(from Lat. contrapunctus, from contra punctum: ‘against note’; Fr. contrepoint; Ger. Kontrapunkt; It. contrappunto).
A term, first used in the 14th century, to describe the combination of simultaneously sounding musical lines according to a system of rules. It has also been used to designate a voice or even an entire composition (e.g. Vincenzo Galilei's Contrapunti a due voci, 1584, or the contrapuncti of J.S. Bach's Art of Fugue) devised according to the principles of counterpoint. (See also Polyphony, §I.)
1. Discant of the 13th and 14th centuries.
2. Early note-against-note writing.
3. Treatises of the 14th and 15th centuries.
5. Three-part composition in the 15th century.
7. Composition in four or more parts.
9. Zarlino and aspects of dissonance treatment.
10. Galilei and his innovations, 1587–91.
11. 16th–century double counterpoint.
12. The term ‘counterpoint’ after 1600.
14. Free style: ‘licentious’ and ‘harmonic’ counterpoint.
16. The Classical and Romantic eras.
KURT-JÜRGN SACHS (1–11), CARL DAHLHAUS (12–17)
The theory of counterpoint, which existed by about 1330, developed from the older theory of discant, but differs from it in ways that a comparison of the two makes clear. The technique of discant occurs in two distinct forms. Works dealing with ‘interval succession theory’ (‘Klangschritt-Lehre’) merely list possible single progressions of an added voice for all usual successive intervals of the cantus, considering only the consonances of unison, octave, 5th (and occasionally 4th); for example: ‘If the cantus ascends by a 2nd and the opposed part begins at the octave, then the opposed part descends by a 3rd and forms [with the cantus] a 5th, or descends by a 7th and coincides with the cantus’ (CoussemakerS, ii, 191). General guidelines on compositional technique are found only in the work of Franco and his followers, apart from traditional instructions on contrary motion (see Eggebrecht and Zaminer, 1970; CoussemakerS, ii, 494; AnnM, v, 1957, 35). Franco was clearly concerned to emphasize the consonant or dissonant quality of sounds in the formulation of general statements on compositional technique, but did not go beyond individual aspects (CSM, xviii, 69–73):
Every discant is ordered by consonances … Every imperfect dissonance [major 2nd, major 6th, minor 7th] sounds well immediately before a consonance … The discant begins at the unison, octave, 5th, 4th, or major or minor 3rd [i.e. on any of the ‘consonances’], then proceeds in consonances and occasionally mixes them at suitable points with dissonances, so that when the tenor is ascending, the discant is descending and vice versa. It should be noted that tenor and discant occasionally ascend or descend simultaneously for the sake of the beauty of the piece … and also that consonances are always used in all [rhythmic] modes at the beginning of the perfectio [mensural unit].
Anonymus 2 tried (c1300) to analyse the role of imperfect consonances in composition technique: ‘Imperfect [consonances] are the major and minor 3rd, which are good in the progression from a 5th to a 5th or from a 5th to a unison and vice versa; and the major 6th, which is good before an octave’ (CoussemakerS, i, 311).
Early counterpoint diverges clearly from the theories of Franco and Anonymus 2 by taking only two-part note-against-note composition into consideration, thus ignoring dissonances and, at first, note values; by changing the classification of the sounds, apparently little, but radically, by reclassifying the 4th (which was a ‘medium’ consonance and becomes a dissonance); and by making the difference in quality between perfect and imperfect consonances the basis of a regular system. Textbooks, typically, list consonances, perfect and imperfect, and provide rules for their succession.
The subdivision of consonances always leads to the contrast between the unison, 5th and octave as ‘perfect’ and the 3rd and 6th as ‘imperfect’. It is immaterial whether the consonances are given Greek names, as happened particularly in the early stages, or Latin names (in other words, whether 3rds, for example, were described separately as semiditonus and ditonus or jointly as tertia); it is also immaterial whether and to what extent intervals greater than the octave are mentioned and classified, and whether the perfect consonances were called consonantiae and the imperfect dissonantiae (as occasionally happened). But terminology and the number of named consonances do give information about the traditions and phases of theory.
The difference in quality between the two groups of consonances is particularly shown in the directions referring to important sections in the composition or to parallel part-writing: the beginning and end should be perfect consonances and the penultimate note an imperfect consonance; parallel successions of identical intervals are strictly forbidden with perfect consonances but emphatically recommended with imperfect ones. This differentiation is based on the fact, remarked on by Anonymus 2, that three consonance sequences (3rd–unison, 3rd–5th and 6th–octave) have particular advantages: close melodic connections through conjunct motion, independent part-writing through contrary motion, and change in sound through the transition from imperfect to perfect consonance (which 14th-century writers called ‘striving’: requirere, tendere). According to the theory of Marchetto da Padova (c1318) – repeatedly taken up in the 15th and 16th centuries though without becoming the norm in theory or practice – one of the two parts was also supposed to move by a semitone, as in ex.1. This also determined the basis of counterpoint even in contexts where ‘ideal’ sequences occur only occasionally. This happens when the theory offers, as recommendations (mandata arbitraria), progression to nearby notes, contrary motion, and alternation between imperfect and perfect consonances. For combinations that respect only one mandatum arbitrarium, the strict prohibition (mandatum necessarium) of parallel similar perfect consonances on the one hand, and the permitted succession of similar imperfect, dissimilar imperfect and dissimilar perfect consonances on the other, are both valid. The repetition of a note, causing oblique motion, is sometimes permitted only in the cantus, but may be used in either part (or even in both simultaneously, as a repeated note); it is not however the recommended ‘next step’. On the basis of these directions, a given cantus yields a note-against-note composition, in which 15th-century theorists required two essential qualities: first, difference between the two parts, in the interests of which parallel progression in similar perfect consonances, usual in polyphony of the 9th century to the 13th, was now forbidden (‘If one person sings the same as the other … that does not fulfil the aim of contrapunctus; for its aim [intentio] is that what the one sings be different [diversum] from what the other sings’ – Prosdocimus de Beldemandis, 1412; CoussemakerS, iii, 197); and second, indeterminate structure, ensured by the fact that there were always several permitted consonances to choose from, and thus many possible resolutions for the part added to a cantus (‘Contrapunctus is the indeterminate setting [positio] of a single note in high or low position against a single note in any cantus. … Contrapunctus is related simply [simpliciter] and without predetermination [indeterminate] to all settings [positiones] of high and low notes in the musical system’ – Ugolino of Orvieto, c1430; CSM, vii/2, p.4).
Music examples from counterpoint treatises may illustrate different features of the method of composition. In ex.2a contrary motion is dominant; parallel imperfect consonances are used sparingly; when one part moves by leap the other moves by step or has a repetition; (the added part, according to some treatises, should be restricted to the range of a hexachord). In ex.2b, parallels of up to four similar imperfect consonances are relatively frequent; they usually lead to the adjacent perfect consonance (as in intervals 6, 9 and 20) but can also lead to one or more imperfect consonances of another kind (14–15); simultaneous skips are not excluded (10–11, 15–16), but involve contrary motion and change of interval type.
By way of contrast in pre-contrapuntal note-against-note compositions, combinations of unison, 5th and octave, where parallels of similar intervals are not impossible, predominate over 3rds, which usually only serve as a bridge between unison and 5th (ex.3); the still consonant 4th also sometimes appears, while the 6th is rare (see the examples in Sachs, 1974, pp.121–2).
From the time of the earliest surviving textbooks on counterpoint, the number of treatises on composition technique increased markedly and the term ‘contrapunctus’ quickly came into use. This was surely a matter of cause and effect; the explanation is probably to be found in the novelty of the technique designed for note-against-note composition. There are isolated references to a contraponchamens or contrapointamens in the brief discussion of musical genres and polyphonic practices in Peire de Corbiac's Provençal Tesaur (c1250), but there is no mention of the word ‘contrapunctus’ in music theoretical writings until its appearance in the new theory of composition about 1330, since all known authors from Johannes de Garlandia (c1240) to Jacques de Liège (c1260–after 1330) used the general term ‘discantus’ when discussing composition technique.
Among the earliest didactic contrapuntal works are probably the brief piece attributed to Johannes de Muris, Quilibet affectans (CoussemakerS, iii, 59–60a), which was widely read, and the compilation of Petrus frater dictus Palma ociosa, written c1336 (Wolf, 1913–14). Philippe de Vitry, too, seems to have taught counterpoint even if no versions of the treatises attributed to him (e.g. CoussemakerS, iii, 23–7) can be regarded as authentically his in their surviving form.
Most of the works on counterpoint up to the 15th century are anonymous, and it is not usually possible to fix their dates or places of origin accurately. Treatises that help establish a chronology for the development of the theory include Goscalch (1375; excerpt in Sachs, 1974), Antonius de Leno (c1400; CoussemakerS, iii, 307–28), Prosdocimus de Beldemandis (1412; CoussemakerS, iii, 193–9), Ugolino of Orvieto (c1430; CSM vii/2), Johannes Legrense (c1460; CoussemakerS, iv, 383–96), Johannes Tinctoris (1477; CoussemakerS, iv, 76–153), Guilielmus Monachus (c1480; CSM, xi) and Florentius de Faxolis (between 1484 and 1492; excerpt in Seay, 1963, p.85). The reliability of the sources increased with the appearance of printed works on counterpoint, by Ramos de Pareia (Musica practica, 1482), Nicolaus Burtius (Musices opusculum, 1487), Franchinus Gaffurius (Practica musicae, 1496) and others.
The treatise Cum notum sit (probably mid-14th century) contains a definition of counterpoint as ‘nothing but a setting of note against note’ (‘non … nisi punctum contra punctum ponere vel notam contra notam ponere vel facere’) and the ‘basis of discant’ (‘fundamentum discantus’; CoussemakerS, iii, 60). Discant, the ‘newer’ form in this case, denotes the manner of composition whose basis is contrapuntal note-against-note composition. The second part of the treatise (‘De diminutione contrapuncti’) elucidates the relation between the two types of composition: since the contrapunctus – the part added to the tenor, in breves of equal length – ‘can be divided’ into smaller notes in various ways, the work lists rhythmical possibilities of this kind and illustrates them with musical examples. The examples (22, according to the most reliable sources) all have the same tenor, and each follows a rhythmic formula; they are all based on the same note-against-note composition, whose degree of diminution increases systematically from example to example for each of the four basic mensurations, as in ex.4 (the beginning of the examples for tempus perfectum cum prolatione maiori; cited in Sachs, 1974, p.146). The work illustrates the technique, known from other treatises, of creating a diminished version of an added part, by ‘filling out’ the breve units or by the ‘interpolation’ of notes, but does not mention the dissonances (2nds, 4ths and 7ths) that thus occur. The lack of such comment probably does not mean that dissonance could be used freely but that its application still lay outside the contrapuntal system. References to the use of dissonance, however, occasionally occur in 14th- and early 15th-century counterpoint treatises.
Petrus frater dictus Palma ociosa said that dissonances could appear briefly, by step in ascent or descent to a consonance. According to Antonius de Leno, who allowed note against note, two notes against one and three notes against one, the middle of three short notes of equal length could be dissonant. Another work allows a third of a semibreve to be dissonant (CoussemakerS, iii, 27) in the so-called ‘cantus fractibilis’. Goscalch, who apparently knew Cum notum sit, went further, and proposed to ‘divide notes into parts, i.e. to sing several notes in the cantus instead of one’. At the same time he demanded observance of the rules of counterpoint and confirmed the prohibition of parallel perfect consonances for both immediately consecutive shorter note values, and for the contrapuntal framework. He considered that having only consonances was ‘impossible or very difficult and irksome’, and thus assumed the use of dissonance. He allowed dissonance even at the beginning and end of a figural unit, if it took up less than half the value of the figure (or, in the case of syncopation, even as much as half).
In spite of the evident closeness in material and method of note-against-note and figured composition, the two forms were largely separate in theory and terminology until Tinctoris's work published in 1477 (see §6 below): most of the treatises do not mention diminution or dissonance, and there was criticism of the extension of the meaning of the word ‘contrapunctus’ which already occasionally meant the setting of ‘several notes against one’ (see CoussemakerS, iii, 194; CSM, vii/2, 4).
The first works on counterpoint that allow three-part composition were probably written not earlier than the 15th century; they are not genuine extensions of the theory (as was the case with contrapunctus diminutus) but simply explanations of how the rules of two-part note-against-note composition should be applied to an increased number of voices. Since the intervals between various pairs of parts have to be considered and coordinated in three-part composition, the theories deal with problems liable to occur when the norms of two-part composition are applied. Most importantly, the basic rule of allowing only consonances in note-against-note writing must be observed, but with two precautions.
First, since two added parts can be mutually dissonant although each must be consonant with the tenor, thus corresponding to the norms of two-part composition, the books warn against the 2nd created between two added parts respectively a 5th and a 6th above the tenor (CoussemakerS, iii, 93), the 9th resulting from 5ths simultaneously above and below a tenor, and similar combinations (see Sachs, 1974, p.127). Second, because two added parts, each consonant with the tenor, often form a 4th, which in two-part note-against-note composition has to be avoided as a dissonance, treatises indicate the possibility of using the 4th in three-part note-against-note composition as long as it remains hidden (Gaffurius, iii, 6) by not involving the bottom part (CSM, xxii/2, p.27).
Some texts list the possible complementary notes for the contratenor as well as all the usual consonances of tenor and discant (CoussemakerS, iii, 93–5, 465–6). This clumsy method, which in the 16th century even stretched to a fourth voice, shows that general principles of composition had hardly been formulated. Warnings against unison and octave as ‘equal’ or ‘equivalent’ consonances between the added parts are rare (CoussemakerS, iii, 92), but show that even then there was a preference for ‘complete’ sounds.
The rules for the sequence of consonances in two-part composition remained valid for an increased number of parts. Theory was, however, not consistent about the prohibition of parallel 5ths. The permitting of 4ths was based on their incidental creation (between added voices) and this covered parallel 4ths as well (although these are seldom mentioned, and only in the technique of Fauxbourdon; CSM, xxii/2, p.27; CSM, xi, 39; Gaffurius, iii, 5). From there it would have been a small step to concede the analogous parallel 5ths, which could be explained as caused by the inversion of added parts. Occasionally they were indeed permitted (CoussemakerS, iii, 466; CSM, xi, 42–3), and that may justify phrases such as the one in ex.5. But other texts forbid parallel 5ths (CSM, xxii/2, pp.147–8; Sachs, 1974, p.131); this latter position gained acceptance probably because a difference between ‘primary’ and ‘secondary’ composition, although theoretically useful for chord construction, was subordinate to the general compositional viewpoint where rules of progression were concerned.
Standards for the melodic structure of the individual parts varied in their strictness: discant and tenor should avoid leaps of 6ths and 7ths while the contratenor was allowed not only these but even sometimes a leap of a 9th. The special character of the contratenor is based on the concept of the successive composition of parts customary in the 15th century, for which Burtius (ii, 5) gave two possibilities: first cantus (supranus), then tenor, and lastly contratenor; first tenor (usually as a given cantus planus), then superius, and lastly contratenor.
The contratenor, which is thus added to a discant and tenor framework, was in the first instance a ‘filler’ (‘pro replecione sonorum seu vocum’; Sachs, 1974, p.131). The added character of the contratenor is also to be seen in the typical endings (clausulas, conclusiones) that theorists had fixed for the parts since about 1500. The formulae for discant and tenor reach the final note (ultima) ascending or descending by step to produce the 6th–octave progression (ex.6a–c). The contratenor, on the other hand, normally a 5th below the tenor on the penultimate note, moves to one of the possible perfectly consonant final notes, forming an octave leap (ex.6a), 4th leap (ex.6b), or falling 5th (ex.6c) cadence. Only when the tenor cadences by descending a semitone to mi does the contratenor, in order to avoid a diminished 5th, take the 3rd below the tenor on the penultimate interval and close on the 5th below (ex.6d). The antepenultimate interval, which contemporary examples also include, varies within certain limits.
A particular 15th-century three-part technique is found in those compositions where two parts constantly run in similar imperfect consonances between the first and last note, while a third, usually the contratenor, has complementary notes or also takes part in the parallel progression. Guilielmus Monachus described and provided examples of such patterns (see Sachs, 1974, pp.132ff): with parallel 3rds (ex.7a, b), and 6ths (ex.7c, d), where the contratenor either alternates between the unison and 5th (ex.7a, c), or between the lower 5th and lower 3rd (ex.7b, d); with parallel 10ths, between which there is a middle voice, either written in parallel 6ths or 5ths (ex.7e), or which progresses like a cantus firmus in fairly long note values (ex.7f); or with simultaneous parallel 3rds and 6ths (ex.7g). These patterns, which considerably simplify the construction of three-part texture, have advantages for textbook purposes and for practice in improvisation, but have little value for composition.
The most tightly knit, comprehensive and important 14th- or 15th-century treatise on counterpoint is Tinctoris's Liber de arte contrapuncti (1477). Counterpoint is here described as ‘restrained and thought-out polyphonic composition created by setting one sound against another’ (‘moderatus ac rationabilis concentus per positionem unius vocis contra aliam effectus’; CSM, xxii, 2, p.14). It divides into contrapunctus simplex (note against note) and diminutus (several notes, of either equal or varying length, against one), and can be extemporized (mente) or written down (scripto). But Tinctoris called the improvised form ‘straightforward’ (absolute) counterpoint (or super librum cantare), and the written form res facta or cantus compositus (CSM, xxii/2, pp.105ff). This terminology – unknown before Tinctoris and used afterwards only with reference to him – should not be taken to imply that the aim of the theory of counterpoint was improvisation. Tinctoris seems to have wanted to emphasize something else: that, particularly in composition for more than two voices, the result of an improvisation relating several parts contrapuntally to a given tenor (CSM, xxii/2, p.110) differs from carefully planned composition; the inevitable lack of strictness in improvisation is a concession, not the aim of counterpoint.
In the first part of his treatise Tinctoris gave a basic description of the consonances and their relations in contrapunctus simplex. The tenor and the added part both progress either by step, or in leaps of a 3rd, a perfect 4th and a perfect 5th. The second part is a survey of the dissonances and their systematic application in contrapunctus diminutus.
According to Tinctoris, the correct use of a dissonance depends on its rhythmic and melodic position. The yardstick for the rhythmic position of a dissonance is the note value determining the basic movement of a musical piece, which Tinctoris called mensurae directio (or ‘nota, secundum quam … cantus mensuratur’; CSM, xxii/2, pp.124–38); Adam of Fulda called this value, acting as a pulse or beat, tactus (1490; GerbertS, iii, 362), and 16th-century Italian theory called it battuta. In prolatio maior (ex.8, bars 1–7) it is the minim (transcribed as a crotchet), in prolatio minor (bars 9–11) the semibreve (transcribed as a minim), and in proportions the equivalent of those values. Tinctoris used the fact that both values are divisible by two in the respective mensurations to formulate three basic rules for the rhythmic values of dissonances (ex.9).
First, if the first part of a mensurae directio (α) or the beginning of the first and second parts (β) is consonant, a dissonance of equal and smaller value can follow. This rule covers unstressed dissonances, whose maximum length corresponds to the consonant part of a mensurae directio. Unstressed dissonances can occur anywhere in the composition, but stressed dissonances (i.e. those falling on the beginning of a mensurae directio, which appear only as prepared suspensions resolved by stepwise descent) are for Tinctoris always designed to prepare for an immediately following final sound (perfectio or conclusio). This is usually restricted to perfect consonances, unless it concludes an internal section and simultaneously opens a continuation (as in ex.8 where F appears in parentheses). Because syncopated dissonances are thus dependent on a cadence, Tinctoris's other rules are both related to properties of the penultimate note in a phrase of the tenor.
Second, where there is a penultimate note equal in value to two mensurae directio, consisting either (α) of a single note or (β) of two notes identical in pitch and length, the first part of the first mensura nearly always has a dissonance set against it. Third, if the penultimate is equal in value to one mensurae directio, then the first part (α) can be dissonant, or, when preceded by stepwise descending notes of equal value (β), the first part of each note can be dissonant (ex.9). Since Tinctoris formulated rules of dissonance according to the greatest permissible value in each case, it is not surprising to find that the rhythmically short formulae of prolatio maior also occur in prolatio minor (in parentheses in ex.8).
As regards melodic position, Tinctoris confirmed that each dissonance is preceded by an ‘adjacent’ (stepwise) consonance, and the following note will be a 2nd or ‘very rarely’ a 3rd away (ex.8, bar 4). When a dissonance is introduced and left by step, one should not return to the starting note unless the dissonance is ‘so short that one can hardly hear it’ (CSM, xxii/2, p.141); thus, in Tinctoris’s examples the ‘nota cambiata’ usually appears as the fusa, while the passing notes are also minims and semiminims. The leap of a 3rd from a dissonance is less rare in Tinctoris's examples, and in 15th-century music in general, than his book suggests, and it also occurs descending from a syncopated dissonance. Occasionally the leap of a 4th also occurs after a dissonance, but usually it is a substitute for a cambiata (ex.8, bar 1: leap to the 3rd above instead of a return to the pitch of the preceding note, which appears in another part). The eight general rules of the third part of Tinctoris's treatise offer both traditional norms (but often modified for composition in more than two parts) and more general recommendations about the wider context of composition (its structure and varietas); they are neither as concrete nor as important as the dissonance rules, however, which for the first time make possible an understanding of the period's compositional techniques.
The acceptance into theory of four-part note-against-note composition was another extension of contrapuntal apportionment: intervals between discant and tenor were filled out by the addition of two parts. The bottom part takes precedence, since it must avoid the formation of 4ths (while making them possible between other parts by supplying a 3rd or a 5th), and it is sometimes more precisely determined (e.g. the penultimate note is usually a 5th below the tenor). The lists and tables customary since Aaron (1523), who enumerated possible four-part note formations, usually follow the order discant–tenor, bass, alto; but they illustrate only the process of contrapuntal disposition of the individual chord. The old method of working out the parts in succession fell into disuse during the 16th century; as Aaron confirmed, the moderni considered ‘all the voices simultaneously’, thus improving consonance formation and part-writing, and avoiding unsatisfactory unisons, rests or leaps. The catalogue of chords strictly avoids secondary dissonances and 4ths in the bottom part, of course, and favours complete formations (in the sense of full triads).
As early as Cochlaeus (1479–1552) there are examples showing the typical concluding formulae of the parts (see ex.6), including the quarta vox (altus); they show the interchangeability of the formulae between the parts (ex.10). In general, four was the maximum number of voices in 16th-century contrapuntal theory and four-part writing was the highest form of compositional technique illustrated by examples of figural music. Gaffurius mentioned the creation of a fifth part ‘according to the rules of counterpoint’ (iii, 11), and Tinctoris used it in an example (CSM, xxii/2, pp.107ff). Florentius de Faxolis contrasted the two-part counterpoint of the veteres with the composition of the moderni for three to six or more parts, which he described as ‘composition, i.e. the contrapuntal method, extended to several voices’ (Seay, 1963, p.87). Even though writers discussed instances of going beyond four-part composition, they did not deduce from them any new aspects of theory.
The development of contrapuntal theory in the 16th century consisted, first, of a drawing together of contrapunctus simplex, contrapunctus diminutus and composition for more than two voices, often still separate in the 15th century; second, an expansion of matters treated to include, particularly, the modes, techniques of imitation and inversion, and the relation between text and music; and third, improved, more precise rules for the use of dissonance. This development reached its peak in the third book and part of the fourth of Zarlino's Le istitutioni harmoniche (1558), the most comprehensive and influential 16th-century work on counterpoint. It contains the best and most refined analysis of the composition technique used in sacred music, particularly at the time of Willaert, Zarlino's teacher; and it surpasses Willaert's other pupil Nicola Vicentino's ingenious, somewhat earlier but in many respects very similar L'antica musica ridotta alla moderna prattica (1555), both in clarity and in detail. Almost all the many, usually printed, 16th-century works on counterpoint relate to the prima prattica style. The first two attempts to incorporate innovations from secular vocal music into the theory were thus all the more pioneering: Vicentino used chromatic madrigals as examples and recognized liberties (in progression, harmony and mode) justified by text meaning or the affect of the words; and Galilei discussed and defended freer uses of dissonance.
The ‘arte del contrapunto’ as the theory of polyphonic composition was for Zarlino the centre of musica pratica and at the same time the most comprehensive amalgam of themes in all music theory. Zarlino not only considered in detail all traditional aspects of counterpoint but also tried to define additional requirements and conditions of polyphonic composition. The soggetto, or thematic subject, is composition's point of departure, ‘without which one can create nothing’ (iii, 26), and which can consist of a given or newly created cantus firmus, cantus figuratus or even several imitative parts. The soggetto influences the choice of church mode, and that in turn affects the coordination of parts. The mode of the tenor, which determines the tonality of the composition, is usually shared by the soprano in four-part composition, while the bass and alto take it over with changed compass (‘plagal’ instead of ‘authentic’, or vice versa); and this corresponds to a difference of almost an octave between the ranges of the two pairs of parts (illustrated in ex.11 on the basis of the combination of soprano, alto, tenor and bass clefs frequent in Zarlino).
The restrictions on mode and compass affect imitative technique, harmonic structure and cadence formation. Zarlino divided up the possibilities for imitation according to whether the ‘leading’ (guida) and ‘following’ (conseguente) parts have equal or differing interval patterns. The former he called fuga (whose entries could be at the octave, 5th, 4th and unison), the latter imitatione. Both fuga and imitatione could follow the canon ‘strictly’ (as legata) or move ‘freely’ (as sciolta) in its continuation, and take up either some or all of the parts (iii, 54–5).
The principle of harmony was to create consonances by combining 3rd and 5th (or 6th), or their equivalents in other octaves, to make a harmonia perfetta, or, in modern terms, a triad. Zarlino considered the triad with a major 3rd more perfect than that with a minor 3rd, and declared that, while successions of ‘many’ triads with major 3rds were harmless, those with minor 3rds had a ‘very melancholy’ effect (iii, 31).
Each mode had its own final notes for the normal cadences (iv, 18ff). The breaking up of a composition by cadences which, like the ‘full stops in a sentence’, created resting-points and marked off the sense, was an important part of the layout (iii, 51). The cadences, which normally used syncopated dissonances, separated sections of the text from one another and made possible musical variety and change in the successive parts of a composition; they could, however, also be deliberately avoided (‘fuggir le cadenze’) in favour of a larger context if one part avoided by a leap or a rest the expected (perfect) consonance (as indicated in ex.12a).
Zarlino's teaching was aimed at four-part composition, which contained ‘all perfection of harmony’. This concept of perfection explains why Zarlino tried to describe the characters of the parts by comparison with the four elements: the bass, as the earth, was the deepest voice, often slow-moving, and ‘carried’ the harmony; the tenor was the equivalent of water (it ‘surrounded’ the bass and ‘ruled’ the composition as regards the combination of modes); the alto was the air, and mediated between tenor and soprano (fire), in whose glow it ‘shone’; the soprano, as the highest, most stirring and most powerful voice, was like the life-giving fire of the sun (iii, 58).
Zarlino required that the music should suit the character of the words, and related this problem to the ordering of modes and to particular affects (iv, 32). For text underlay he made a set of rules which may be summarized as follows. The length of a syllable shall be reflected in the corresponding note value or values. Notes with their own syllable include, always, the first and last note of a piece or a section and the first note of every ligature, and usually every non-tied note of greater value than a semiminim or crotchet (exceptionally a semiminim, after a dotted minim), but never notes of smaller value than a semiminim, or the dot after a note. A change of syllable can normally occur only after notes of value larger than a semiminim, except that it may follow a semiminim after a dotted minim. Repetition of words is permitted in cantus figuratus (but not in cantus firmus), as long as the repetitions consist of meaningful phrases, not just individual words or syllables (iv, 33).
Zarlino's rules for dissonance mostly use the simplest ‘forms’ of exercise, in which two minims, four semiminims or a minim and two semiminims in the added part each sound against one semibreve of the soggetto, and also consider the suspension (see ex.13). First, since two minims occur on the downbeat (battere) and the upbeat (levare) of the semibreve tactus (battuta), and are correspondingly prominent, both shall be consonant; ‘unstressed’ notes may be dissonant only in stepwise ascending or descending sequences of minims. Second, the first and third semiminim in a group of four must likewise be consonant, while the second and fourth may be dissonant in stepwise progression. Third, the first of two semiminims may be dissonant where they both descend by step after a stressed minim (or a syncopated semibreve); Zarlino's example (ex.12b) indicates that this licence is based on the elementary character of the three-note melodic formula, which, depending on the following note, either fills a descending 4th (x) or embellishes a 2nd (y), for both consonant (C) and syncopated dissonant (S) uses are normal. Fourth, for normal suspensions, Zarlino required consonant preparation and stepwise descending resolution, which he illustrated by decorative figures with note repetition (which Jeppesen called ‘Portament’; see ex.12c at P) and paired fuse (quavers). He also discussed special cases; in particular he permitted preparation by a 4th above the lower part (iii, 61; Jeppesen, ‘quarta consonans’) and under some circumstances the irregular resolutions of 2nd into unison and of 4th into the diminished 5th (iii, 42).
Zarlino's directions on the rhythmic structure of the composition and of individual parts are also instructive. The beginning must always be on the downbeat. If a part entered later, it should be after at least a minim pause (often with a syncopated semibreve). The rhythmic movement should not be too fast at first so that it could gradually speed up; it was best for the acceleration to be achieved by transition to the next smaller note value. The introduction of semiminims after a semibreve should coincide with the levare, not the battere (iii, 45; ex.13b). In two-part composition with a soggetto in semibreves Zarlino made a strict distinction between two positions of the dotted minim and semiminim group: he used the ‘stressed’ position only at the beginning (ex.13c, α), while the ‘unstressed’ position is used both in the middle of the piece and, after a rest, at the beginning (β).
The many details on composition technique mentioned by Zarlino are essential for the examination of prima pratica works; but they are not quite complete. Two figures should be mentioned, each of which contains a characteristic freedom in the treatment of dissonance, which in modern terminology is with confusing ambiguity called ‘cambiata’.
The first of these is a five-note group consisting of four semiminims descending by step, the second and third of which are dissonant, followed by a step upwards. This formula is usually part of a cadence and goes with the preparation for a suspension. What is probably the oldest description of this usage, by G.M. Artusi (L'arte del contraponto, i, 1586; see ex.14a), stresses its ‘very good effect’. It is unlikely that Stephano Vanneo was referring to this when he prescribed the consonance of the first and last of four semiminims as the norm (Recanetum de musica aurea, 1533). Berardi called the irregularly dissonant third note a ‘cambiata’ (Miscellanea musicale, 1689), and Jeppesen termed it a ‘relatively stressed passing dissonance’.
The second consists, mostly, of four notes: an unstressed semiminim dissonance leaping down to the lower 3rd; the upper 2nd precedes it and usually follows the leap in order to balance it out. It appeared in various textbook examples (often in Tinctoris; ex.14b is from Pontio, Ragionamento di musica, 1588), but there is no known description of the usage in 16th-century treatises. Popularity and freedom in dissonance treatment seem to be based on the good style of its melodic outline, as in the formula shown in ex.14b: the ascending form is rare, but the descending form occurs in both dissonant (the progression is usually 8–7–5) and consonant (6–5–3; ex.14c) contexts, and can even appear, rhythmically extended and metrically displaced, in a part that continues with the resolution of a suspension (ex.14b, at broken bracket). Fux (Gradus ad Parnassum, 1725), Jeppesen and others called the semiminim irregularly leaping from a dissonance ‘cambiata’; Merritt described it as a ‘changing note group’. (See also §13 below.)
Galilei's treatises contain the first systematic attempt to accommodate the theory of counterpoint to the recent innovations in composition technique, attributed particularly to Cipriano de Rore and proclaimed by Monteverdi in 1605 as the hallmarks of seconda pratica. These innovations are in effect liberties in dissonance treatment and are based on the view that dissonances are not only passing formations, dependent on consonance, but themselves carry musical expression. Galilei particularly enriched composition theory by allowing the following means of making dissonances more urgent, sharper and more surprising (see Palisca, 1956, and Rempp, 1980).
First, in a conjunct sequence of four semiminims, two (apart from the forms in exx.13a and ex.14a) can be dissonant in any position, and occasionally three can be consecutively dissonant (ex.15a, b). Second, suspensions, apart from the forms in exx.9 and ex.13a, can be resolved by leap to a consonance (ex.15c), by progression to a new dissonance (ex.15d), by ascent to a consonance (ex.15e) and, apart from the form in ex.14b, simultaneously with a chromatically progressing added part (ex.15f); they can occur several at once (ex.15g). Third, dissonances can also sometimes occur in the stressed position without syncopated preparation if a regular resolution follows (ex.15h, i).
Within the context of their imitative and canonic techniques, Vicentino and Zarlino also discussed the systematic transposition of parts in composition to other keys, which they called contrapunto doppio (Vicentino also used the term compositione doppia, iv, 34). They thus gave out for the first time a method (considerably older, no doubt) of producing especially ‘artificial forms of counterpoint’ (Zarlino, iii, 56). This technique requires an understanding of the harmonies and progressions that can occur in various forms of composition. The knowledge of the respective complementary intervals is fundamental: for harmonic intervals of the same kind in the basic (Zarlino: principale) and in the inverted version (replica) always complement each other to make the ‘inversion interval’. In its simplest form, an octave exchange of the upper and the lower part, the intervals 3rd and 6th (imperfect consonances), 2nd and 7th (dissonances) and the unison and octave (both perfect) are paired complementary intervals. This kind of counterpoint is thus much the most productive and needs no special theory. The possibilities of transposition at the 12th and 10th are more limited but can also well be used; Zarlino especially used them, even within the same piece (see ex.16). The complementary intervals for double counterpoint at the 12th and 10th are easily derived by ensuring that the pairs of figures add up respectively to 13 and 11 (thus a 3rd and a 10th, for example, will form double counterpoint at the 12th).
It is thus possible to deduce the contrapuntal conditions for ex.16a, which may be inverted in either way: the consonances of unison, 3rd, 5th, octave and 10th (and 12th) remain consonant; in order to avoid unacceptable parallels the piece must progress in contrary motion or leap consonantly in oblique motion; passing dissonances are possible, but not suspensions. As a further form the authors also taught the transposition of both parts in inversion (ex.16d). In this case all the changes in interval of the principale remain intact in the replica. The restriction on composition technique consists in the fact that melodic formulae that are persuasive only in one direction (ascending or descending) are to be avoided.
‘Counterpoint’ has been used to convey different meanings in literature on music and music theory from the 17th century to the 20th. The enumeration of these meanings is essential if confusion is to be avoided. First, the concept of counterpoint has been equated with the ‘art of strict composition’ (J.P. Kirnberger, 1771–9), thus being used to describe regulated part-writing regardless of whether the style is polyphonic or homophonic (‘counterpoint’ is a technical category, ‘polyphony’ a stylistic concept). Second, more narrowly, counterpoint has been taken to refer to the technique of polyphonic, as distinct from homophonic, writing. Third, still more narrowly, the concept of counterpoint has been confined to the technique of vocal polyphony before 1600 (and in addition Bach's instrumental polyphony). Fourth, a number of 20th-century theorists have proposed a distinction between polyphony, the combining of equal voices, and counterpoint, a type of writing in which the voices are brought into relief against each other functionally and by virtue of their relative importance. Generally, however, ‘polyphony’ has been used to refer to matters of style or aesthetics, and ‘counterpoint’ to refer to matters of technique: polyphony is an end, counterpoint a means.
The assumption that the theory of counterpoint deals with the horizontal and that of harmony with the vertical dimension of music is as trivial as it is misleading. In the study of harmony, it is not just the structure of chords but also their progressions that must be dealt with; and similarly, in the theory of counterpoint it is a question not only of melodic part-writing but also of the chords formed by the parts. Second, the stylistic aims of counterpoint – which are directed to the simultaneous deployment of characteristic melodic parts – should be distinguished from the technical problems a composer must solve in order to realize these aims, above all in the regulation of simultaneities (joining consonances together, manipulating dissonances). It is the technical rules rather than the stylistic maxims that primarily constitute the subject for study. (A guide to contrapuntal or polyphonic style, such as that of Kurth, 1917, is not to be confused with a work of technical instruction.)
The historians' idea that an epoch of counterpoint can be identified as distinct from an epoch of harmony, with the year 1600 representing the dividing line between the two, came about through lack of conceptual clarity. If harmony is understood as referring to a regulated joining together of simultaneities – and there is nothing to justify the restriction of the concept of harmony simply to tonal, chordal harmony – then music before 1600 also bears a harmonic imprint, even if of a different kind from that of later music. Kurth's assertion that early counterpoint was based on mere ‘intervallic compatibility’, and hence that the technique of joining together simultaneities fulfilled only the negative aim of avoiding perturbations in the linear exposition and thus of avoiding obtrusive sequences of consonances or conspicuous dissonances, is mistaken: it is contradicted by the fact that the progressions (in contrary motion) from the major 6th to the octave, from the major 3rd to the 5th, and from the minor 3rd to the unison, were reckoned to be especially clear and compelling, and were thus understood (comparably with the progression from the chord of the dominant 7th to the tonic triad in tonal harmony) as harmonic phenomena. Harmony before 1600 differs fundamentally from that of later times: earlier harmony proceeded from two-note intervals and not from three-and four-note chords (a three-note simultaneity was considered a secondary combination of intervals rather than a primary entity in itself); and tonality was shown less by chordal sequences than by melodic formulae.
Kurth's hypothesis that the linear polyphonic deployment of melodic parts was inhibited by tonal harmony is not wholly erroneous, but a distortion of the truth. Aesthetically it may be correct, in the case of narrowly restricted musical perception, to say that attention is directed either to the phenomenon of harmony and sonority or to that of melody and polyphony; and no doubt many composers have drawn the conclusion that in order for music to remain in the realm of the comprehensible either harmony or counterpoint must come to the fore. But strictly speaking the contrary is true: the fact that chord progressions constitute musical continuity and comprehensibility frees the part-writing from the necessity to take account of aspects that would be indispensable in composition consisting of interval sequences. Thus the harmonic and tonal basis of free style is not technically an impediment to linearity but a prerequisite for the unrestricted deployment of the melodic in music. Bach too – contrary to Kurth's interpretation of his simultaneities as mere resultants – conceived harmonic tonality as a support for melodic linearity.
Counterpoint theory, which until the 17th century was the only kind of instruction in composition, has had to share its dominant position with harmony theory since the 18th century; and the relation between the two disciplines has become increasingly complicated. Free composition appears in the work of many theorists as ‘practical harmony’ and in the work of others, by contrast, as ‘licentious’ counterpoint; it is possible on the one hand to conceive of the (theoretical) study of harmony – the awareness of the harmonic significance of notes – as a prerequisite for strict writing, and on the other to conceive of strict writing – the foundation on which free composition as a set of permitted departures is built – as a prerequisite for the (practical) study of harmony.
As a didactic discipline, counterpoint has been justified both speculatively and pragmatically. Fux and Padre Martini were convinced that the norms of strict counterpoint were founded in the very nature of music, which, though it might be transformed by changing styles and fashions, was not to be destroyed (free style was understood as a permitted departure from strict style rather than as a suspension of it). In contrast, since the later 18th century the rules of counterpoint have been seen as historically specific, hence alterable, norms (and the nature of music has been sought in the rudiments of harmony); they were taken over either in order to avoid a break in the continuity of the development of the style of sacred music (Albrechtsberger) or in a revivalist spirit (Bellermann). Since the break with tradition that occurred around 1910, the custom of continuing to teach counterpoint in the Fuxian manner is generally justified by arguing that it is pedagogically necessary to discipline musical thought by means of exercises in ‘dead material’. (No other style can be codified to the same extent as can the technique of Palestrina.)
The distinction between strict and free style, which contrapuntal theory since the 17th century has taken as its starting-point, can be explained by constructing (in Max Weber's sense) antithetic ‘ideal types’: complexes of characteristics which cohere closely and clearly, but also contrast with the characteristics of the other type. Strict style is the older type, passed down from the 16th century, and typical for church music (in Catholic regions); it is based on cantus firmus, is modal in character, and proceeds from two-part writing; the cohesion of its sounds comes from interval progressions; parallel perfect consonances are stringently prohibited and rigorous rules are formulated to govern dissonances and false relations; the didactic method is the system of five ‘species’. Free style is the later type, originating in the 17th century and constantly evolving, and typical for chamber or theatre music; it is based on ‘superposed two-part writing’ (Hindemith, 1937) between melody and bass, is tonal and harmonic in character and proceeds from four-part writing, from the chord as the primary datum; the cohesion of its sounds comes from chord progressions; there are looser regulations forbidding parallel perfect consonances and governing dissonances and false relations; didactically, rhythmically differentiated counterpoint is developed from note-against-note writing by means of figuration.
Although the ideal types of strict and free style are scarcely encountered in their actual form in the history of music theory – most theorists have tried to find some compromise because, while respecting the tradition of strict writing, they have not wanted to neglect the apparent requirements of the day – the antithetical presentation is necessary: it serves as a point of reference among the confusion of doctrinal opinions, and even constitutes a criterion for the assessment of contrapuntal theories, since logical flaws almost always result from deviations from ideal types. When, for instance, Albrechtsberger postulated that one should conduct a harmonic and tonal analysis of a cantus firmus before building a counterpoint on it, it is, strictly speaking, not understandable why he should have started out from two-part writing, hence from an incomplete and therefore technically more difficult presentation of the harmony, instead of beginning with four-part writing as did J.S. Bach and Kirnberger. And when Dehn held that in strict three-part writing a dissonant suspension was a relationship not to another note, but to a chord (2/1883), he was led by the bias of 18th- and 19th-century listening habits to ignore fundamental principles of intervallic writing, and his mistake has technical consequences.
Strict style – contrappunto osservato – was codified by Fux in a form whose didactic merits sufficed to make his Gradus ad Parnassum (1725) a classic textbook for at least two centuries. If Fux consequently appears as the founder of a pedagogic tradition, the content of his book represents the inheritance of a tradition reaching back to Zarlino. The prohibition of hidden parallels, most simply formulated in the tenet that a perfect consonance must be reached by contrary motions, has been expressed in the form of four rules (contrary motion from one perfect consonance to another; unrestricted motion from a perfect consonance to an imperfect consonance; unrestricted motion from one imperfect consonance to another; and contrary motion from an imperfect consonance to a perfect consonance) since the time of Diruta (1609). However, the prohibition held good only for the outer parts, although theorists often laid down stricter regulations. The classification of the rhythmic relations between cantus firmus and counterpoint into five ‘species’ (note against note; two notes against one; four notes against one; syncopation in the second voice; contrapunctus floridus) can be found as early as 1610 in Banchieri's Cartella musicale (1610). This scheme, often criticized and ridiculed as pedantic, has been perpetuated with a pedagogically motivated tenacity; it is hardly reconcilable with the historical reality of Palestrina's style, which provides less an example of cantus firmus composition than a way of writing based on pervasive imitation between textually characterized, rhythmically differentiated parts. The relatively stressed passing dissonance lasting a semiminim (crotchet), permissible in certain cadential formulae in Palestrina's style, was referred to by Berardi (1689) as ‘nota cambiata’, since the consonance and dissonance change their usual places on the stressed and the unstressed beats (ex.17a). Fux, on the other hand, used the concept of ‘cambiata’ (‘Fux's appoggiatura’) to refer to a dissonance that leaps down a 3rd, whose orthodox resolution, as Jeppesen has it (1925), is immediately retrieved with a rising 2nd (ex.17b).
The Fux tradition so much predominated in the teaching of strict style during the 18th and 19th centuries (it constituted the rudiments of the study of composition for Haydn, Mozart and Beethoven) that other systems can claim any raison d'être only by virtue of their departure from his system in certain essential features: at first with compromises between strict writing and free, then later (from the middle of the 19th century) with the tendency to historicize. Albrechtsberger (1790) emphasized that harmonic and tonal examination of the cantus firmus should be undertaken before counterpoint is written; Cherubini (1835) renounced the church modes; Sechter (1854) regarded writing for two or three parts as reductions of four-part writing, which was his starting-point.
If, in consequence, strict counterpoint moved nearer to free style in the late 18th century and the early 19th – through attempts to assimilate it into the changing practice of the ecclesiastical style, whose theory was moulded by it – the exact opposite happened during the 19th century when the combination of historical awareness in contrapuntal theory (Bellermann, 1862) with revivalist endeavours in compositional practice (Haller, 1891) led to a tendency to see the rules of counterpoint in a narrower, stricter light. It was desired to re-establish, both in theory and in practice, the technique of Palestrina, the ‘classical ecclesiastical style’, exactly (to quote Ranke's historiographical dogma) ‘as it actually had been’. Traditionalism, with its unconscious traffic between past and present, yielded to a historicism motivated partly by philology and partly by aesthetics. In the 20th century, after the decline of the Cecilian movement, strict style became petrified into musical mental exercises in a dead language – the Latin of musical instruction. The apparently indispensable didactic considerations cannot always be wholly reconciled with historical endeavours to give a precise description of Palestrina's style: even Jeppesen's textbook (1930), a paragon of pedagogic exposition by a historian, results from an (unacknowledged) compromise.
In spite of secondary changes, the theory of strict style is essentially that of a narrowly confined technique of composition, historically speaking, the style of Palestrina; however one interprets the system of rules – as a norm grounded in the very nature of music, as a body of dogma attaching to a historical style, or as rules of the game for didactic exercises – it is unequivocally certain to which fragment of musical reality it relates. The concept of free style, on the other hand, is a catchment area for extreme varieties of style that have primarily in common a negative characteristic, their departure from the norms of strict style. The usual procedure (in appendixes to textbooks on counterpoint or in the instructions for part-writing in practical textbooks on harmony) of describing free style solely in terms of its permitted deviation from strict style, instead of apprehending it from within, in the form of an ‘ideal type’, according to its own postulates, has arisen for a number of reasons; such description seems a deficiency, albeit an excusable one. It results, first, from the practice of isolating harmonic theory from the theory of counterpoint, from the splitting up of the rudiments of modern compositional technique into two disciplines; second, from the difficulty of extracting from a conglomerate of styles a single internally (and not simply in a negative sense) coherent system of rules; third, from the fact that even individual styles (such as Bach's counterpoint) cannot be so exhaustively, precisely and synoptically codified as can the technique of Palestrina; and finally, from the observation that the laws governing the evolution of counterpoint from the 17th century to the 20th have consisted in counterpoint's progressive emancipation from the norms of prima pratica. (Compare this with the 15th and 16th centuries, when the course of development was precisely the opposite: from a less rigorous to a stricter regulation of composition.)
The stile moderno of the 17th century, which included the monodic, the concertante and the madrigal styles (as did Monteverdi’s term seconda pratica), was founded, on the one hand, as ‘licentious’ counterpoint, on the transgression of the norms of strict style – a transgression grounded in the tendency to emotional expression and pictorial or allegorical word-painting. On the other hand, as ‘harmonic’ counterpoint, it was distinguished from the prima pratica of the 16th century and from the ecclesiastical style that preserved that tradition by being rooted in tonal harmony. However, licentious counterpoint ought not to be equated simply with harmonic counterpoint: not every deviation from contrappunto osservato is motivated by tonal harmony. The best-known such deviations – the irregularities in Monteverdi's madrigals, abominated by Artusi, and seen by Fétis as the earliest document of modern tonality – arise from other causes. The downward leap of a dissonant suspension from a 7th to a 3rd (as in ex.18) is in Monteverdi an expressive figure that owes its pathos to its striking departure from the rules of strict writing, but this licence cannot be interpreted in terms of tonal harmony (one cannot speak of ‘movement within the chord’). Bernhard (c1657) explained this figure, which he considered among the tools of musical rhetoric, as a ‘heterolepsis’ (a ‘recourse to another melodic part’): the upper voice changes its usual resolution, the 6th, for the 3rd, which really belongs to the middle voice.
After its uncertain beginnings in Monteverdi, the use of tonal harmony as a basis for counterpoint gradually increased from the late 17th century, though it did not become universal; theoretical signposts in this development include the writings of Masson (1694) and, particularly, Rameau (1722). The development was never complete: the belief that in harmonically tonal music every detail was determined by means of tonal harmony is an exaggeration resulting from over-systematic thinking. In harmonically tonal writing (and also in contrapuntal writing) harmonies, namely triads and chords of the 7th, constitute the primary, directly available entities from which the composer started out. From this basis in harmony there results the distinction between chordal dissonances, which belong to the harmony (the 7th in the chord of the 7th), and notes foreign to the harmony, which constitute an external adjunct to it. A chordal dissonance must be resolved, but need not be prepared; and for its own part, as a component of the harmony, it can function as the resolution of a note foreign to it. (In bar 4 of Mozart's ‘Jupiter’ Symphony even the octave is a note foreign to the harmony, a suspension leading to the 7th.) Naturally a 7th does not always count as a chordal dissonance, but only when its resolution coincides with a change of root (as in ex.19a) and thus when the dissonance is a determining factor in the harmonic development as represented by the root progression (see Basse fondamentale). Conversely, if the note to which a dissonance relates remains unmoved (as in ex.19b), then the 7th is to be understood as a note foreign to the harmony, i.e. a suspension.
Since
the later 17th century, composers' use of free counterpoint has been
characterized by the fact that dissonant figures taken from licentious
counterpoint – accented passing notes or downward-leaping suspensions – have
been conceived in terms of the requirements of harmonic counterpoint, and hence
related to triads and chords of the 7th instead of to individual notes. It is
true that contrapuntal theory admitted harmonically founded phenomena only
hesitantly. In Bernhard's attempt to sketch out a contrapuntal theory of seconda
pratica (thus, to codify what is not really susceptible of codification),
the dissonant figures of licentious counterpoint, the stylus luxurians,
are described without regard to their harmonic preconditions or implications.
Phenomena such as the accented passing note (transitus inversus), the
upward- or downward-leaping appoggiatura (superjectio or subsumptio)
and the resolution of a suspension by leap (syncopatio catachrestica) or
by a step upwards (mora) are scarcely problematic; and their nature as
exceptions to strict counterpoint, which is clear from the fact that they are
referred back to the norm from which they deviate, is not open to dispute.
However, in a quotation from a recitative (ex.20a), which Bernhard reduced to a bare
skeleton (ex.20b) in order to elucidate its free style as
a paraphrase of a piece of strict counterpoint, thus explaining it as an
agglomeration of licences – an ellipsis (e' instead of f'–e'),
a quaesitio notae (c'
–d' instead of d') and an anticipatio
(e') – there may be doubt as to whether it is not simply a matter of a
broken diminished 7th chord. Hence one may question whether Bernhard was
describing what he heard or whether his musical perception has been
misrepresented in his theory for want of other than contrapuntal terminology.
In their descriptions of free style, Heinichen (1728) and Mattheson (1739), too, started out from the categories of licentious counterpoint: in clear contradiction of the listening habits of their time, and even their own perceptions, they explained as an anticipatio transitus the unprepared use of the 7th in the dominant 7th chord on a strong beat. The 7th, which in strict writing should appear only on a weak beat as a passing note, is interpreted as being anticipated on the strong beat. Kirnberger (1771–9), who took over the basic propositions of Rameau's theory of harmony, outlined a theory of ‘free composition’ sustained by an awareness of tonal harmonic implications; he took as his starting-point four-part writing rather than two-part; dissonances are classified either as ‘essential’ (dissonant chords) or ‘fortuitous’ (notes foreign to the harmony); and ‘embellished or variegated’ counterpoint proceeds from the figuration of a harmonic framework.
From a chorale with continuo accompaniment (ex.21a) – the seemingly two-part writing implies four-part writing by the continuo – Kirnberger evolved a motivic counterpoint ( ex.21b). The upper part decorates dissonant chords melodically (chords of the 2nd, a 6-5 and a 7th) and is to be understood not as an intervallic progression (as which it would be absurd) but as free movement within the chord, with anticipatory dissonances, hence notes foreign to the harmony, on every fourth quaver. The part-writing is justified by the chords that constitute the implicit or (in the continuo) explicit background to the composition.
Alongside the style of Palestrina, the instrumental polyphony of J.S. Bach constitutes one of the models that have determined contrapuntal theory. Whereas Palestrina's style allows barely any doubt over its rules, or at least its basic rules, the technique of Bach's counterpoint has not yet been adequately described and there is some controversy about the principles on which it is founded.
The habit of defining polyphony as a combination of equal melodic parts, the prestige of the fugue as a consummate expression of instrumental counterpoint, and a one-sided concentration on organ and keyboard music (as in Spitta's thesis of the primacy of organ style in Bach's output) all contributed to neglect of the fact that another type of polyphony, borne along by a continuo bass and with the melodic parts not of equal importance but graded, is not less characteristic of Bach's music than is the fugal type. To distort the title of a book by Halm (1913), it is possible to speak of ‘two cultures of counterpoint’ in Bach.
‘Continuo polyphony’ – or ‘concertante counterpoint’ – is founded on the principle of a functional differentiation between the parts: the counterpoint is hierarchical. In Bach's arias, where the writing is undeniably contrapuntal, the vocal part, the concertante instrument and the underpinning of the continuo make up a kind of three-part writing, differing from fugal writing principally in that the parts fulfil different functions throughout rather than fulfilling the same functions (e.g. subject, counter-subject or characteristic counterpoint, complementary counterpoint) in alternating groupings.
In continuo polyphony of the late Baroque period there is a coalescence of heterogeneous traditions, and it is precisely because of this variety that it displays an unsurpassed abundance of contrapuntal possibilities. These traditions included the idea of polyphonic writing originating with the prima pratica: a polyphony ‘eloquent’ in every one of its melodic parts; monodic style as the realization of a declamatory or cantabile, expressive or allegorical type of vocal melodic writing; the principle of concertante writing, with which the growth of idiomatic instrumental motif was closely associated; and, finally, the continuo as bearer of chord progressions, through whose harmonic tonal definition a ‘linear’ deployment of the melodic parts was not impeded or restricted but rather, on the contrary, sustained (as already mentioned).
The idea of deducing a theory of Bachian counterpoint less from his fugal technique than from his typical concertante continuo polyphony ought not to appear too strange. For insofar as the period between 1600 and 1730, when technical developments culminated in Bach's compositional technique, has properly been described as the ‘continuo period’ (Riemann) and as the ‘age of the concertante style’ (Handschin), a historian will find it natural to affirm that concertante continuo polyphony represents the essential paradigm (resulting from the particular circumstances of the time) for Bach's counterpoint.
Since Kurth (1917) coined the term ‘linear counterpoint’ – a term whose subsequent use as a watchword he regarded as a misunderstanding – the controversy over whether Bach's counterpoint was primarily linearly or harmonically determined has continued to rage. In order to avoid an excessively obdurate opposition between conflicting dogmas, the technical aspect of the problem may be distinguished from the aesthetic. Technically (or ‘logically’) speaking, Bach's counterpoint is virtually always grounded in tonal harmony, and where the thematic aspect of his music comes into conflict with the harmonic, it is the thematic rather than the harmonic that is adjusted.
The
dissonance sequence in bar 28 of the Invention in D minor (ex.22a) would be absurd if it were not heard as
an embellishment of the chord of A minor: notes belonging to the chord in the
bass coincide with accented passing notes in the upper part, and notes
belonging to the chord in the upper part with unaccented passing notes in the
bass. The converse is rare: the fact that in bars 11 and 12 of the same piece ( ex.22b) a passage of counterpoint is in itself
comprehensible as a progression of intervals while the chordal significance of
bar 11 as a whole remains uncertain (oscillating between G minor with added 7th
and B
major with a
lower 3rd) represents an exceptional case. Consequently, Kurth's theory that
the harmony is always a resultant rather than a starting-point or precondition
– a theory intended as a suggestive hypothesis, and hence unable to bear
interpretation as a dogma – becomes questionable or even erroneous as an
assertion about Bach's contrapuntal technique. It can still remain reasonable
as an aesthetic postulate, or as a requirement to be met by musical perception.
It will then mean that listeners are expected to give their attention primarily
to the ‘movement feature’ of the individual parts and understand simultaneities
as means to support the music's ‘linear dynamics’.
The fact that – technically, or logically, seen – many such movement features result from the necessity to resolve dissonances, and thus that the ‘energetic’ impetus originates in the music's harmony rather than in its linearity, need not however prevent one from perceiving aesthetically the dissonances as means of reinforcing movement features. These will thus be accorded aesthetic priority even though, in technical respects, they represent a resultant: what is logically primary will appear as aesthetically secondary, and vice versa. (The attempt totally to psychologize the theory of counterpoint, as an encroachment of a manner of aesthetic perception into the description of technical rudiments, would undermine the theory.)
If, then, Bach's counterpoint is grounded in tonal harmony, it is also motivically characterized. Neither ‘lines’ in Kurth's sense of the word (which are to be found in Ockeghem rather than in Bach) nor melodic designs that imitate the rhythms and pitches of speech, but rather motifs and figurations of instrumental origin represent the prime substance found in Bach's polyphony. (Fugue subjects and counter-subjects are complexes of motifs and figurations.)
In bars 9 and 10 of the bourrée from French Suite no.6 (ex.23), the simple root progression in 5ths and the formulaic melodic figures overshadow the irregular dissonances: the contrapuntal details remain aesthetically unobtrusive, since logically, in the structure of the writing, they are subsidiary. The interval sequences that in the style of Palestrina were the very essence of counterpoint have now become merely a by-product of the tonal–harmonic and motivic characterization of the polyphony.
Contrapuntal phenomena that cannot be explained by reference to the usual categories may often result from the superimposition of melodic parts that move according to different rhythmic levels. In the second movement of the trio sonata from Bach's Musical Offering, bars 49–51, the outer voices form a chromatic chain of 6ths and 7ths in a crotchet rhythm (the bass being thematic). But the progression can be reduced to a diatonic model in minims (ex.24), a contrapuntal procedure that dates back to the 15th century. It is to this diatonic, reduced version that one must relate the inner part if the harmonies, which deviate from the norms of tonal harmony, are to become comprehensible: the notes g' in bar 50 and f' in bar 51, which appear to be dominant 7ths left unresolved, are in fact 5ths. The apparent chords of the dominant 7th are an incidental result of the rhythmic and chromatic modification of an original contrapuntal model.
The fact that defining Bach's counterpoint becomes a complicated business, since one has to speak both of concertante continuo polyphony and of hierarchically organized counterpoint, ought not be thought a deficiency. It is precisely to the multiplicity of historical conditions on which it is based that Bach's polyphony owes, first, its abundance of figural material (and that has always been a cause for admiration) and, second, its numerous determining factors, which could only fail to be appreciated when it was sought to deduce the counterpoint from a single principle, that of ‘linearity’.
The period between the later years of the 18th century and the beginning of the 20th is accounted one in which counterpoint sank to being a mere academic exercise, leaving barely recognizable traces in the practice of composers of piano and operatic music. Yet an immense landscape of musical works bearing a primarily homophonic imprint is relieved by isolated polyphonic works or groups of works which, in both spirit and technique, recall older styles. Archaistic counterpoint, looking back to the models of Palestrina or Bach, was by no means the only one; types can be cited that distinguish this period from earlier centuries (provided one does not cut off access to the phenomena that constitute the typical counterpoint of the 19th century by the use of a definition restricting the concept of genuine counterpoint to the older style).
The revival of Palestrina's style, a throwback for which the spirit of the Romantic movement was responsible, was sustained by the enthusiastic belief that only 16th-century vocal polyphony could be ‘true church music’: a maxim shared by Protestant writers (such as E.T.A. Hoffmann and Thibaut) and Catholic alike. Since it remained restricted to sacred music, this reverence for Palestrina could even be totally reconciled with the championing of musical ‘progress’ which the New German school believed it stood for: Liszt sympathized with the aims of the Cecilian movement, and that left its mark on his compositions. In the 19th century, of course, the most important aspect of Palestrina's style used to inculcate a devotional frame of mind was not so much the strict technique of composition as rather the ‘seraphic tone’ of a music whose tempo was dilated so that it could be made to convey the notion of hallowed strains felt to be emanating from some Great Beyond. Although Bellermann's work in laying down precise rules for composition in this style (1862) came about in connection with the church music revival, it also indicates that the objective task of historical reconstruction became divorced from Romantic enthusiasm.
While the revival of Palestrina's style appears primarily to have been a matter of resuscitation and performance of existing music, and only secondarily intruding into the realm of composition, the influence of Bach’s counterpoint was of concern to composers: it was a matter of their professional equipment. The influence exerted by Bach on Chopin and Mendelssohn, Schumann and Brahms should not be sought solely in fugues and fughettas: it can also, and indeed particularly, be felt in their character-pieces. The problem that Romantic composers sought to solve by referring back to Bach consisted in the difficulty of writing in a ‘strict style’ – hence without falling into the technical heedlessness of the general run of operatic and keyboard music – while producing works that were poetic rather than prosaic (under which heading Schumann categorized not just light music but also the merely technical work of art). What they saw realized in exemplary fashion in the music of Bach was the idea of music at once contrapuntal and full of character, at once strict and eloquent: music in which the characteristic and the eloquent features of a contrapuntally differentiated texture were not forced on it from outside but were actually generated by it.
In the instrumental music of the Classical and Romantic eras the fugue represents a kind of counterpoint thought of as ‘strict’, although actually it was a special case of ‘free style’. However, sonata and fugue – or rather, sonata form and fugal technique – were closely related: there was a tendency for the ‘two cultures of music’ to coalesce into a third. On the one hand, as demonstrated by Haydn's evolution from op.20 to op.33, fugue and fugato were prerequisites of thematic working out in the technique of Classical and Romantic development sections. On the other, as the tendency grew for thematic development to spread over entire movements, it became logical to characterize the development section by an intensification of motivic work to the point of fugal technique and thus mark it out as distinct from the exposition and the recapitulation. In Beethoven's late quartets, in Brahms and even in Liszt, fugal technique was in effect displayed as a consequence of thematic working.
The continuation of the second subject in the first movement of Schubert's String Quintet in C, a melody in canon, provides a perfect example of the realization of an idea that constantly recurs in the 19th century, in operatic ensembles as well as in subsidiary themes of Bruckner symphonies: the idea of a cantabile counterpoint, or of a contrapuntal cantabile style. The fact that to aestheticians this must have seemed a hybrid, since it flouted the convention whereby cantabile was associated with homophonic style and polyphony with an unbending thematic style, was seen by composers less as an inhibiting factor than as a challenge to transform this contradiction into an aesthetic proposition and thus a benefit. Indeed, it was characteristic of the 19th century that it tended to bring together apparently mutually exclusive opposites.
The thematic combinations in the prelude to Wagner’s Die Meistersinger and in the final duet of Siegfried – the simultaneous, not wholly unforced, presentation of leitmotifs that had been independently coined – were felt by Schenker to be a betrayal of the concept of counterpoint; Richard Strauss on the contrary praised them as the only adequate form of counterpoint in an age of ‘expressive’ music (and took the idea to technical and aesthetic extremes in Salome and Elektra, as ‘psychological counterpoint’). Here it is undoubtedly a matter of counterpoint as an expression of literary ideas: the motifs are not related as melodic lines but associated aesthetically as symbols of ideas and emotions, while being technically pieced together as encrustations around one and the same chord (not without fissures and flaws). The procedure may be thought technically questionable; but during a period typified by music drama and symphonic poems – genres bearing a strong literary stamp – it should not seem surprising if these literary tendencies infiltrated contrapuntal technique. Or, to put it another way, if one is going to condemn literary counterpoint, one's judgment must also include literary music as a whole.
Polyphony written around chords, and there less for its own sake than for the fact that it imparts a richer and more variegated effect to the orchestral sound, has come into disrepute as ‘pseudo-polyphony’. This term, either explicitly or tacitly, contains the aesthetico–moral reproach that counterpoint, which ought to be an end, has here been relegated to the role of a means, a factor subservient to the quality of sound: instead of being rendered clear by means of instrumentation, the exact opposite happens and it is made to serve as a vehicle of sonority. (Instruments whose parts are characterized by expressivity make a better sonorous impact, even though the details of what they have to say are quite inaudible.) In this judgment is concealed a prejudice that the parameters of music fall into an unalterable hierarchical order: according to this, contrapuntal structure would as a matter of course be the primary factor and instrumentation merely secondary. In the evolution of composition during the mid-20th century this prejudice has been overthrown, so that in retrospect even a historical phenomenon such as the ‘degradation’ of counterpoint to a means towards richness of sonority appears in a very different aesthetic light.
Textbooks, which for didactic reasons are inclined to simplify matters by setting up clear antitheses, suggest that counterpoint functions as an ‘opposite’ to harmony, thus promoting the view that an evolution of harmony embracing varied chordal structures and methods of linking chords must necessarily entail a suppression of polyphony. But in the music of Brahms and Wagner the opposite is patently the case. The harmonic richness characteristic of Brahms forms a corollary to a kind of melodically conceived bass writing (instead of being confined to a small number of supporting notes); and the relationship of such a bass to the melodic line becomes a contrapuntal framework for the compositional technique. In Wagner's harmony it is the individual characterization of chords by means of dissonances and chromatic variants that creates consequences in the contrapuntal writing: on the one hand the dissonant, complicated chords impel their own part-writing; on the other, since the root progression in the bass is often weak and not capable of sustaining its load, chords must be linked by motivic part-writing. Hence the part-writing must tend towards polyphony if the juxtaposition of chords is to have the effect of a compelling progression.
The emphasis on counterpoint in music after 1910 can be seen as a corollary of the diminishing importance of tonal harmony. Chordal coherence lost its fundamental importance, and did so regardless of whether tonality was dissolved (Schoenberg, Berg, Webern) or metamorphosed (Stravinsky, Bartók, Hindemith). The various types of expanded tonality (whose principal feature is not, however, expansion) appear as hierarchically ordered systems analogous to traditional tonality; but it is less chords than individual notes round which they spin a web of relationships, so that it is more natural for the tonal structures to be characterized by melodic and polyphonic than by homophonic style.
Among the techniques that dissolved tonal harmony, bi- or polytonality is notable for its tendency to promote a contrapuntal style. Although it appears to proceed from the superimposition of chords of different keys (as in Strauss's Elektra), it is possible to consider the contrapuntal manifestation (as in Milhaud) as the truly representative one. Polytonal (or polymodal) counterpoint is a paradox of compositional technique in that the tonal atomization of the style as a whole requires a particularly clear tonal characterization of the individual parts; otherwise polytonality – whose aesthetic import consists in the pointedness of its effect – will turn into the grey on grey of tonal indistinguishability.
The problems of 12-note counterpoint inevitably raise the problems of 12-note technique as a whole; here it is necessary to restrict the discussion to comments on some misunderstandings or details that have been taken out of context. First, the ‘emancipation of the dissonance’, the liberation of dissonances from the necessity of resolution, merely means that the specific difference between consonances and dissonances, which gave rise to the dependence of dissonances on consonances, has been abolished, and not that chords no longer possess varying degrees of consonance and dissonance with which the composer can work (Krenek, 1940). In 12-note counterpoint, too, there is a ‘harmonic gradient’ (Hindemith, 1937). Second, Schoenberg's procedure of formulating a 12-note row in such a way that the first half of the original form together with the first half of the inversion transposed down a 5th form a 12-note complex (what Babbitt called ‘combinatoriality’) represents a way out of the dilemma: for the principle of dodecaphony, the non-repetition of notes before a row has been stated in its entirety, is contravened as soon as incidental note repetitions are produced by the simultaneous use of different forms of the row. Where the row itself is a primarily melodic principle, combinatoriality presents itself as a sustaining principle of a kind of ‘strict writing’ in 12-note counterpoint. Third, dodecaphonic counterpoint in Schoenberg (though not in Webern) is to be understood as thematic or motivic counterpoint. Schoenberg did not construct 12-note rows in an abstract way, but as thematic shapes (though naturally they would be modified for constructional purposes); and the assertion that by virtue of dodecaphonic technique – as distinct from free atonality, which tended either towards dependence on a text or towards an aphoristic style – it would once more be possible to compose large-scale forms in instrumental music simply means that dodecaphonic technique permitted the formulation of themes capable of sustaining a large-scale musical structure.
The term ‘linear counterpoint’ (Kurth, 1917) should not be mistaken as a synonym for a heedless sort of polyphony paying no attention to vertical simultaneities. Its distinctive feature is rather the concept of melody, which served as the starting-point for the adherents of the ‘new objectivity’ when they set up linear counterpoint as an anti-type to the Romantic harmony they despised: the notion of a kind of melodic writing not reliant on chords and chordal progressions, but evolved from the alliances and oppositions of leaps and steps, ascents and descents, long and short values, indeed a kind of structure of pitch and rhythm representing a ‘state of energy’ (Kurth) and striving towards an equilibrium which, however, it can only achieve at the very last, so that the melodic movement will not come to a standstill before the final cadence. Counterpoint, however, is in this style nothing more than multiple melody, and is subject to the same criteria of energy as is a single melody: the parts support, enhance or contradict each other; they cross or complement each other.
for modern editions and facsimiles see individual articles
Prosdocimus de Beldemandis: Contrapunctus (1412)
Guilielmus Monachus: De preceptis artis musicae (MS, c1480)
B. Ramos de Pareia: Musica practica (Bologna, 1482)
N. Burtius: Musices opusculum (Bologna, 1487)
G. Guerson: Utilissime musicales regule (Paris, c1490)
F. Gaffurius: Practica musicae (Milan, 1496, 2/1497)
N. Wollick: Opus aureum musicae (Cologne, 1501)
J. Cochlaeus: Musica (n.p., c1504, enlarged 2/c1505 [in D-LEu, anon. in source], 3/1507, abridged 4/1515)
D.M. Durán: Súmula de canto de órgano, contrapunto y composición, vocal y instrumental prática y especulativa (Salamanca, c1504)
A. Ornithoparchus: Musicae activae micrologus (Leipzig, 1517/R)
G. Rhau: Enchiridion musicae mensuralis (Leipzig, 1520, 2/1530, 10/1553)
P. Aaron: Thoscanello de la musica (Venice, 1523/R; rev. with suppl. as Toscanello in musica, 2/1529/R, 3/1539/R, 4/1562)
G.M. Lanfranco: Scintille di musica (Brescia, 1533/R)
S. Vanneo: Recanetum de musica aurea (Rome, 1533/R)
H. Glarean: Dodecachordon (Basle, 1547/R)
A.P. Coclico: Compendium musices (Nuremberg, 1552/R)
N. Vicentino: L'antica musica ridotta alla moderna prattica (Rome, 1555/R, 2/1557)
G. Zarlino: Le istitutioni harmoniche (Venice, 1558/R, rev. 3/1573/R)
G.M. Artusi: L'arte del contraponto ridotta in tavole (Venice, 1586)
V. Galilei: Discorso intorno all'uso delle dissonanze (MS, 1588–91, I-Fn)
V. Galilei: Il primo libro della prattica del contrapunto intorno all'uso delle consonanze (MS, 1588–91, I-Fn)
P. Pontio: Ragionamento di musica … ove si tratta de' passaggi … et del modo di far motetti, messe, salmi et altre compositioni (Parma, 1588)
O. Tigrini: Compendio della musica (Venice, 1588)
G.M. Artusi: Seconda parte dell'arte del contraponto, nella quale si tratta dell’utile et uso delle dissonanze (Venice, 1589)
S. Calvisius: Melopoeia (Erfurt, 1592)
P. Pontio: Dialogo … ove si tratta della theorica et prattica di musica (Parma, 1595)
T. Morley: A Plaine and Easie Introduction to Practicall Musicke (London, 1597/R)
J.P. Sweelinck, attrib.: Compositions-Regeln (MS, c1600, A-Wm, D-Bsb)
S. Cerreto: Della prattica musica vocale et strumentale (Naples, 1601, 2/1611)
G. Diruta: Seconda parte del Transilvano, dialogo diviso in quattro libri (Venice, 1609)
A. Banchieri: Cartella musicale nel canto figurato fermo e contrappunto (Venice, 1610, 3/1614)
J. Lippius: Synopsis musicae novae omnino verae atque methodicae universae (Strasbourg, 1612) [largely a republication of Disputatio musica secunda (Wittenberg, 1609) and Disputatio musica tertia (Wittenberg, 1610)]
P. Cerone: El melopeo y maestro (Naples, 1613/R)
G. Coprario: Rules how to Compose (MS, before 1617, US-SM)
C. Angleria: La regola del contraponto, e della musical compositione (Milan, 1622)
L. Zacconi: Prattica de musica: seconda parte (Venice, 1622/R)
M. Effrem: Censure … sopra il sesto libro de madrigali di M. Marco da Gagliano (Venice, 1623)
J. Crüger: Synopsis musica, continens rationem constituendi et componendi melos harmonicum, conscripta variisque exemplis illustrata (Berlin, 1630, enlarged 2/1654)
M. Scacchi: Cribrum musicum ad triticum Syfertianum, seu examinatio succinta psalmorum (Venice, 1643)
P. Syfert: Anticribratio musica ad avenam Scacchianam (Danzig, 1645)
M. Scacchi: Breve discorso sopra la musica moderna (Warsaw, 1649)
A. Kircher: Musurgia universalis (Rome, 1650/R)
J.A. Herbst: Arte prattica et poëtica, das ist Ein kurtzer Unterricht wie man einen Contrapunct machen und componiren sol lernen (Frankfurt, 1653)
G. Avella: Regoli di musica, divise in cinque trattati (Rome, 1657)
C. Bernhard: Tractatus compositionis augmentatus (MS, c1657)
L. Penna: Li primi albori musicali per li principianti della musica figurata (Bologna, 1672, 4/1684/R, 5/1696)
G.M. Bononcini: Musico prattico che brevemente dimostra il modo di giungere alla perfetta cognizione di tutte quelle cose, che concorrono alla composizione de i canti e di ciò ch'all'arte del contrapunto si recerca, op.8 (Bologna, 1673/R)
A. Berardi: Documenti armonici (Bologna, 1687)
A. Berardi: Miscellanea musicale (Bologna, 1689)
A. Berardi: Arcani musicali (Bologna, 1690)
C. Masson: Nouveau traité des règles pour la composition de la musique (Paris, 1694)
G.A. Angelini Bontempi: Historia musica (Perugia, 1695/R)
J.G. Walther: Praecepta der musicalischen Composition (MS, 1708, D-WRtl)
J.-P. Rameau: Traité d'harmonie (Paris, 1722/R)
J.J. Fux: Gradus ad Parnassum (Vienna, 1725, 2/1745)
J.D. Heinichen: Der General-Bass in der Composition, oder Neue und gründliche Anweisung (Dresden, 1728)
J. Euler: Tentamen novae theoriae musicae (St Petersburg, 1739)
J. Mattheson: Der vollkommene Capellmeister (Hamburg, 1739/R)
F.W. Marpurg: Abhandlung von der Fuge nach dem Grundsätzen der besten deutschen und ausländischen Meister (Berlin, 1753–4/R, 2/1858)
F.W. Marpurg: Handbuch bey dem Generalbasse und der Composition mit zwey-drey-vier-fünf-sechs-sieben-acht und mehreren Stimmen (Berlin, 1755–8/R, suppl., 1760/R; 2/1762/R [vol.i only]: Anhang (Berlin, 1760/R)
J.P. Kirnberger: Die Kunst des reinen Satzes in der Musik (Berlin and Königsberg, 1771–9)
G.B. Martini: Esemplare, ossia saggio fondamentale pratico di contrappunto sopra il canto fermo, i (Bologna, 1774), ii (Bologna, 1775)
J.P. Kirnberger: Gedanken über die verschiedenen Lehrarten in der Komposition (Berlin, 1782)
J.G. Albrechtsberger: Gründliche Anweisung zur Komposition (Leipzig, 1790)
MGG2 (‘Kontrapunkt’; C. Palisca, W. Krützfeld)
A. Reicha: Cours de composition musicale, ou Traité complet et raisonné d’harmonie pratique (Paris, 1818; Eng. trans., 1854/R)
F.-J. Fétis: Traité du contrepoint et de la fugue (Paris, 1824, enlarged 2/1846)
A. Reicha: Traité de haute composition musicale (Paris, 1824–6)
L. Cherubini: Cours de contrepoint et de fugue (Paris, 1835; Eng. trans., 1837)
A.B. Marx: Die Lehre von der musikalischen Komposition praktisch-theoretisch, i (Leipzig, 1837, 10/1903; Eng. trans., 1852); ii: Die freie Komposition (Leipzig, 1837, 7/1890); iii (Leipzig, 1845, 5/1879); iv (Leipzig, 1847, 5/1888; Eng. trans., 1910)
J.C. Lobe: Compositionslehre oder Umfassende Lehre von der thematischen Arbeit (Leipzig, 1844)
J.C. Lobe: Lehrbuch der musikalischen Komposition (Leipzig, 1850–67, 5/1884–7)
S. Sechter: Die Grundsätze der musikalischen Komposition (Leipzig, 1853–4)
S. Dehn: Lehre vom Contrapunkt, dem Canon und der Fuge (Berlin, 1859, 2/1883)
J.G.H. Bellermann: Der Kontrapunkt (Berlin, 1862, 4/1901)
A. de la Fage: Essais de dipthériographie musicale (Paris, 1864)
E.F. Richter: Lehrbuch des einfachen und doppelten Kontrapunkts (Leipzig, 1872; Eng. trans., 1874)
L. Bussler: Der strenge Satz (Berlin, 1877, 2/1905)
S. Jadassohn: Musikalische Kompositionslehre (Leipzig, 1883–9)
H. Riemann: Lehrbuch des einfachen, doppelten und imitierenden Kontrapunkts (Leipzig, 1888, 3/1915; Eng. trans., 1904)
E. Prout: Counterpoint, Strict and Free (London, 1890/R)
M. Haller: Kompositionslehre für polyphonen Kirchengesang mit besonderer Rücksicht auf die Meisterwerke des 16. Jahrhunderts (Regensburg, 1891)
E. Prout: Double Counterpoint and Canon (London, 1891, many later edns)
C. de Sanctis: Trattato di contrappunto e fuga (Milan, 1895, 2/1934)
T. Dubois: Traité de contrepoint et de fugue (Paris, 1901)
F. Draeseke: Der gebundene Styl: Lehrbuch für Kontrapunkt und Fuge (Hanover, 1902)
P. Goetschius: Counterpoint (New York, 1902, 5/1915)
H. Riemann: Grosse Kompositionslehre, i: Der homophone Satz (Berlin and Stuttgart, 1902, 2/1912); ii: Der polyphone Satz (Berlin and Stuttgart, 1903, 2/1912); iii: Der Orchestersatz und der dramatische Gesangstil(Berlin and Stuttgart, 1913)
B.E. Scholz: Lehre vom Kontrapunkt und den Nachahmungen (Leipzig, 1904)
C.H. Kitson: The Art of Counterpoint and its Application as a Decorative Principle (Oxford, 1907, 2/1924)
S. Krehl: Kontrapunkt (Leipzig, 1908)
S.I. Taneyev: Podvizhnoy kontrapunkt strogogo pis'ma [Invertible counterpoint in the strict style] (Leipzig and Moscow, 1909; Eng. trans., 1962)
P. Goetschius: Exercises in Elementary Counterpoint (New York, 1910)
H. Schenker: Neue musikalische Theorien und Phantasien, ii/1 (Vienna, 1910); ii/2 (Vienna, 1922)
A.O. Halm: Von zwei Kulturen der Musik (Munich, 1913, 3/1947)
F. Corder: ‘The Difficulties of Counterpoint’, PMA, xl (1913–14), 1–13
J. Wolf: ‘Ein Beitrag zur Diskantlehre des 14. Jahrhunderts’, SIMG, xv (1913–14), 504–34
E. Kurth: Grundlagen des linearen Kontrapunkts (Berne, 1917, 5/1956)
W. Hohn: Der Kontrapunkt Palestrinas und seiner Zeitgenossen (Regensburg, 1918)
E. Kurth: ‘Zur Stilistik und Theorie des Kontrapunkts’, ZMw, i (1918–19), 176–84
H. Riemann: Geschichte der Musiktheorie im IX.–XIX. Jahrhundert (Berlin, 2/1921/R; Eng. trans. of pts i–ii, 1962/R, and pt iii, 1977)
R.O. Morris: Contrapuntal Technique in the 16th Century (Oxford, 1922)
H. Grabner: Der lineare Satz (Stuttgart, 1925, 2/1961)
K. Jeppesen: Der Palestrinastil und die Dissonanz (Leipzig, 1925; Eng. trans., 1927, 2/1946)
R.O. Morris: Foundations of Practical Harmony and Counterpoint (London, 1925)
C. Koechlin: Précis des règles du contrepoint (Paris, 1926; Eng. trans., 1927)
H. Roth: Elemente der Stimmführung (Stuttgart, 1926)
C.H. Kitson: Invertible Counterpoint and Canon (London, 1927)
C.S. Macpherson: Studies in the Art of Counterpoint (London, 1928)
H. Anglès: ‘Dos tractats medievals de música figurada’, Musikwissenschaftliche Beiträge: Festschrift für Johannes Wolf, eds. W. Lott, H. Osthoff and W. Wolffheim (Berlin, 1929/R), 6–12
C.L. Seeger: ‘On Dissonant Counterpoint’, MM, vii/4 (1929–30), 25–31; repr. in Classic Essays on Twentieth-Century Music, ed. R. Kostelanetz and J. Darby (New York, 1996), 179–84
P.S.H. Günther: Moderne Polyphonie (Berlin, 1930)
K. Jeppesen: Kontrapunkt (Vokalpolyfoni) (Copenhagen, 1930, 3/1962; Eng. trans., 1939)
F.T. Arnold: The Art of Accompaniment from a Thorough-Bass as Practised in the 17th and 18th Centuries (London, 1931/R)
R.W. Wood: ‘Modern Counterpoint’, ML, xiii (1932), 312–18
P. Nalli: ‘Regulae contrapuncti secundum usum Regni Siciliae’, Archivio storico per la Sicilia orientale, xxxix (1933), 277–92
F. Wright: The Essentials of Strict Counterpoint (Brooklyn, NY, 1935)
M.F. Bukofzer: Geschichte des englischen Diskants und des Fauxbourdons nach den theoretischen Quellen (Strasbourg, 1936/R)
L.K. Feininger: Die Frühgeschichte des Kanons bis Josquin des Prez (Emsdetten, 1937)
T. Georgiades: Englische Diskanttraktate aus der ersten Hälfte des 15. Jahrhunderts (Würzburg, 1937)
P. Hindemith: Unterweisung im Tonsatz, i: Theoretischer Teil (Mainz, 1937, 2/1940; Eng. trans. of i–ii as Craft of Musical Composition, 1942, 2/1948)
E.T. Ferand: Die Improvisation in der Musik (Zürich, 1938)
R.H. Robbins: Beiträge zur Geschichte des Kontrapunkts von Zarlino bis Schütz (diss., U. of Berlin, 1938)
J.N. David: ‘Der Kontrapunkt in der musikalischen Kunst’, BJb, xxxvi (1939), 50–61
V. Ferroni: Corso di contrappunto e fuga, ed. E. Pozzoli (Milan, 1939)
A.T. Merritt: Sixteenth-Century Polyphony: a Basis for the Study of Counterpoint (Cambridge, MA, 1939)
E.J. Dent: ‘The Teaching of Strict Counterpoint’, MR, i (1940), 201–13
E. Krenek: Studies in Counterpoint (New York, 1940)
R. Casimiri: ‘Teodono de Caprio, non Teodorico de Campo, teorico musicale italiano del secolo XV: un suo tratto inedito’, NA, xix (1942), 38–42, 93–8
E. Pepping: Der cantus-firmus-Satz, Der polyphone Satz, i (Berlin, 1943, 2/1950)
R.B. Henning: The Use of Contrapuntal Techniques by Contemporary Composers (diss., Radcliffe College, 1947)
E. Krenek: A Discussion of the Treatment of Dissonances in Ockeghem's Masses as Compared with the Contrapuntal Theory of Johannes Tinctoris (St Paul, MN, 1947)
A.I. McHose: The Contrapuntal Harmonic Technique of the 18th Century (New York, 1947)
W. Piston: Counterpoint (New York, 1947)
A. Bush: Strict Counterpoint in the Palestrina Style (London, 1948)
C.W. Fox: ‘Modern Counterpoint: a Phenomenological Approach’, Notes, vi (1948–9), 46–62
H. Lemacher and H. Schroeder: Lehrbuch des Kontrapunkts (Mainz, 1950)
B. Blacher: Einführung in den strengen Satz (Berlin, 1953)
M. Hoffman: A Study of German Theoretical Treatises of the Nineteenth Century (diss., U. of Rochester, 1953)
K. Sikorski: Kontrapunkt (Warsaw, 1953–7)
J. Hein: Die Kontrapunktlehre bei den Musiktheoretikern im 17. Jahrhundert (diss., U. of Cologne, 1954)
H. Scare: Twentieth Century Counterpoint (London, 1954)
V. Soudères: ‘Le sens actuel de la pensée contrapuntique: inventaire des techniques redactionnelles’, Polyphonie, nos.9–10 (1954), 5–16
P. Hamburger: Studien zur Vokalpolyphonie, i (Copenhagen and Wiesbaden, 1956); ii in DAM, iv (1964–5)
C.V. Palisca: ‘Vincenzo Galilei's Counterpoint Treatise: a Code for the seconda pratica’, JAMS, ix (1956), 81–96
E. Pepping: Übungen im doppelten Kontrapunkt und im Kanon, Der polyphone Satz, ii (Berlin, 1957)
M. Thaling: Der Kontrapunkt bei Mozart (diss., U. of Basle, 1957)
H.K. Andrews: An Introduction to the Technique of Palestrina (London, 1958)
J.M. Chomiński: Historia harmonii i kontrapunktu (Kraków, 1958)
E. Krenek: Tonal Counterpoint (New York, 1958)
T.W. Adorno: ‘Die Funktion des Kontrapunkts in der neuen Musik’, Klangfiguren: Musikalischen Schriften, i (Berlin, 1959)
A. Seay: ‘Paolo da Firenze: a Trecento Theorist’, L'Ars Nova italiana del Trecento I: Certaldo 1959, 118–40
S. Hermelink: Dispositiones modorum: die Tonarten in der Musik Palestrinas und seiner Zeitgenossen (Tutzing, 1960)
E. Rubbra: Counterpoint: a Survey (London, 1960)
R. Schlötterer: ‘Struktur und Kompositionsverfahren in der Musik Palestrinas’, AMw, xvii (1960), 40–50
C. Dahlhaus: ‘Zur Theorie des klassischen Kontrapunkts’, KJb, xlv (1961), 43–57
R.L. Crocker: ‘Discant, Counterpoint, and Harmony’, JAMS, xv (1962), 1–21
C. Dahlhaus: ‘Bach und der “lineare Kontrapunkt”’, BJb, xlix (1962), 58–79
C. Dahlhaus: ‘Domenico Belli und der chromatische Kontrapunkt um 1600’, Mf, xv (1962), 315–40
C. Dahlhaus: ‘Die “Nota Cambiata”’, KJb, xlvii (1963), 115–121
A. Schoenberg: Preliminary Exercises in Counterpoint, 1936–50, ed. L. Stein (London, 1963)
A. Seay: ‘The “Liber musices” of Florentius de Faxolis’, Musik und Geschichte/Music and History: Leo Schrade zum sechzigsten Geburtstag (Cologne, 1963), 71–95
E. Apfel: Beiträge zu einer Geschichte der Satztechnik von der frühen Motette bis Bach (Munich, 1964–5)
C. Dahlhaus: Untersuchungen über die Entstehung der harmonischen Tonalität (Kassel, 1968)
H. Eggebrecht and F. Zaminer: Ad organum faciendum (Mainz, 1970)
K.-J. Sachs: ‘Zur Tradition der Klangschritt-Lehre: die Texte mit der Formel “Si cantus ascendit … ” und ihre Verwandte’, AMw, xxviii (1971), 233–70
E. Apfel: Grundlagen einer Geschichte der Satztechnik (Saarbrücken, 1974)
K.-J. Sachs: Der Contrapunctus im 14. und 15. Jahrhundert: Untersuchungen zum Terminus, zur Lehre und zu den Quellen (Wiesbaden, 1974)
J. Rothgeb: ‘Strict Counterpoint and Tonal Theory’, JMT, xix (1975), 260–84
P.P. Scattolin: ‘La regola del “grado” nella teoria medievale del contrappunto’, RIM, xiv (1979), 11–74
F. Rempp: Die Kontrapunkttraktate Vincenzo Galileis (Cologne, 1980)
K.J. Snyder: ‘Dietrich Buxtehude's Studies in Learned Counterpoint’, JAMS, xxxiii (1980), 544–64
D. de la Motte: Kontrapunkt (Munich, 1981)
E. Apfel: Diskant und Kontrapunkt in der Musiktheorie des 12. bis 15. Jahrhunderts (Wilhelmshaven, 1982)
K.-J. Sachs: ‘Contrapunctus/Kontrapunkt’ (1982), HMT
R. Groth: Die französische Kompositionslehre des 19. Jahrhunderts (Wiesbaden, 1983)
K.-J. Sachs: ‘Die Contrapunctus-Lehre im 14. und 15. Jahrhundert’, Die mittelalterliche Lehre von der Mehrstimmigkeit, Geschichte der Musiktheorie, ed. F. Zaminer, v (Darmstadt, 1984), 161–256
B. Cooper: ‘Englische Musiktheorie im 17. und 18. Jahrhundert’, ibid., 141–314
W. Seidel: ‘Französische Musiktheorie im 16. und 17. Jahrhundert’, ibid., 4–140
R. Kramer: ‘“Gradus ad Parnassum”: Beethoven, Schubert and the Romance of Counterpoint’, 19CM, xi (1987–8), 107–20
K.-W. Gümpel and K.-J. Sachs: ‘Das Manuskript Girona 91 und sein Contrapunctus-Traktat’, AMw, xlv (1988), 186–205
R. Groth: ‘Italienische Musiktheorie im 17. Jahrhundert’, Italienische Musiktheorie im 16. und 17. Jahrhundert: Antikenrezeption und Satzlehre, Geschichte der Musiktheorie, ed. F. Zaminer, vii (Darmstadt, 1989), 307–79
F. Rempp: ‘Elementar- und Satzlehre von Tinctoris bis Zarlino’, ibid., 39–220
L. Rogers: Stravinky's Alternative Approach to Counterpoint (diss., Princeton U., 1989)
E. Schroeder: ‘Dissonance Placement and Stylistic Change in the Fifteenth Century: Tinctoris's Rules and Dufay's Practice’, JM, vii (1989), 366–89
E. Seidel: ‘Zur Kontrapunktlehre von Heinrich Bellermann’, Palestrina und die Idee der klassischen Vokalpolyphonie im 19. Jahrhundert: Frankfurt 1987, 231–41
J. Lester: History of Compositional Theory in the 18th Century (Cambridge, MA, 1992)
W. Braun: ‘Deutsche Musiktheorie des 15. bis 17. Jahrhunderts, ii: von Calvisius bis Mattheson’, Vom Magister und Schulkantor zum vollkommenen Kapellmeister, Geschichte der Musiktheorie, ed. F. Zaminer, viii (Darmstadt, 1994)
E. Schwind: Kadenz und Kontrapunkt: zur Geschichte der Kompositionslehre ca.1470–ca.1570 (diss., U. of Freiburg, 1996)