From Delightful to Barbarous : The Decline in Canonic Writing and the Rise of Functional Harmony

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1 From Delightful to Barbarous : The Decline in Canonic Writing and the Rise of Functional Harmony Submitted to The Undergraduate Awards May,

2 Introduction To Zarlino and many other sixteenth-century theorists, canons and imitation 1 are not only delightful but [embody] elegance and art, all the more when [their] movements are well ordered and the contrapoint well regulated (Zarlino [1558] 1983, 126). Nonetheless, by the eighteenth century the interest in canons had declined. Niedt even describes canons as barbarous ([1700/10, 1721 and 1717] 1989, 250). Mattheson s view is more moderate, saying that [p]ractice in this [writing canons] is good [ ] so long as [the composer] does not get carried away and ignore the essence of melody ([1739] 1981, 744). Unfortunately, it seems that these theorists do not sufficiently explain why there was such a change in opinion regarding canons. Indeed, tastes change. Many eighteenth-century musicians preferred the galant style, with a simpler, more homophonic texture. Turgid counterpoint was generally regarded as archaic. 2 However, canons do not necessarily involve complex counterpoint; there are also canons that are described as galant. Commenting on the Goldberg Variations, David Yearsley praises Bach as the greatest master of the galant canon (2002, 139). In other words, canons can co-exist with galant aesthetics. And yet canonic writing declined in the eighteenth century. If social and stylistic changes cannot fully explain the decline of canonic writing, could a theoretical approach such as an examination of contemporary counterpoint treatises give us more insight? In Gründliche Anweisung zur Composition, Albrechtsberger says that complex canons are difficult to invent, [but] [m]any celebrated masters of the Italian, Flemish and German schools [ ] have left good models ([1790] 1855, ). Albrechtsberger implies that canons in the Renaissance were masterly, but by his times canons had become difficult to write. One must note that Albrechtsberger has re-written Fux s essentially modal counterpoint treatise Gradus ad Parnassum ([1725] 1971) to teach tonal counterpoint. Does this imply that the difficulties in canonic writing arose due to the rise of functional harmony? It seems to me that very few theorists have thoroughly explored this question. In order to investigate why canons fell from being delightful to barbarous, and its relationship with the development of functional harmony, I will examine canons and 1 Zarlino does not actually use the terms canon and imitation, but what he calls fuga sciolte and fuga legate are what we now understand to be imitation and canon at the unison, octave, fourth and fifth, respectively ([1558] 1983, ). What he calls imitation sciolte and imitation legate are what we call imitation and canon at any interval, respectively (ibid, 135). 2 For more details on the galant style and galant composers attitude towards counterpoint, see Pestelli 1984,

3 imitation in the works of Bach, Haydn and Mozart. Bach is chosen as the starting point because in the Baroque, some interest in canons was retained and several of Bach s compositions show a mixture of modal and tonal practices. This is contrary to the common view that Bach s compositions are completely tonal. 3 Mozart and Haydn are chosen because during their times, the popularity of canons declined whereas functional harmony became more firmly established. Canons written with a mixture of modal and tonal practices will be discussed in Section 1, those written in functional harmony in Section 2. Section 3 will investigate how the compositional procedures for canons changed due to functional harmony, and the consequences of such changes. I will examine theoretical texts from Zarlino to Jadassohn, especially those related to counterpoint and canons. I will also consider whether the principles in the prescriptive and didactic texts were reflected in actual musical practice. To facilitate the discussion below, some key terms have to be defined. From the eighteenth century onwards, the term canon commonly means imitation maintained among two or more parts from beginning to end of a composition (Collins 1992, 122). This essay takes this as the definition of canon. If imitation occurs between two or more parts but is not carried out to the end of the piece or a separate section of a piece, this essay simply calls it imitation (Collins 1992, ). Functional harmony comprises two main aspects, namely: directionality [italics in original], resulting from tension and resolution, expressed most effectively in the tonic/dominant axis and unification [italics in original], produced by relating all harmonic structures and procedures to a single center (LaRue 2011, 53). The chord progressions of the music usually conform to the pattern tonic intermediate harmonies dominant tonic while deviations can be explained as embellishing chords. 1. Canons between modality and tonality LaRue calls the Baroque period the middle ground between modality and tonality (2001, 293). To understand how the system between modality and tonality affects canonic writing, I shall first give an overview of the harmony in this middle ground period. During this period, the modal system existed alongside the newly emerging tonal system. 4 Dahlhaus describes the harmony in this period as a coordinate 3 For example, Benjamin argues that in Bach s music there is a strong, directional harmonic progression (1986, 1). Likewise, Kennan suggests that in Baroque counterpoint [t]he lines must imply a good harmonic succession (1999, 19). 4 For a comprehensive discussion on the co-existence of the modal and tonal systems in the 3

4 structure (Nebenordnung), in which sonorities are linked one after the other without giving rise to the impression of a goal-directed development ; in contrast, major-minor tonality is a subordinate structure (Subordination), since one chord is the central goal to which other sonorities are subordinated (1990, 141). In other words, the harmony in this middle ground period exhibits less directionality and unification characteristic of functional harmony. To facilitate our discussion, this essay describes music exhibiting the mixture of tonality and modality, to whatever degree, as being in the mixed system. Since the coordinate structure is less goal-directed, the modality of a composition before functional harmony might be obscure, in contrast to the preference for tonal clarity in pieces within functional harmony in the eighteenth century. There are Renaissance compositions which could scarcely be analyzed as being in any mode. Pietro Aaron calls these compositions canti euphonaci (translated in Strunk [1952] 1981, 19). Similarly, in this middle ground period, the tonality or modality of the piece was sometimes ambiguous. Bach s BWV 1073 exemplifies how the ambiguity in the mode or key facilitates the composition of stacked canons. 5 EXAMPLE 1: J. S. Bach, BWV1073, bs.1 3 Denis Collins identifies this piece as a stacked canon, in which the successive voices begin at a fifth above the previous voice (2002, 16). When he analyzes this canon in tonal terms, which is in general the commonest approach to Bach s compositions, he finds progressions such as V ii IV which are unidiomatic in functional harmony (Collins 2002, 27). This suggests that a purely tonal analysis of Bach s music may be, in some cases, insufficient. Taking a slightly unorthodox approach, in her book Bach s Modal Chorales (1995), Lori Burns suggests that some of Bach s works can be seventeenth and eighteenth centuries, see Lester The term stacked canon was first coined by Alan Gosman. It is a canon in which any voice which is a comes could itself also serve as a dux and any two consecutive voices will be related by the same interval (1997, 289). 4

5 analyzed as being modal. In light of Burns s view and our previous discussion on the mixed system, I suggest that analyzing this canon as mixing modal and tonal practices is more insightful than Collins tonal approach. In this canon, if the voices are analyzed separately, each voice suggests a different mode or key, although these melodies do not emphasize the characteristic species of the modes concerned. As a whole, the tonality of the composition is ambiguous, but one might assign this piece to C major because of the progression of the bass. In Liber de natura et proprietate tonorum, Tinctoris says that individual voices of a polyphonic piece might be assigned to different modes, yet the overall mode of the composition is determined by the mode of the tenor voice ([1476] 1976, 24 25). Here, the way different voices suggest different modes is similar to the Renaissance practice described by Tinctoris. The modal or tonal ambiguity in the mixed system makes the composition of stacked canons easier, for Bach can focus on the individual lines without having to produce functional harmonic progressions. Therefore, despite being a stacked canon, whose technical challenge is well known, this canon spans 16 bars with long and flowing phrases. The mode of a composition before functional harmony is even more ambiguous when modal mixture or commixture appears. The mode is mixed if the music spans the ambitus of the plagal and authentic modes of the same final; commixed if the modes concerned have different finals (Judd 2002, 371). In contrast to the concept of modulation in tonal music, in which the music progresses from one tonal area to another, mixture or commixture is a bipolar relationship as a permanent state of affairs (Dahlhaus 1990, 224), since the features of different modes are present simultaneously. Modal commixture is similar to what LaRue (2001) calls bifocal tonality, which he has observed in many of Bach s compositions. Bifocal tonality is characterized by oscillation between major and relative minor [ ] The two centers seem to be of approximately equal importance (LaRue 2011, 52 53). Bifocal tonality is seen in Bach s Vom Himmel Hoch Variation 4, which is an augmentation canon at the octave. In this piece, C major is mixed with A minor. In b.1 the top and bottom voices suggest A minor whereas the middle voice suggests C major. Afterwards, the structural pitches of both keys appear in metrically important positions (circled in Example 2). 5

6 EXAMPLE 2: J. S. Bach, Variation 4 from Vom Himmel hoch, da komm ich her, BWV 769, bs.1 3 A minor? C major? A minor? Thomas Benjamin argues that canons at the octave can easily exhibit harmonic monotony and static tonality (1986, 127). The harmony can be even more monotonous in augmentation canons at the octave, since the augmented voice drags the harmonic rhythm. Bach here uses bifocal tonality to make this piece harmonically colourful even though it is an augmentation canon at the octave. Since individual voices may suggest different modes or keys in the mixed system, it may be difficult to employ all voices to form a harmonic progression leading to an authentic cadence. Perhaps this is one reason for modal counterpoint to use linear cadences approaching the final by step from above and below. This type of cadence encourages greater continuity of the music, and often there is no strong cadence until the piece ends (Sheldon 1990, ). Zarlino even devotes a chapter in The Art of Counterpoint to discuss methods of evading cadences ([1558] 1983, ). Influenced by the modal practice, the internal cadences in this middle ground period are often weak or evaded. Weak cadences are used for modulations in Bach s Canon per tonos from Musikalisches Opfer (Example 3). Every modulation up a second is completed by a V6/5 i6 cadence when the canon is repeated. As we shall see later, in tonal compositions, usually a stronger cadence is used to make the modulation more convincing. Many canons written in functional harmony (to be discussed in Section 2) either do not modulate, or are broken for the sake of modulation. In contrast, Bach achieves modulation in this piece without breaking the canon. 6

7 EXAMPLE 3: J. S. Bach, Canon per tonos, from Musikalisches Opfer, BWV 1079 Canon repeats Non-functional chromaticism is also used to smooth out the modulations in this canon. In the mixed system, since the harmony is less directed and less unified towards a central goal, chromaticism often has purely local effects. As Dahlhaus says, [I]n contrast to the leading-tone chromaticism of the 17 th and 18 th centuries, that of the 14 th and 15 th centuries lacks a tonal or modal function. (1990, 176) In this canon, Bach s use of chromaticism for coloration and local effects (circled in Example 3) resembles the Renaissance practice. To use Dahlhaus s term, only at the end of the canon does Bach use leading-tone chromaticism to achieve modulation. In a minor piece, the modulation schema is usually tonic tonic parallel (i.e. relative major) dominant tonic (Dahlhaus 1990, 212). In Example 3, modulating to the supertonic minor successively is slightly unusual. As Geck notices, This element of illusory infiniteness recalls the works of Netherlandish and German sixteenth-century composers, in which upward or downward modulations are executed through the sophisticated use of accidentals [ ] Bach may have known such works. (2006, 639) Bach s modulation by a major second upwards resembles more the modal than the tonal practice. He colors the music with chromaticism to ease into the necessary leading-tone chromaticism at 7

8 cadences, which may sound abrupt without the chromaticism for coloration earlier in the piece. From these observations, features of the mixed system, such as modal or tonal ambiguity and weak cadences, actually aid the composition of complex canons. Perhaps these are some reasons why complex canons were still frequently written in the mixed system, as they were in the modal system. 2. Canons and imitation in functional harmony During the late-eighteenth century, functional harmony started to appear consistently in compositions. 6 Many composers then preferred tonal clarity, especially at the beginning of the piece. Modulations, which became an important means of creating harmonic variety, were highlighted by changes in harmonic rhythm and strong cadences. To achieve these features, the composer must be able to effectively control the harmonic progressions. Unfortunately, this is very difficult in a canon. The rise of functional harmony brought with it the preference for establishing the key clearly at the beginning of the composition. For Marpurg, every beginning of a good melody must be written with such notes that give a clear concept of the key in which the piece goes [daß aller Anfang einer guten Melodie mit solchen Klängen gemacht werden muß, welche einen deutlichen Begriff von der Tonart, aus welcher das Stück geht, geben] ( , 258). This view was not uncommon amongst eighteenth-century theorists. In canons at the octave, especially those employing many voices, the clarity of the key at the beginning of the leading voice usually leads to extremely slow harmonic rhythm. Der Schuster bleib bei seinem Leist by Haydn is a case in point. 6 Grove Music Online, s. v. Harmony in the section 3. Historical Development (ii) the Classical era (by Carl Dahlhaus), (accessed 28 December 2014). 8

9 EXAMPLE 4: Haydn, Der Schuster bleib bei seinem Leist Alan Gosman notices that the canon stays in tonic harmony throughout (2000, 47). Since there are eight imitative voices at the same pitch level, the music dwells in the same harmony for a long time. A dux melody clearly showing the key of the piece brings about extremely slow harmonic rhythm in a canon with many voices. In a canon at the octave or unison, even if the leading voice moves to another chord quickly, the harmonic pattern often repeats when other voices enter. This is seen in Bach s Canon in F major, BWV EXAMPLE 5: J. S. Bach, Canon in F major, BWV 1078, bs.1 9 This is a canon at the octave with seven voices in addition to a non-canonic bass. The 9

10 harmony simply oscillates between the tonic and dominant (vii and V). In this canon, it seems that the harmonic stasis is the result of the composer trying to accommodate many canonic voices. In contrast, in a canon at intervals other than the octave or unison, even if the leading voice clearly establishes the tonic at the beginning, the entries of other voices quickly push the harmony away from the tonic. This is seen in Variation 6 in Bach s Goldberg Variations, a canon in the second above in G major. EXAMPLE 6: J. S. Bach, Variation 6 from Goldberg Variations, bs.1 8 The chord labels in the middle of the staff in Example 6 show the harmonic progression without the non-canonic bass. The sonorities create the impression that the music passes through several tonalities without directionally establishing G major as the tonic center, especially due to the progression I6/4 ii in bs.5 6. Nonetheless, the non-canonic bass regulates the harmony. Chord labels below the staff show the harmonic progression with the non-canonic bass. The chord in b.6 becomes vii ø 4/3, and bs.4 7 assume the dominant function with the I6 in b.5 serving as an embellishing chord. Without this free bass voice, the canon itself does not articulate G major clearly. Arguably, canons at intervals other than the octave or unison might be regarded as overlapping melodic sequences. It is difficult to control the harmonic progression in such canons due to their sequential nature. According to Louis and Thuille, in sequences, [h]armonic context [ ] exists only secondarily. Tonal relationships, however, recede completely into the background (cited and translated in Schwartz 1982, ). The harmony in sequences and in canons at intervals other than the 10

11 octave or unison resembles what LaRue calls migrant tonality, in which the music passes constantly from one temporary key center to another without establishing consistent directions or any central gravitational goal (2011, 52). Perhaps this is the reason why, in the Classical period, sequences and imitation are mostly used in development or transition sections, which generally have faster harmonic rhythm. One example is Movement I of Mozart s K.515. There is a double canon towards the end of the development section. In bs , the cello imitates the first violin at the seventh below (1 st canon) whereas the first viola imitates the second violin at the fifth below (2 nd canon). EXAMPLE 7: Mozart, Movement I, Quintet in C Major K. 515, bs (canonic voices only) 1 st canon 2 nd canon In music theory, retrospective opinions are often insightful. Writing a hundred years later than Mozart, Riemann observes that it is very hard to control the harmonic 11

12 progression in a canon at a seventh or second ([1888] 1904, 158). It is therefore not surprising that Mozart here chooses to write the first canon at the seventh below. At this interval, it is easy to create quick harmonic rhythm. In bs , the harmonic rhythm is one chord per bar with a chain of secondary dominants. This suggests modulatory tendencies, suitable for the development section which explores more foreign keys. Towards the end of the development section, the harmony needs to stay in the dominant to prepare for the recapitulation in the tonic. In bs , the harmony oscillates between V(7) and i6/4. It is very difficult to create such harmonic stability in a canon at the seventh below, but easier in a canon at the octave or unison (c.f. Example 5). Hence the canon is broken in b.190. Indeed, harmony is not the sole concern in designing the end of the development section; perhaps Mozart also wants to change the texture in order to highlight the end of the development section. However, even if Mozart wanted to maintain the canonic texture until the end of the development section, such a change in harmonic rhythm would require at least a change in the canonic interval, which necessitates breaking the canon. In Example 7, the chain of secondary dominants creates a tonicizing effect. In a canon, while it is relatively easy to achieve tonicization, convincing modulations are difficult. Compared to the Baroque, modulations in the galant style are usually more dramatic and achieved by strong cadences (Marshall 1976, ). Since a change in the harmonic rhythm can effectively highlight a cadence (LaRue 2011, 49), the difficulties in controlling the harmonic rhythm in canons may also hinder modulations. These challenges might have led Mozart to break the canon in the Andante un poco Allegretto section of his K

13 EXAMPLE 8: Mozart, Andante un poco Allegretto from String Quartet No.5, K. 158, bs.1 8 Canon broken here The imitation in bs.1 4 is broken at b.5. There the harmonic rhythm quickens, but slows down to one chord per bar from b.7 onwards, highlighting the cadence modulating to C major. This change in harmonic rhythm is hard to achieve if the canon is maintained. Indeed, not every modulation involves breaking the canon, but the canon may not modulate to the key the composer wants. Mozart s K. 406 is an example. EXAMPLE 9: Mozart, Trio from Quintet in C Minor K. 406, bs.1 14 Broken here This is a double canon by inversion. Mozart breaks the canon at b.13 to articulate an authentic cadence and modulate to G major, the dominant key. If he had not broken the canon there, a perfect cadence might have still been written, but modulating to F 13

14 major instead (see Example 10). EXAMPLE 10: Mozart s K.406, bs. 5 14, if he had not broken the canon Indeed, modulating to the subdominant is not uncommon in functional harmony, but it is not the key Mozart wants here. Without breaking the canon, modulations are more limited than they otherwise are. Some canons (see Examples 4 6) avoid the problem by not modulating at all; these canons are usually short in length. Perhaps this is because, as Kirnberger says, As soon as a composition is somewhat long, it is not good to remain in the same key throughout; melody and harmony must gradually be led to different keys but at the end must be returned again to the original key. ([ ] 1982, 121) In writing canons in functional harmony, many composers either forsake modulations or the complexity of canonic techniques due to difficulties in controlling the harmonic rhythm. Again, retrospective opinions are often enlightening. Jadassohn in the nineteenth century suggests that a canon without non-canonic parts should not modulate to foreign keys, nor use chromatic progressions or complicated canonic techniques ([1884] 1904, 18). 7 Some composers use imitation instead, which can be broken when difficulties in controlling the harmonic rhythm arise. 3. The Relationship Between Compositional Procedures and Canons This section examines the compositional procedures for counterpoint and canons in theoretical literature from the seventeenth to the nineteenth century, as this will illuminate us further on how functional harmony influenced canonic writing. While the linear aspect was the prime concern for composing counterpoint in the Renaissance, from the seventeenth century onwards some theorists emphasized more the harmonic implications of counterpoint. These theorists were probably influenced 7 Jadassohn s Die Lehre vom Canon und von der Fuge (1884) is the vol. 3 of Musikalische Kompositionslehre: Die Lehre vom reinen Satz, translated under the title A Course of Instruction on Canon and Fugue by Wolff in

15 by the chordal compositional approach, which arose along with the rise of functional harmony. In contrast to the more conventional view that the chordal and linear compositional procedures were incompatible, Lester argues that theorists and composers mixed them. 8 Some composers incorporated characteristics of chordal compositional techniques in writing counterpoint. Other composers used the chordal approach in some genres but emphasized the linear aspect in composing counterpoint. The growing concern for harmonic implications in counterpoint led theorists to devise new compositional procedures for canons. For instance, in Musical Poetics, Burmeister suggests composing canons with a harmoniola ([1606] 1993, ): the composer first composes a short passage involving all voices, and then links the melodic fragments of the voices together as the leading voice of the canon. If the melodic fragment of the bass does not begin the canon, it must be added as a free voice when the second voice enters. While useful for controlling the harmony in the canon, it seems that the harmoniola is only applicable to canons in similar motion. Burmeister does not mention using the harmoniola to compose canons with more than one subject or more complex canons such as inversion canons. Neither do Gosman (2000, ) and Collins (1992, ), who have further developed the concept of harmoniola in recent years. On the other hand, it is easier to write complex canons when the rules about harmonic progressions are relaxed. Marpurg s method for composing inversion canons (translated in Mann 1987, 148) is an example. Although in some occasions Marpurg believes that counterpoint has harmonic implications, 9 in composing inversion canons, Marpurg emphasizes lines more than vertical harmonies. This inconsistency can be explained by Lester s argument that Marpurg treats theory and practice differently (1992, ). In composing inversion canons in a major key, Marpurg suggests juxtaposing an ascending scale and a descending scale as shown in Example 11: EXAMPLE 11: Marpurg s method of writing inversion canons 8 For a more thorough discussion on the interaction between harmony and counterpoint in the eighteenth century, see Lester 1992, For instance, see the discussion on the Marpurg-Kirnberger disputes in Lester 1992,

16 Here the vertical sonorities in bs.4 7 appears not to conform to functional harmonic progressions in C major. This suggests that Marpurg relaxes the rules on harmonic progression in composing inversion canons. Also, with this method, it is very hard to write authentic cadences without breaking the canon, since all parts move by step but an authentic cadence often requires a leap by a fourth or fifth. On the other hand, in the Renaissance practice, an imperfect cadence is formed when the two lines end on a sixth (Barnett 2002, ). This type of cadence can be easily formed with Marpurg s model here. In the nineteenth century, Jadassohn shows that Marpurg s approach of juxtaposing scales in opposite directions in different voices can be extended to composing double canons in inversion, when the voices move in parallel thirds ([1884] 1904, 55 56). EXAMPLE 12: Jadassohn s theoretical example for double canon in inversion ([1884] 1904, 56) Like Marpurg, Jadassohn is unable to write an authentic cadence at the end of the canon. It is very difficult, if possible at all, to write inversion canons conforming strictly to functional harmony. Even though Jadassohn generally suggests that counterpoint should produce correct harmonic progressions, 10 in composing double canons in inversion, Jadassohn stresses the primacy of lines over vertical sonorities. Just like inversion canons, it is easier to write retrograde canons when rules concerning functional harmonic progressions are relaxed. To Mattheson, in counterpoint, good melodic lines are more important than correct harmonic 10 See Jadassohn s method of teaching counterpoint in [1884] 1887, Jadassohn s Lehrbuch des einfachen, doppelten, drei- und vierfachen Contrapunkts (1884) is the vol. 2 of Musikalische Kompositionslehre: Die Lehre vom reinen Satz, translated under the title Treatise on Single, Double, Triple and Quadruple Counterpoint by Wolff in

17 progressions. 11 This is probably because [h]armony is nothing other [ ] than a combining of different melodies (Mattheson [1739] 1981, 307). This view is reflected in his method for writing retrograde canons (Mattheson [1739] 1981, ): he suggests composing half of the leading voice, and then write the counterpoint above or below it. Afterwards, put the voices in retrograde. Arguably, Mattheson s relaxed view on correct harmonic progressions and his linear view of harmony account for the relative ease in his method of composing retrograde canons. With the rise of functional harmony, some theorists resorted to simpler canonic techniques in order to achieve good harmonic progression. Other theorists relaxed rules on good harmonic progression in order to employ more complex canonic techniques, such as inversion and retrograde canons. It is therefore not surprising that canons examined in Section 1 tend to be more complex, such as stacked canons and augmentation canons, and those examined in Section 2 tend to be simpler, such as canons in similar motion. Even though Mozart s K.515 (Example 7) contains a double canon, it is broken after a few bars due to harmonic problems. Similarly, the inversion canon in Mozart s K.406 (Example 9) has to be broken in order to achieve a modulation to the dominant key. The composer falls between two stools in achieving functional harmonic progressions and using complex canonic techniques. Conclusion Many theorists explain the decline of canonic writing by citing causes such as the rise of the galant style and the preference for a homophonic texture. While these are all valid explanations, the picture is incomplete without discussing in depth the impact of the rise of functional harmony, which played an important role in shaping the music of the eighteenth century. To fill this gap, this study examines how the rise of functional harmony has led to the decline in the interest in and quality of canonic writing. This is done through analyzing canons written in the eighteenth century and changes in the compositional procedures for counterpoint and canons in theoretical treatises from the seventeenth to the nineteenth century. An examination on the development after the Classical period may further illuminate us in this regard. Harold Owen argues that, in the Romantic era, [c]ontrapuntal texture served very well as a medium for the new chromaticism which would eventually lead to the end of absolute sovereignty of the major-minor system (1992, 302). In other words, the Romantic period saw the resurgence of interest in polyphony 11 [A]s regards a fine passage, one has to consider the cohesiveness of the melody in each voice more than the strict observation of harmonic procedure. (Mattheson [1739] 1981, 517) 17

18 which eventually led to the decline of tonality. In the twentieth century, Schoenberg says that it is easy to write canons in the twelve-tone system, because the second, third, fourth, and further voice has only to begin two or more notes later and there will never occur parallel octaves (1984, 248). Schoenberg s comment generates another question: are there other similarities between the modal or mixed system and the twelve-tone system, besides the absence of functional harmony, making canonic writing easier? This is a direction that future studies may pursue. 18

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