlled succession of perfect and imperfect intervals; perfect intervals had indeed to be adjusted so that they were intervallically correct, and they were to be correctly approached from a 3rd or a 6th by a semitone step in one part. The few theorists who devote a sentence or two, or even a separate chapter, to musica ficta usually append discussion of it to counterpoint precepts, and link it to producing correct interval successions. The rules may not be called ficta rules; the counterpoint should be adjusted anyway, and if necessary by musica ficta. Strict counterpoint theory dealt in consonances (some dissonances were permitted in florid counterpoint and in composition), and was dyadically based until the late 15th century and beyond. The common objection, that such simple theory helps us little with composed part-music using dissonance, can be met by treating strict counterpoint as the background skeleton of which a piece is implicitly a composing out. Theorists identify such counterpoint as the basis both of florid counterpoint and of (implicitly multi-voice) composition.
14th-century counterpoint teaching stressed not only correct perfect intervals but that they should be approached correctly from an imperfect interval, with a semitone step in one or other part, whether ascending or descending (e.g. Johannes de Muris; and see ex.1). In the definition of Prosdocimus (early 15th century), musica ficta was devised solely in order to ‘colour’ consonances that could not otherwise be coloured (ed. Herlinger, 1984, pp.70–95). That he here includes the approach to perfect consonances becomes clear when he extends the principle of proximity also to the antepenultimate. Ugolino invokes such inflections not only for sweeter harmony, but in order to give the imperfect interval even ‘closer adhesion’ to the perfect interval to which it resolves (ed. in CSM, vii/2, p.48).
Many theorists reserve ficta for situations that cannot be corrected by recta (e.g. Johannes de Muris, Ars nove musice, 1321, GerbertS, iii, 307: ‘if we can discant by vera, then it is illicit to discant by ficta’), giving rise to a proposal that recta should be used in cases of equal choice; this would mean that a cadence on octave A should normally be approached from a 6th with recta B in the lower rather than ficta G in the upper part. In practice, however, this does not always seem to apply. Prosdocimus appeals, unusually, to the judgment of the (trained) ear, recommending whichever sounds best: if the signs sound better in the tenor they should be applied there, if in the discantus, there (Herlinger, 94–5). This makes it less likely that he (and perhaps others) imply recta preference when saying that ficta should not be used except where necessary. He cannot mean ‘avoid it, even if bad intervals result that go against strong contrapuntal precepts’. But he could mean ‘do not use it unless necessary, but if it is necessary, you must use it’; or, addressing the composer, ‘avoid situations that will require the performer to use it’. Differing interpretations of theorists' rules arise according to whether they are taken as instructions to the notator or to the singer.
In his dictionary (Diffinitorium, 1472) Tinctoris defined musica ficta as ‘cantus praeter regularem manus traditionem editus’ (‘a way of singing outside the regular ordering of the [Guidonian] hand’). In 12 treatises (c1472–85) he set out the concepts of gamut, hexachord system, proportions, mode and counterpoint, but giving only brief mention to the needs of musical practice or elements outside the system. His few important observations on interval correction have again received opposing readings according to different assumptions.
The term musica ficta was still used by German theorists (including Wollick, Opus aureum musicae, 1501; Rhau, Enchiridion, 1517; Heyden, De arte canendi, 1540; Listenius, Musica, 1537; Finck, Practica musica, 1556) but declined after the middle of the century; the latest appearance (except to refer to obsolete practices) seems to be with Walther (Musicalisches Lexicon, 1708). Otherwise, in the 16th century, the term was largely replaced by coniuncta, especially by humanist theorists, and by new ways of explaining inflections. There are scattered references to some standard older definitions, such as tone-semitone substitution, and a marked return to explanations involving transposition (e.g. Adam von Fulda, De musica, 1490, and Cochlaeus, Tetrachordum musices, 1511, for whom transposition down a 5th is equated with musica ficta). Vernacular forms include ‘fained musicke’ (Dowland's English translation, 1609, of Ornithoparchus's Musicae activae micrologus), ‘fremde Stimmen’ (M. Agricola, Musica figuralis deudsch, 1532) and ‘musica finta’ (Vicentino, L'antica musica ridotta alla moderna prattica, 1555). Examples of cantus fictus, melodies with flatward spiral accomplished by leaps of 4ths and 5ths, are found in Listenius and Ornithoparchus.
The 16th century saw the breakdown of late-medieval solmization and of the hegemony of the three-hexachord system. Instead of (or at least, in addition to) presenting the full recta gamut with F, G and C hexachords, theorists (especially in Germany) gave the scalar equivalents as two distinct forms, each representing only two and not three hexachord-types, and in some cases recognizing octave equivalence. The scala b duralis on Γ gave equal access to the members of the hard and natural hexachords but a lower priority to the soft hexachord. In the absence of a signature, B and B thus lost their previously equal status and written B began to express a priority of B over B. The scala mollis on low F (with one-flat signature) included the natural and soft but not the hard hexachords. Depending on the absence or presence of a signature, B or B gained priority over the alternative if not excluding it. A third scale signed with two flats, segregated as the scala ficta or cantus fictus, transposed whole scales by a two-flat displacement (see Solmization, §I, 5). Full solmization atrophied in favour of a ‘lazy’ short-cut solmization, allowing fa super la to be sung without mutation. This meant, in effect, that the entire rationale of medieval solmization, namely to identify the semitone (as mi–fa) and give surrounding context to it, was eroded. Once it was no longer interval-specific and hence functional, solmization became a mere pious anachronism (F is fa for example in Morley, A Plaine and Easie Introduction, 1597). There is some evidence that the efficacy of the mi contra fa prohibition was undermined by a growing habit of not changing solmization to accommodate semitone cadential inflections. The underpinnings of the tonal system shifted partly in response to humanistic changes in music theory, which restored the status of the modes (Tinctoris; Glarean, Dodecachordon, 1547).
The new models were not only octave-based but keyboard-anchored (Ramis de Pareia, Musica practica, 1482), sometimes with fixed ‘three-position’ designations for , and degrees (Hothby, Calliopea legale, ed. in CSM, xlii, 1997). It was above all the rise of the keyboard and associated treatises that challenged traditional vocally based explanations of musical rudiments; Schlick (Spiegel der Orgelmacher und Organisten, 1511) refers negatively to ‘alien notes’ in the context of the keyboard. Pressure to accommodate to the exigencies and compromises of the keyboard prompted change in the status of B. When theorists from Ramis onwards sought to give B accidental status in accordance with its keyboard position, they appealed for authority back to Guido, for whom that note had ‘added’ status. Aaron used the hexachord terminology of mi contra fa to describe collisions and their rectification (exceptions are mentioned: see SpataroC, 66.20); but he also used the keyboard-based terms proprio or naturale and accidentale not only for musica recta versus ficta, but also for white and black notes.
Musical developments from the last quarter of the 15th century onwards prompted significant changes in the treatment of inflections. They include a gradual increase in the normal number of voice parts for vocal polyphony, the multiplication of variant versions of works and self-help indications (including more explicit notation) as a result of the invention of music printing and its markets, a tightening of the theory and practice of dissonance treatment, and compositional control of the relationship of all voices to each other, hence between voices outside the dyadic core. But despite these changes and their different formulation, Zarlino still affirms (citing Gaffurius and common practice) that octaves are approached from major 6ths.
Rich documentary evidence about specific problems in composition, notation and performance is available from testimony of 16th-century musicians and theorists, in formal debates and correspondence (notably involving Spataro, Del Lago and Aaron: see SpataroC). In the 1550s the Roman singer and writer Ghiselin Danckerts illustrated the problem citing a dispute between two singers which must have occurred between 1538 and 1544 over the proper way to inflect a composition by the papal singer Juan Escribano. Danckerts was asked to judge the matter, and explained his decision in substantial detail (Lockwood, 1965).
Downward hexachordal spirals by 5ths occur in some incontrovertible cases, such as the essential duo of Willaert's originally four-part Quid non ebrietas (see above, §1(ii)). This exercised contemporary theorists because of the tuning implications of a piece in which the tenor ends on a notated 7th sounding an octave with the discantus (Lowinsky, 1943, 1956; Bent, 1984). Other cases are Greiter's Passibus ambiguis (Lowinsky, 1956–7), and Costeley's Seigneur Dieu (see above, §1(ii)), both clearly set up to end lower than they began. This may also apply to the repertory of ‘secret chromatic’ motets (Lowinsky, 1946), a hypothesis that has generated controversy on grounds of modern ideals of tonal stability and minimal intervention. Often convincing on purely musical grounds, many of Lowinsky's solutions were supported by extra-musical theory and considerations of textual content which led him to disqualify some musically similar compositions (for an example by Obrecht see, among others, Lowinsky, 1972, Bent, 1984, and Berger, 1987).
For the period from the mid-15th century onwards, lute and other instrumental tablatures are in principle interval-specific, and have been applied to support views of the intended musical results in vocal models (Apel, 1942; Brown, 1971; Toft, 1992; Newcomb, 1997). This extremely rich evidence needs to be used with some caution. Chronological and geographical lag between original and arrangement may restrain a literal application, not to mention varying competence by intabulators that sometimes yields incompletely edited results. Intabulators may apply eccentric performers' licence but, above all, chordally conceived instrumental solutions cannot necessarily be carried over into vocal practice, approached by singers with a linear-hexachordal training accustomed to making contrapuntally-based adjustments. The sometimes necessary sacrifice of line to chord in contrapuntal polyphony is often exaggerated on a chordal instrument.
Musica ficta, §3: Practical application
The accidental signs that found their way on to the pages of manuscripts and prints include pitches that fall within the system of musica recta as well as many that lie outside it. Additional inflections required in performance similarly include both recta and ficta notes. It is therefore not correct to equate musica ficta simply with added accidentals.
Most scholars accept that inflections were and should be applied according to partly or largely unnotated tradition, but this view has been challenged by some scholars (Harden, 1983; Brothers, 1997) who observe that theorists often notate inflections in their treatise examples and say nothing about an unwritten tradition. Slight direct and indirect support for such a tradition might be drawn from quotations such as the following, from Arnulf of St Ghislain's Tractatulus (c1400; trans. C. Page, JRMA, cvii, 1992, pp.1–21), f.67v: ‘Who will not marvel to see with what expertise in performance some musical relationship, dissonant at first hearing, sweetens by means of their skilful performance and is brought back to the pleasantness of consonance?’ Another interpretation of Prosdocimus's rule against using ficta except where necessary (see above, §2(iii)) is: ‘do not usually write it in but leave it to the performer's initiative’. This reading has some confirmation from his explicit abhorrence that over-notation might incur as many signs as notes (ed. Herlinger, 1984, pp.78–9). An often-quoted and mistranslated passage can now be invoked (as translated by Leofranc Holford-Strevens, cited in Blackburn, 1998, p.635) to support unnotated inflection: ‘But these are frequently present virtually in B fa B mi although not always notated’ (Berkeley MS, I.1, ed. Ellsworth, 1984, p.45). Tinctoris (Liber de natura et proprietate tonorum, 1476) brands as asinine the unnecessary notation of flats to correct melodic tritones (see above, §2(iii)), and his own examples do not always notate the inflections called for by his text. Aaron (Toscanello in musica, 1529) endorses the role of performers as divining the ‘secret intent of the composer’. Although it is commonly alleged that he advocates the full notation of accidentals in general, the polyphonic contexts of his examples, cited as single parts from known pieces, show that he has chosen situations where, as he says, arrivals on simultaneities cannot be anticipated, and where without the help of the signs the singers might first commit error by not perfecting the intervals, clearly implying that the help he recommends was not always forthcoming (Bent, JM, 1994). But by 1600 full notation was largely in place.
13th-century theorists already defined signs for notating musica ficta on the staff. Johannes de Garlandia said that each tone is divisible into two semitones, which can be notated by the ‘signs of semitones’ (CoussemakerS, i, 166). Lambertus prescribed and b for the points at which mutations are to be made (CoussemakerS, i, 258). The ‘signs of musica ficta’ are called neither chromatic nor (until the 16th century) accidentals. For most of our period, they are simply the signs of ‘hard’ B (b) and ‘soft’ B (), the signs of mi and fa – in other words, semitone boundaries, not indeed confined to fictive notes outside the recta gamut. Theorists up to and including Prosdocimus and Ugolino (first half of the 15th century) admitted only these two signs, to distinguish the soft and hard forms of B. The exception is Marchetto (Lucidarium, 1317 or 1318), who used a sign to distinguish the semitone step F–F from the smaller mi-fa semitone F–G. Although scribes used either or for the hard B, the distinction seems rarely to have been meaningful. Occasionally the letters F, C and G are used instead of the sign to indicate the soft forms of those pitches. The 14th century saw an increase in marked accidentals until, around 1400, D, D, G, A and G are specifically notated and intended in certain sophisticated repertories such as those of the Chantilly and Old Hall manuscripts. Other sources remained very sparing in their indications, and there is a general decline in the number and range indicated from about 1400 onwards.
Before 1450, few theorists directly admit that or b necessarily cause individual pitch inflection. Those who do include Petrus frater dictus Palma ociosa (ed. J. Wolf, SIMG, xv, 1913–14, pp.504–34) and the author of the Berkeley treatise. But for most theorists b simply denotes mi, and fa; that is, they indicate where the semitone lies in relation to the sign. The signs express a relationship, not absolute pitches within a system. Most theorists explain the alteration of tone and semitone in the melodic context of its hexachordal access, and avoid saying that b raises or that lowers an individual note from a fixed place. ( on F or b on B, for example, rarely do anyway.) Rather, the sign increases or diminishes the (linear) ascent or descent (‘ lessens the ascent and b augments it’: Prosdocimus, ed. Herlinger, 76–7; ‘on la sol la [A G A] the sol should be raised and sung as fa mi fa': Johannes de Muris, CoussemakerS, iii, 73). The coniuncta is simply the moment of change at which the singer sings a semitone for a tone, or vice versa.
In rare cases (Ugolino's treatise and some practical examples), notated mi or fa may be used to bring not the signed note but its neighbour to a semitone distance from it and not vice versa. A mi sign on F will usually mean that F is to be pronounced mi and that the interval F–G, instead of being a tone as in musica recta, will be sung as a semitone. Nearly always this means that F will be construed and sung as F, but occasionally the semitone interval, though notated in the same way, may have to be F–G, more normally notated with the fa sign on G, which could in some circumstances produce the same result as a mi sign on F (Bent, 1972; Hughes, 1972; Memelsdorff, 1999). Lebertoul's O mortalis homo (GB-Ob Can.misc.213, f.41v) has a G fa signature producing Fs (Brothers, 1997, pp.40ff). In the more rarely used signs further round the spiral in either direction, the signs on G or D may mean either flat/natural or natural/sharp, depending on context. Since any note is mutable in this way, a ‘two-position’ rather than a ‘three-position’ system is in operation. Any note may be mi or fa in relation to its neighbour, but which semitone is not necessarily defined. F fa can be in our terms F, F, or even F.
Although means of notation existed throughout the period, the usage of accidentals and signatures in musical manuscripts bears little relationship to modern notions of consistency; the placing of signs often seems casual or capricious. Some scribes placed the sign near, above or below the affected note, without regard for its alignment on the staff: this is particularly common in some late 14th- and early 15th-century Italian and south German sources. Other scribes placed it well in advance of – or even after or simply near – the note to which it applied. In view of the close connection between the ‘signs’ of musica ficta and the practice of solmization, such pre-placing may serve as an advance warning of mutation. Thus the progression fa–mi (between which no mutation can take place) is very often preceded, rather than divided, by the b sign indicating mi. A consequence of this (solmization) function of a sign is that it does not necessarily have longer validity than for the note to which it most directly refers. In some situations a larger context will be affected, but an accidental, written or not, may easily be overruled (for the sake of contrapuntal propriety) on subsequent appearances of the affected note. Tinctoris (Liber de natura et proprietate tonorum, 1476) says that the ‘signature flat’ at the beginning of the staff affects the whole segment for which it is given, but does not make it clear whether he means a segment of music or of staff; the ‘accidental’ flat, however, lasts as long as the hexachord segment (the deductio) before which it is placed – this indeed could be a very small local segment. Inconsistencies within pieces and between sources abound, from the Notre Dame manuscripts (ed. E.H. Roesner, Les quadrupla et tripla de Paris, Monaco, 1993, p.xc) to the 16th century. Most scholars see this as a consequence of their inessential notational status, early notation not being considered imperfect by its own standards; rather, that composers and notators expected singers to complement it on the basis of shared internalized contrapuntal training, as a literate reader can construe an unpunctuated text; and that the results of this process are largely recoverable as part of the implicit text and the intended sounding results (e.g. Bent, EMc, 1994, 1998; Cross, 1990). Others treat early notation as approaching the prescriptive force of modern notation, and the notated manuscript accidentals as (almost) self-sufficient; they therefore keep editorial ‘intervention’ to a minimum. Such face-value readings of notation, or the belief that singers were capable of applying only melodic rules, often conflicts with elementary counterpoint precepts, requiring the construction of a partly independent theoretical tradition to account for the resulting eccentricities (Harden, 1983; Hirshberg, 1996; Brothers, 1997).
Different versions of the same piece often notate different, though rarely conflicting, signs; proponents of an unnotated performing tradition usually seek to reconcile these as largely complementary explicit testimony to implicit practice; others see variants as indicators of different intended sounding results. Dahlhaus even believed that the notated counterpoint is largely abstract, and that the composer may have been indifferent to the actual sound (1969). At the other extreme, Cross believes that recoverable composers' intentions fully determine a single intended result, to the extent that she does not distinguish manuscript-authorized from editorial accidentals in the musical text of her edition of Machaut's Messe de Nostre Dame (New York, 1998). From a position closer to the latter, Bent (passim) holds that some intentions are largely recoverable from theorists’ own prioritization of rules, while leaving other inflections elective, dependent (as in the punctuation and rhetorical delivery of a text) on some latitude of interpretation and articulation by performers. If the notation of ‘accidentals’ was optional (‘accidental’), performers were expected to apply their training and knowledge of conventions to the realization of the under-notated music. By a combination of compositional and notational indicators, the composer could tease the performer to fulfil, sidestep or frustrate expectations. As in all repertories, there are cases where composers seem to defy standard contrapuntal precepts, but the number of such anomalies can be considerably reduced by situating them in relation to norms. Despite different emphases, scholars strive to reconcile theoretical, musical and source evidence. There is general agreement on the need to prioritize rules that frequently conflict, but disagreement remains as to how this should be done.
Musica ficta, §3: Practical application
Where flats are indicated at the beginning of the staves, the number often differs between voice parts of the same piece, the lower part or parts having, usually, one flat more than the upper (partial signatures, sometimes called conflicting or contrasting). From the top downwards, a three-part piece might have parts with signatures of —, —, B; —, B, B; B, B, B + E; B, B + E, B + E. They may come and go within a copy, or vary between sources, and their interpretation has been hotly debated. Apel claimed that they implied bitonality (1938); Hoppin proposed modal transposition, since they affect pitch levels about a 5th apart (1953, 1956). Lowinsky saw them as practical reflections of cadence structures in voices lying a 5th apart, the signature being omitted when no note of that pitch was required (1954). But this would suggest that the fear of a vertical imperfect octave was less than of an imperfect 5th (Berger, 1987, p.66); some theorists say the opposite. All these views accord the signature its modern significance of inflecting all notes written at that pitch level and perhaps of octave equivalents. But if B is available by recta in an unsignatured part, what is the purpose of flat signatures? The possibility remains that they denote the transposition of hexachord systems, especially since hexachords rather than modes form the basis of medieval discussions of ficta in polyphony (Lockwood, Grove6; Bent, 1972). If the hexachords on G, C and F are transposed one degree flatwards, in the case of a single flat in the signature the hexachords for that part will be on C, F and B, leaving two hexachords common to both a signatured and an unsignatured part, and thus a considerable range of recta notes, including B, which a simultaneous unsignatured part is perfectly free to use. If the whole part is in ficta, there would be no recta/ficta orientation to govern performers' choices. Such flatward transpositions of the hexachord system (with hexachords on B, F and C, making E readily available) may have been counted as transposed recta (not all agree), as distinct from the individual transpositions of ficta hexachords. Where there is a signature, the transposed recta priorities would be established for the duration of the signature, leaving the singer of a signatured part equally free to raise B for a leading note as to sing F in an unsignatured part. The distinction between applying chromatic alteration by means of transposition and by means of individual emendation does, after all, go back to the 11th-century theorists. The idea that a flat signature might effect downward transposition by a 5th of a combined recta and ficta system of hexachords was tentatively deduced from Ugolino (ii.48–50) by Bent (1972), extended with cognizance of the ambiguity by Hughes (1972), and dismissed without explanation of the abiding anomaly by Berger (1987). Aaron (Toscanello in musica, 1529) rejects the practice of partial signatures, along with the allegation that they help to avoid false 5ths, on the grounds that it confounds the interval species and the octaves.
One example of a piece involving sectional transposition by clef and flats is Pycard's Credo (Old Hall MS, no.76). There are occasional examples of signatures of E alone, and some progressively flattening pieces only sign the more extreme flats. There also exist about a dozen pieces, mostly from the 15th century, whose only clefs are flat signatures (fa signs) detached from letter names (the ‘less principal clefs’). The relationship between the parts is easily inferred; such pieces (preserved alongside ‘normal’ pieces) can be performed without the need to name the pitches, even though two flats a 5th apart might notionally be thought of as B and F (or E and B) in an upper part and E and B (or A and E) in a lower. Similar problems arise in canons notated on a single staff such as Ockeghem's Prenez sur moi, and in his Missa cuiusvis toni, notated without letter-clefs and capable of more than one resolution (for bibliography on these works see Ockeghem, Jean de).
A few rare cases of sharp signatures date mostly from the 14th century, and sharps occur frequently as accidentals. By the late 15th century notated sharp signs, on the other hand, become quite rare. Sharp signatures are used for rare examples of canon at the 5th, as in Ockeghem's Prenez sur moi and in Willaert's Musica nova (1559). From 1540 on, especially in Italian prints, the sharp sign becomes more frequent, but its placing is still free and sometimes ambiguous. Harrán (1976, 1978, following Kroyer, 1902; see also Ficker, 1914) proposed an ingenious but flawed interpretation of sharps as ‘cautionary signs’ with the opposite of their normal meaning, in order to overcome certain types of false relations in note nere Venetian madrigals of the 1540s. Instead of confirming an expected inflection, the signs are alleged to warn the singer not to inflect. Godt (1978, 1979: see under Harrán, 1976) challenged this view on logical, historical and musical grounds. Some of the problems which his hypothesis addressed can be overcome by recognizing verbal boundaries and permitting F to follow F after a sense break; the same is true of the problems in Willaert discussed (also without text) by Lockwood (1968).
The normal sign for the sharp is , but variants of this sign appear. The sign , which had been the traditional sign for B quadratum in contradistinction to B rotundum, returned around 1540 as a distinctive symbol and attained its modern meaning; Einstein (The Italian Madrigal, 1949, i, 412) noted its use in a Vicentino madrigal collection of 1542.
13th-century theorists gave reasons both of consonance and melody, stressing perfect vertical consonances on 5ths, octaves and other perfect intervals (Lambertus, CoussemakerS, i, 258) and requiring ‘leading notes’ to be a semitone from their destination (Garlandia, CoussemakerS, i, 115). These principles were more fully expounded in the 14th century, most clearly by Johannes de Muris, who stated that, for melodic progressions, lower returning notes (e.g. in the progression G–F–G) should be raised (G–F–G); and that leading notes approached by any other means (e.g. by leap) should be raised (e.g. D–F–G; CoussemakerS, iii, 71–3). This is also implied by the author of the Quatuor principalia (CoussemakerS, iv, 250), who gave the widespread prohibition of mi against fa in vertical perfect intervals and stated that a perfect interval should be approached by the nearest imperfect interval: a major 3rd will expand to a 5th, a major 6th to an octave, a minor 3rd will contract to a unison, and so on; where one part proceeds by step, it will be a semitone (ex.1a–b). The so-called double leading-note cadence of ex.2a results from the superimposition of the two-part progressions exx.2b and 2c; it has nothing to do with perfecting the vertical 4th, which was not during this period considered a perfect interval for purposes of counterpoint, despite its acoustical status. As the 15th century progressed, composers cultivated different cadence forms; not to sharpen the third in ex.2a may avoid angularity but evades real issues of cadence structure (Dahlhaus, Untersuchungen, 1968, pp.75–6; Eng. trans., 340–41).
Theorists of the 13th to 15th centuries said surprisingly little about the melodic interval of the tritone, although it was disqualified in earlier chant treatises. Prosdocimus's music examples observe the leading-note principle even when the leap preceding it has to be a tritone. An anonymous 15th-century theorist from Seville (Gallo, 1968) did state explicitly that melodic tritones should be avoided when they return within their own confines, that is, when they are not ancillary to an upward-resolving leading note; this rule became common from then on. In his treatise on the modes, Liber de natura et proprietate tonorum (1476; chap.8, on the 6th tone), Tinctoris made clear that in practice the F modes, properly formed with B, often require singers to use B to mollify such tritone outlines. But in order to establish priority between conflicting rules of correction he introduced into this treatise on modes in chant a surprising and isolated detour into considerations of polyphony, showing that in two-part writing the correction of simultaneous 5ths must take a higher priority than tritone correction. The melodic tritone should be corrected, except where this would result in a false simultaneity. The tritone is suffered only for such intervallic correction, not for modal integrity. His famous comment that notation of obvious Bs for tritone avoidance is asinine should not be applied incautiously to the notation of all accidentals. He corroborates the priority of vertical correction over tritone avoidance also for other modes, and his examples use naturals to confirm that. The tritone is easier to sing mediated than as a direct leap.
Two commonly cited rules of musica ficta originate from the 16th century or even later. Although both are expressed in solmization syllables, they betray internally the decay of that tradition. The jingle ‘una nota super la semper est canendum fa’ (‘a note above la is always to be sung fa’; not attested in that form before Praetorius, Syntagma musicum, iii, 1618) itself denies the medieval semitone definition of mi–fa. It is understood to mean that the top of a phrase bounded by a 6th or a 4th or even a tone which descends within itself (D, F or A up to B and down again) should be rounded off so that the boundary interval is a minor 6th, a perfect 4th or a semitone; earlier theorists expressed it more precisely in terms of melodic tritone avoidance.
The other famous jingle, ‘mi contra fa est diabolus in musica’ (‘mi against fa is the devil in music’), short-circuits to a sobriquet for the diabolic tritone (properly the augmented 4th, which was not, at that time, synonymous with the diminished 5th), and lacks essential qualifiers. Both of the above are anachronistic, even for the 16th century, and need to be replaced by more careful formulations. For example, the widespread prohibition of sounding mi against fa (mi contra fa) is often quoted without two qualifications which alone make sense of it, given to its older formulation by medieval writers from the fully functioning hexachordal tradition: the rule applies only in perfect intervals (i.e. 5ths and octaves, understood as arrival points) and in counterpoint (i.e. between parts that are in dyadic contrapuntal relationship, not just anywhere in the texture).
Many attempts have been made to compile theorists’ rules for musica ficta; these have naturally varied according to the priorities observed by individual scholars and their different readings of various theorists.
For many years, the most thorough account was by Lowinsky (1964), who equated with necessity (causa necessitatis): I.1, the prohibition of the simultaneous sounding of mi against fa, interpreted as diminished octaves and 5ths between (any) two simultaneously sounding voices; I.2, the ‘una nota super la’ rule (see above) to prevent a linear tritone when a line ascends above the syllable la (Aaron, Lucidario, 1545, showed that this was by no means a universally applicable doctrine); and I.3, the prohibition of false relations. Under the heading causa pulchritudinis Lowinsky included: II.1, the raising of the leading note at cadential formulae; II.2, the rule of propinquity, that is, approaching a perfect consonance in two voices by the nearest imperfect consonance; and II.3, the rule of ending on a complete triad (according to Lowinsky this was known only in the 16th century).
However, this classification represents a conflation and does not prioritize the rules to address their frequent conflicts. Necessity interpreted as the correction of consonances was indeed historically associated with I.1, but also with II.1 and II.2, because the approach (e.g. from 6th to octave) encapsulates the defining mi–fa or fa–mi progression (e.g. G–A or B–A) by which the perfect interval is reached (Bent, 1972). I.2 was not so formulated by theorists until the solmization system (whose raison d'être was the mi-fa semitone) had atrophied; irrespective of the solmization in which it is expressed, this formulation does not address how it should be reconciled with I.1 when, as often happens, they conflict. I.3 has been understood to apply not only to simultaneous but also oblique false relations, which are not explicitly discouraged until Zarlino and are often artfully exploited in earlier music; this rule can be subsumed under a more precise formulation of I.1, but it cannot be avoided all the time.
Aaron referred to ‘ordinary and special rules devised by musicians’; his prioritization of rules in the supplement to Toscanello in musica can be inferred from his examples and commentary (Bent, JM, 1994, pp.324–5). He indeed, like Tinctoris, adjusts the melodic tritone when it returns within itself, but will tolerate it in the interests of achieving a simultaneous perfect 5th or octave, which, especially between lower parts and on strong beats, always takes priority over melodic correction. Quoting a passage from the bass part of the third Agnus Dei of Josquin's Missa ‘L'homme armé’ super voces musicales (ex.3), Aaron explains that the tritone f–b cannot be changed to f–b since that in turn would cause a diminished 5th b–e: ‘thus the singer will be obliged to sing the harsh tritone for the sake of that interval [a 5th] or rather that syllable which occurs in the position of hypatē mesōn, called E la mi; because in order to accommodate the interval in the most convenient way, he is forced to break the rule’.
There remains considerable disagreement as to how the theoretical and musical evidence should be calibrated and interpreted. Urquhart argues (passim) that rules affecting simultaneities, such as the mi contra fa prohibition, are directed at composers, and that singers were able only to apply melodic principles. Bent suggests that performers could, by contrapuntal training, rehearsal and aural anticipation (aided by lateral displacement and suspension in composed music), balance and prioritize the claims of (1) simultaneous combinations and (2) melodic smoothness (Bent, 1984, EMc, 1994, 1996). Both accept false relations caused by cadential collisions (see also, for example, Boorman, 1990; Bray, 1970–71, 1978), Bent on grounds that in earlier music they usually arise between parts not governed by the prohibition, and in later music were sometimes excepted by theorists; Urquhart shows a wider tolerance for other kinds of contrapuntal dissonance. The quest for viable solutions that meet both theoretical and practical criteria continues; it will always be hampered by our unavoidable oral and aural disconnection with the music as heard and intended in its own time.
By the early 17th century the practice of musica ficta in the current sense, that is, the introduction during performance of unnotated chromatic alterations according to a set of commonly accepted principles, had largely become obsolete, except occasionally among certain circles of musicians, such as Roman church choirs, whose repertories also continued to include earlier, 16th-century polyphony (see S.R. Miller: Music for the Mass in Seventeenth-Century Rome, diss., U. of Chicago, 1998, p.448). In spite of that, scores continued to include many notes that lacked accidental signs but nevertheless required alteration. Until the later 18th century, when modern conventions fell more or less into place (for instance, an accidental remains in force to the end of the bar), notational practices were far from uniform and often show an unpredictable mixture of older and newer habits, but the most common circumstances in which accidentals were omitted are described below.
To begin with, there remained as legacy from the Renaissance a somewhat casual attitude towards the notation of accidentals, which may in part be responsible for the current misapprehension that musica ficta continued to be practised well after 1600. When working under pressure, copyists are more likely to commit errors of omission than errors of commission, and during the early 17th century they were more likely to omit a sharp or a flat sign than an entire note. This did not represent a musica ficta practice, as the omissions follow no systematic or consistent pattern and largely correlate with the overall lack of accuracy of the text. In carefully prepared autographs, presentation copies or engraved prints, omissions of clearly necessary accidentals tend to be rare; they are much more frequent in manuscripts that show other signs of hasty copying or in prints using movable type (which often harbour errors of all kinds). The editorial procedure for supplying unintentionally omitted accidentals is, nevertheless, to some extent similar to the guidelines followed for adding musica ficta, including the ‘correction’ of certain diminished or augmented intervals and cadential chord progressions, although, even more than with the earlier practice, caution must be exerted not to subvert intended expressive effects.
The casual attitude towards the notation of accidentals extended to their positioning. During the Middle Ages and the Renaissance an accidental had often appeared well ahead (i.e. to the left) of the note that was supposed to be altered, and was understood to indicate a shift in the hexachord governing the entire passage rather than the raising or lowering of an individual pitch. By the early 17th century such distant placement had become rare, but accidentals were sometimes positioned above, below or somewhere else in the general vicinity, particularly when there was insufficient space immediately to the left of the note. Certain scholars have pointed to situations where accidentals even appear to have been placed after (to the right of) a note, and dubbed these seemingly backward-acting signs ‘retrospective accidentals’. Most often the accidental is followed by another note at the same pitch (ex.4 presents a typical situation) and, since these omissions are not consistent, it might make more sense to regard them as instances of the casual practice described earlier than of a curious, backward-reading convention.
The question that arises most frequently with early scores is whether a notated accidental applies only to the note that immediately follows or also to subsequent notes of the same pitch. In this regard a fairly wide range of practices is encountered, and the editor or performer is challenged to determine which is applicable. At one extreme, the accidental applies only to the note that follows; every note that needs to be inflected is given its own appropriate accidental, including repeated notes. Under this policy cancellation signs are superfluous and generally not supplied; as a result there is a danger of misreading chromatic passages such as shown in ex.5. This extreme practice is rarely encountered after the very early 1600s. Usually, an accidental remains in force for notes that are immediately repeated, sometimes also during ornamental subdivisions of a beat such as written-out trills, or even over a more extended passage, possibly continuing across a bar-line. Cancellation signs (still most often in the form of sharps to cancel flats and flats to cancel sharps: ex.6) continued to be rarely used except to cancel accidentals prescribed by key signatures, and editors or performers thus need to judge the range of action of an accidental on the basis of musical context, relevant stylistic practice, and notational habits followed elsewhere in the score.
Modern editions often include far more editorial accidentals than 17th-century taste would have demanded. This may be due in part to the aforementioned misguided application of musica ficta practice, but sometimes also to an attempt to make the work conform to later principles of major/minor tonality. In early 17th-century music (as in 20th-century jazz practice) degree inflections are usually determined by the local harmony (that is, the underlying chord and sometimes the chord that follows) rather than by the key or mode of the entire passage. Close juxtaposition of major and minor forms of a chord and various types of cross-relation – not excluding vertical major–minor clashes – were favoured expressive devices; they were to become much rarer towards the end of the century without, however, vanishing altogether. Still in the 1660s a composer such as Matthias Weckmann liked to exploit such devices, which by this time had become unusual enough that he felt a need to confirm his intentions with special warning signs (see the ‘+’ signs as well as ‘NB’ by the two conflicting pitches in ex.7); despite these signs, a 20th-century editor of the work changed the A in the second violin part to an A.
Unnotated accidentals often do need to be added by the performer when executing ornaments such as trills and mordents, and also when realizing figured basses. The notating of degree inflection in bass figures was ruled by conventions that varied strongly with time and place, and the modern principle that the realization must observe the key signature unless the figures prescribe otherwise does not always apply. For example, in many 17th-century continuo basses the 5th is always to be played perfect, regardless of the key signature, unless the figure 5 with a sharp or a flat (or a slash across the figure) appears above the bass, even if in those same basses the 3rd is to be played major or minor according to the key signature (unless contradicted by a figure). Another almost universal convention is that the final chord of a movement or a section should be played as a major chord, regardless of what is implied by the signature; the required alteration is almost never noted in the figures, although it may be indicated in the other parts when those include the 3rd of the chord.
HDM2 (W. Apel)
MGG1 (‘Laurentius de Florentia’; N. Pirrotta)
MGG2 (‘Musica ficta’, §B; P.W. Urquhart)
RiemannG
SpataroC
C.-E.-H. de Coussemaker: Histoire de l'harmonie au Moyen Age (Paris, 1852), 295–349
A. de La Fage: Essais de diphthérographie musicale (Paris, 1864/R)
G. von Tücher: ‘Zur Musikpraxis und Theorie des 16. Jahrhunderts, v: Accidentien und Musica ficta’, AMZ, new ser., viii (1873), 1–6, 17–21, 33–7, 49–54, 65–9, 81–7, 129–33, 161–5, 177–82, 193–6, 209–16
R. Schlecht: ‘Über den Gebrauch des Diesis im 13. u. 15. Jahrhundert’, MMg, ix (1877), 79–98, 99–108
R. Hirschfeld: ‘Notizien zur mittelalterlichen Musikgeschichte (Instrumentalmusik und Musica ficta)’, MMg, xvii (1885), 61–7
P. Spitta: ‘Die Musica Enchiriadis und ihre Zeitalter’, VMw, v (1889), 443–82
G. Jacobsthal: Die chromatische Alteration im liturgischen Gesang der abendländischen Kirche (Berlin, 1897/R)
W. Schmidt: Die Calliopea legale des Johannes Hothby (Leipzig, 1897)
T. Kroyer: Die Anfänge der Chromatik im italienischen Madrigal des XVI. Jahrhunderts (Leipzig, 1902/R)
J. Wolf: Geschichte der Mensural-Notation von 1250–1460 (Leipzig, 1904/R), i, 109ff
A. Einstein: ‘Claudio Merulo's Ausgabe der Madrigale des Verdelot’, SIMG, viii (1906–7), 220–54, 516 only
H. Riemann: Verloren gegangene Selbstverständlichkeiten der Musik des 15. und 16. Jahrhunderts (Langensalza, 1907)
E. Wilfort: ‘Glareans Erwiderung’, ZIMG, x (1908–9), 337–41
IMusSCR III: Vienna 1909 [incl. articles by E. Bernoulli, O. Chilesotti, T. Kroyer, R. Schwartz, J. Wolf]
R. von Ficker: ‘Beiträge zur Chromatik des 14. bis 16. Jahrhunderts’, SMw, ii (1914), 5–33
K. Dèzes: Prinzipielle Fragen auf dem Gebiet der fingierten Musik (diss., Humboldt U., Berlin, 1922)
K. Jeppesen: Palestrinastil med saerligt henblik paa dissonansbehandlingen (Copenhagen, 1923; Eng. trans., 1927, 2/1946/R as The Style of Palestrina and the Dissonance)
E. Frerichs: ‘Die Accidentien in Orgeltabulaturen’, ZMw, vii (1924–5), 99–106
K. Jeppesen, ed.: Der Kopenhagener Chansonnier (Copenhagen, 1927, 2/1965)
W. Apel: ‘Accidentals and the Modes in 15th- and 16th-Century Sources’, BAMS, ii (1937), 6–7
W. Apel: Accidentien und Tonalität in den Musikdenkmälern des 15. und 16. Jahrhunderts (Strasbourg, 1937/R)
W. Apel: ‘The Partial Signatures in the Sources up to 1450’, AcM, x (1938), 1–14 [see also postscript, AcM, xi (1939), 40–42]
J.S. Levitan: ‘Adrian Willaert's Famous Duo Quidnam ebreitas’, TVNM, xv/3 (1938), 166–92; xv/4 (1939), 193–233
C.W. Fox: ‘Accidentals in Vihuela Tablatures’, BAMS, iv (1940), 22–4
W. Apel: The Notation of Polyphonic Music, 900–1600 (Cambridge, MA, 1942, 5/1961; Ger. trans., rev., 1970), 104ff, 120
H. Hewitt, ed.: Harmonice musices odhecaton A (Cambridge, MA, 1942/R), 16
L. Hibberd: ‘Musica ficta and Instrumental Music, c1250–c1350’, MQ, xxviii (1942), 216–26
E.E. Lowinsky: ‘The Goddess Fortuna in Music, with a Special Study of Josquin's Fortuna d'un gran tempo’, MQ, xxix (1943), 45–77
E.E. Lowinsky: ‘The Function of Conflicting Signatures in Early Polyphonic Music’, MQ, xxxi (1945), 227–60
M. van Crevel: ‘Secret Chromatic Art in the Netherlands Motet?’, TVNM, xvi/4 (1946), 253–304
E.E. Lowinsky: Secret Chromatic Art in the Netherlands Motet (New York, 1946/R)
L. Schrade: ‘A Secret Chromatic Art’, JRBM, i (1946–7), 159–67
M. Johnson: ‘A Study of Conflicting Key-Signatures in Francesco Landini's Music’, Hamline Studies in Musicology, ed. E. Krenek, ii (Minneapolis, 1947), 27–40
J. Smits van Waesberghe, ed.: Johannes Afflighemensis [Cotto]: De musica cum tonario, CSM, i (1950)
R. Hoppin: ‘Partial Signatures and Musica ficta in some Early 15th-Century Sources’, JAMS, vi (1953), 197–215
H. Anglès: Introductions to Cristóbal de Morales: Opera omnia, iii, v, MME, xv (1954); xx (1959)
E.E. Lowinsky: ‘Conflicting Views on Conflicting Signatures’, JAMS, vii (1954), 181–204
S. Clercx: ‘Les accidents sous-entendus et la transcription en notation moderne’, L'Ars Nova: Wégimont II 1955, 167–95
K. Levy: ‘Costeley's Chromatic Chanson’, AnnM, iii (1955), 213–63
G. Reaney: ‘Musica ficta in the Works of Guillaume de Machaut’, L'Ars Nova: Wégimont II 1955, 196–216
R. Hoppin: ‘Conflicting Signatures Reviewed’, JAMS, ix (1956), 97–117
E.E. Lowinsky: ‘Adrian Willaert's Chromatic “Duo” Re-Examined’, TVNM, xviii/1 (1956), 1–36
E.E. Lowinsky: ‘Matthaeus Greiter's Fortuna: an Experiment in Chromaticism and in Musical Iconography’, MQ, xlii (1956), 500–19; xliii (1957), 68–85
L. Spiess: ‘The Diatonic “Chromaticism” of the Enchiriadis Treatises’, JAMS, xii (1959), 1–6
A. Seay, ed.: Ugolino of Orvieto: Declaratio musicae disciplinae, CSM, vii (1959–62)
E.E. Lowinsky: Tonality and Atonality in Sixteenth-Century Music (Berkeley, 1961)
G. Haydon: ‘The Case of the Troublesome Accidental’, Natalicia musicologica Knud Jeppesen septuagenario collegis oblata, ed. B. Hjelmborg and S. Sørensen (Copenhagen, 1962), 125–30
C. Dahlhaus: ‘Zu Costeleys chromatischer Chanson’, Mf, xvi (1963), 253–65
E.E. Lowinsky: Introduction to Musica nova, ed. H.C. Slim, MRM, i (1964), pp.xiii-xxi
G. Massera: ‘Musica inspettiva e accordatura strumentale nelle Scintille di Lanfranco da Tarenzo’, Quadrivium, vi (1964), 85–105
G. Reaney, A. Gilles and J. Maillard, eds.: P. de Vitry: Ars nova, CSM, viii (1964)
L. Lockwood: ‘A Dispute on Accidentals in Sixteenth-Century Rome’, AnMc, no.2 (1965), 24–40
H. Kaufmann: ‘A “Diatonic” and a “Chromatic” Madrigal by Giulio Fiesco’, Aspects of Medieval and Renaissance Music: a Birthday Offering to Gustave Reese, ed. J. LaRue and others (New York, 1966), 474–84
A. Seay: ‘The 15th Century Coniuncta: a Preliminary Study’, Aspects of Medieval and Renaissance Music: a Birthday Offering to Gustave Reese, ed. J. LaRue and others (New York, 1966), 723–37
R.L. Crocker: ‘A New Source for Medieval Music Theory’, AcM, xxxix (1967), 161–71
E.E. Lowinsky: Introduction to O. Petrucci: Canti B, ed. H. Hewitt, MRM, ii (1967), pp.ix-xiv
A. Seay, ed. and trans.: Johannes de Grocheo: Concerning Music (Colorado Springs, CO, 1967, 2/1973)
C. Dahlhaus: Untersuchungen über die Entstehung der harmonischen Tonalität (Kassel, 1968; Eng. trans., 1990, as Studies on the Origin of Harmonic Tonality)
C. Dahlhaus: ‘Zur Akzidentiensetzung in den Motetten Josquins des Prez’, Musik und Verlag: Karl Vötterle zum 65. Geburtstag, ed. R. Baum and W. Rehm (Kassel, 1968), 206–19
F.A. Gallo: ‘Alcune fonti poco note di musica teorica e pratica’, L'Ars Nova italiana del Trecento: convegni di studio 1961–1967, ed. F.A. Gallo (Certaldo, 1968), 49–76
C.G. Jacobs: ‘Spanish Renaissance Discussion of Musica ficta’, Proceedings of the American Philosophical Society, cxii (1968), 277–98
E. Kottick: ‘Flats, Modality and Musica ficta in some Early Renaissance Chansons’, JMT, xii (1968), 264–80
L. Lockwood: ‘A Sample Problem of musica ficta: Willaert's Pater noster’, Studies in Music History: Essays for Oliver Strunk, ed. H. Powers (Princeton, NJ, 1968), 161–82
E.E. Lowinsky: ‘Echoes of Adrian Willaert's Chromatic “Duo” in Sixteenth- and Seventeenth-Century Compositions’, ibid., 183–238
P. Aldrich: ‘An Approach to the Analysis of Renaissance Music’, MR, xxx (1969), 1–21
K.P. Bernet Kempers: ‘Accidenties’, Renaissance-muziek 1400–1600: donum natalicium René Bernard Lenaerts, ed. J. Robijns and others (Leuven, 1969), 51–9
C. Dahlhaus: ‘Tonsystem und Kontrapunkt um 1500’, JbSIM 1969, 7–18
Andrew Hughes: ‘Ugolino: the Monochord and Musica ficta’, MD, xxiii (1969), 21–39
M. Huglo: ‘L'auteur du “Dialogue sur la musique” attribué à Odon’, RdM, lv (1969), 119–71
G. Reaney: ‘Accidentals in Early Fifteenth-Century Music’, Renaissance-muziek 1400–1600: donum natalicium René Bernard Lenaerts, ed. J. Robijns and others (Leuven, 1969), 223–31
D. Crawford: ‘Performance and the Laborde Chansonnier: Authenticity of Multiplicities: Musica ficta’, College Music Symposium, x (1970), 112–13
F.J. Smith: ‘“Accidentalism” in Fourteenth-Century Music’, RBM, xxiv (1970), 42–51
R. Bray: ‘The Interpretation of Musica ficta in English Music c.1490–c.1580’, PRMA, xcvii (1970–71), 29–45
H.M. Brown: ‘Accidentals and Ornamentation in Sixteenth-Century Intabulations of Josquin's Motets’, Josquin des Prez: New York 1971, 475–522
M. Huglo: ‘Der Prolog des Odo zugeschriebenen “Dialogus de musica”’, AMw, xxviii (1971), 134–46
P. Doe: ‘Another View of Musica ficta in Tudor Music’, PRMA, xcviii (1971–2), 113–22
G.G. Allaire: The Theory of Hexachords, Solmization and the Modal System, MSD, xxiv (1972)
M. Bent: ‘Musica recta and Musica ficta’, MD, xxvi (1972), 73–100
Andrew Hughes: Manuscript Accidentals: Ficta in Focus, 1350–1450, MSD, xxvii (1972)
E.E. Lowinsky: ‘Secret Chromatic Art Re-Examined’, Perspectives in Musicology, ed. B.S. Brook, E.O.D. Downes and S. Van Solkema (New York, 1972), 91–135
E. Reimer, ed.: Johannes de Garlandia: De mensurabili musica (Wiesbaden, 1972)
O. Ellsworth: ‘The Origin of the Coniuncta: a Reappraisal’, JMT, xvii (1973), 86–109
H. Tischler: ‘“Musica ficta” in the Thirteenth Century’, ML, liv (1973), 38–56; also pubd in IMSCR XI: Copenhagen 1972, 695–6
D. Harrán: ‘New Evidence for Musica ficta: the Cautionary Sign’, JAMS, xxix (1976), 77–98 [see also I. Godt, JAMS, xxxi (1978), 385–8; D. Harrán, JAMS, xxxi (1978), 388–95; I. Godt, JAMS, xxxii (1979), 364–7]
J. Haar: ‘False Relations and Chromaticism in Sixteenth-Century Music’, JAMS, xxx (1977), 391–418
B.J. Harden: ‘Musica ficta in Machaut’, EMc, v (1977), 473–7
R.E. Voogt: ‘Musica ficta According to Johannes Tinctoris’, Journal of the Graduate Music Students at the Ohio State University, vi (1977), 6–23
R. Bray: ‘16th-Century musica ficta: the Importance of the Scribe’, JPMMS, i (1978), 57–80
C.V. Palisca, ed.: Hucbald, Guido, and John on Music: Three Medieval Treatises (New Haven, CT, 1978)
R. Samuel: Modality, Tonality and Musica ficta in the Sixteenth-Century Chanson (diss., Washington U., 1978)
A. Seay, ed.: Anonymus 2: Tractatus de discantu (Colorado Springs, CO, 1978)
J. van Benthem: ‘Fortuna in Focus: Concerning “Conflicting” Progressions in Josquin's Fortuna d'un gran tempo’, TVNM, xxx (1980), 1–50
K. Berger: Theories of Chromatic and Enharmonic Music in Late Sixteenth Century Italy (Ann Arbor, 1980)
J. Hirshberg: ‘Hexachordal and Modal Structure in Machaut's Polyphonic Chansons’, Studies in Musicology in Honor of Otto E. Albrecht, ed. J.W. Hill (Kassel, 1980), 19–42
H. Schmid, ed.: Musica et Scolica enchiriadis, una cum aliquibus tractatulis adiunctis (Munich, 1981)
T. Noblitt: ‘Chromatic Cross-Relations and Editorial Musica ficta in the Masses of Obrecht’, TVNM, xxxii (1982), 30–44
R.C. Vogel: ‘The Musical Wheel of Domingo Marcos Durán’, College Music Symposium, xxii/2 (1982), 51–66
B.J. Harden: Sharps, Flats, and Scribes: ‘Musica ficta’ in the Machaut Manuscripts (diss., Cornell U., 1983)
M. Bent: ‘Diatonic ficta’, EMH, iv (1984), 1–48
H.M. Brown: ‘La musica ficta dans les mises en tablatures d'Albert de Rippe et Adrian Le Roy’, Le luth et sa musique, ii, ed. J.-M. Vaccaro (Paris, 1984), 163–82
O.B. Ellsworth, ed.: The Berkeley Manuscript, University of California Music Library, MS.744 (olim Phillipps 4450), GLMT (1984)
J. Herlinger, ed.: Prosdocimus de Beldemandis: Contrapunctus, GLMT (1984)
N.C. Phillips: Musica and Scolica enchiriadis: the Literary, Theoretical, and Musical Sources (diss., New York U., 1984)
J. Caldwell: ‘Musica ficta’, EMc, xiii (1985), 407–8
N. Routley: ‘A Practical Guide to Musica ficta’, EMc, xiii (1985), 59–71
D. Pesce: ‘B-flat: Transposition or Transformation?’, JM, iv (1985–6), 330–49
K. Berger: Musica ficta: Theories of Accidental Inflections in Vocal Polyphony from Marchetto da Padova to Gioseffo Zarlino (Cambridge, 1987)
D. Pesce: The Affinities and Medieval Transposition (Bloomington, IN, 1987)
D. Zager: ‘From the Singer's Point of View: a Case Study in Hexachordal Solmization as a Guide to Musica recta and Musica ficta in Fifteenth-Century Vocal Music’, CMc, no.43 (1987), 7–21
B.R. Carvell: ‘Notes on “una nota super la”’, Music from the Middle Ages through the Twentieth Century: Essays in Honor of Gwynn S. McPeek, ed. C.P. Comberiati and M.C. Steel (New York, 1988), 94–111
R. Killam: ‘Solmization with the Guidonian Hand: a Historical Introduction to Modal Counterpoint’, Journal of Music Theory Pedagogy, ii (1988), 251–73
R. Toft: ‘Traditions of Pitch Content in the Sources of Two Sixteenth-Century Motets’, ML, lxix (1988), 334–45
P.W. Urquhart: Canon, Partial Signatures, and ‘Musica ficta’ in Works by Josquin Desprez and his Contemporaries (diss., Harvard U., 1988)
A. Gilles: ‘De musica plana breve compendium: un témoignage de l'enseignement de Lambertus’, MD, xliii (1989), 33–62
S. Boorman: ‘False Relations and the Cadence’, Essays on Italian Music in the Cinquecento, ed. R. Charteris (Sydney, 1990), 221–64
L.E. Cross: Chromatic Alteration and Extrahexachordal Intervals in Fourteenth-Century Polyphonic Repertories (diss., Columbia U., 1990)
K.-W. Gümpel: ‘Gregorianischer Gesang und Musica ficta: Bemerkungen zur spanischen Musiklehre des 15. Jahrhunderts’, AMw, xlvii (1990), 120–47
B. Sydow-Saak: ‘Musica falsa/musica ficta’ (1990), HMT
M.Y. Fromson: ‘Cadential Structure in the Mid-Sixteenth Century: the Analysis Approaches of Bernhard Meier and Karol Berger Compared’, Theory and Practice, xvi (1991), 179–213
C. Page: The Summa musice: a Thirteenth-Century Manual for Singers (Cambridge, 1991)
D. Stern: The Use of Accidental Inflections and the Musical System in Josquin's Period, ca. 1480–1520 (diss., CUNY, 1991)
C. Berger: Hexachord, Mensur und Textstruktur: Studien zum französischen Lied des 14. Jahrhunderts (Stuttgart, 1992)
S. Fuller: ‘Tendencies and Resolutions: the Directed Progression in Ars Nova Music’, JMT, xxxvi (1992), 229–58
R. Toft: Aural Images of Lost Traditions: Sharps and Flats in the Sixteenth Century (Toronto, 1992)
P. Urquhart: ‘False Concords in Busnoys’, Antoine Busnoys: Notre Dame, IN, 1992, 361–87
R.C. Wegman: ‘Musica ficta’, Companion to Medieval and Renaissance Music, ed. T. Knighton and D. Fallows (London, 1992), 265–74
P. Urquhart: ‘Cross-Relations by Franco-Flemish Composers after Josquin’, TVNM, xliii (1993), 3–41
M. Bent: ‘Accidentals, Counterpoint and Notation in Aaron's Aggiunta to the Toscanello in musica’, JM, xii (1994), 306–44
M. Bent: ‘Editing Early Music: the Dilemma of Translation’, EMc, xxii (1994), 373–94
P. Urquhart: ‘An Accidental Flat in Josquin's Sine nomine Mass’, From Ciconia to Sweelinck: donum natalicium Willem Elders, ed. A. Clement and E. Jas (Amsterdam, 1994), 125–44
G. Allaire: ‘Debunking the Myth of Musica ficta’, TVNM, xlv (1995), 110–26
R. Erickson: Musica enchiriadis and Scolica enchiriadis (New Haven, CT, 1995)
P.M. Lefferts: ‘Signature-Systems and Tonal Types in the Fourteenth-Century French Chanson’, PMM, iv (1995), 117–47
M. Bent: ‘Diatonic ficta Revisited: Josquin's Ave Maria in Context’, Music Theory Online, ii/6 (1996) 〈www.smt.ucsb.edu/mto〉
K. Falconer: ‘Consonance, Mode and Theories of Musica ficta’, Modality in the Music of the Fourteenth and Fifteenth Centuries, ed. U. Günther, L. Finscher and J. Dean, MSD, xlix (1996), 11–29
J. Hirshberg: ‘The Exceptional as an Indicator of the Norm’, ibid., 53–64
T. Brothers: Chromatic Beauty in the Late Medieval Chanson: an Interpretation of Manuscript Accidentals (Cambridge, 1997)
A. Newcomb: ‘Unnotated Accidentals in the Music of the Post-Josquin Generation’, Music in Renaissance Cities and Courts: Studies in Honor of Lewis Lockwood, ed. J.A. Owens and A.M. Cummings (Warren, MI, 1997), 215–25
P. Urquhart: ‘Calculated to Please the Ear: Ockeghem's Canonic Legacy’, TVNM, xlvii (1997), 72–98
P. Urquhart: ‘Three Sample Problems of Editorial Accidentals in Chansons by Busnoys and Ockeghem’, Music in Renaissance Cities and Courts: Studies in Honor of Lewis Lockwood, ed. J.A. Owens and A.M. Cummings (Warren, MI, 1997), 465–81
M. Bent: ‘The Grammar of Early Music: Preconditions for Analysis’, Tonal Structures in Early Music, ed. C.C. Judd (New York, 1998), 15–59
B.J. Blackburn: Review of T. Brothers: Chromatic Beauty in the Lute Medieval Chanson, JAMS, li (1998), 630–36
S. Fuller: ‘Modal Discourse and Fourteenth-Century French Song: a “Medieval” Perspective Recovered?’, EMH, xvii (1998), 61–108
E.E. Leach: Counterpoint in Guillaume de Machaut's Musical Ballades (diss., U. of Oxford, 1998)
P. Otaola: ‘Les coniunctae dans la théorie musicale au Moyen Age et la Renaissance (1375–1555)’, Musurgia, v (1998), 53–69
P. Memelsdorff: ‘Le grant desir: cromatica criptica in Matteo da Perugia’, Provokation und Tradition: Erfahrungen mit der alten Musik: Festschrift Klaus L. Neumann, ed. H.-M. Linde and R. Rapp (Stuttgart, 1999)
D. Pesce: Guido d'Arezzo's Regule rithmice, Prologus in antiphonarium, and Epistola ad michahelem: a Critical Text and Translation (Ottawa, 1999)
M. Russo and D. Bonge: ‘Musica Ficta in Thirteenth-century Hexachordal Theory’, Studi musicali, xxviii (1999), 309–26