Rameau and Zarlino: Polemics in the "Traité de l'harmonie" Alan Gosman Music Theory Spectrum, Vol. 22, No. 1. (Spring, 2000), pp. 44-59. Stable URL: http://links.jstor.org/sici?sici=0195-6167%28200021%2922%3A1%3C44%3ARAZPIT%3E2.0.CO%3B2-G Music Theory Spectrum is currently published by University of California Press.
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Rameau and Zarlino: Polemics in the Traite de I'harmonie Alan Gosman Jean-Philippe Rameau is well known for his vociferous attacks against critics who dared to differ even slightly with him. The most celebrated of his arguments are those with Rousseau and the other philosophes.' Somewhat overlooked is a quieter struggle that occupied Rameau more than three decades before these welldocumented debates, a struggle to situate his newly emerging ideas within the legacy of Zarlino. It is in his creative handling of that legacy that we can first observe Rameau attempting to secure the acceptance of his own theories. In his first published writing, the Traite de I'harmonie of 1722, it quickly becomes apparent that Rameau is preoccupied with Zarlino. Rameau frequently footnotes two of Zarlino's treatises, the 1573 version of the Istitutioni harmoniche, and the 1589 version of the Dimostratoni harmorliche included as the second volume of De tutte l'opere. Further, Zarlino is the only person with an entry in the Traiti's Table of Terms.? 'Many authors. including Thomas Christensen and Cynthia Verba, have documented Rameau's reactions to contemporaries who modified and threatened his popular and respected theories. See Thomas Christensen. Ranleau and Musical Thurrght in the Enlightenn~ent(New York: Camhridge University Press. 1993). and Cynthia Verba, Music and the French Enlightennlent: Recoilstruction qfa Dialogue 1750-1764 (New York: Oxford University Press. 1993). 'Jean-Philippe Rameau. Trait4 de I'harnlonie r4drrite u ses principes nuturels (Paris, 17221, xxiv: reproduced in vol. I of The Conlplete Theoretical Writirzgs of Jearz-Philippe Ranleau (1683-17641, ed. Erwin R. Jacobi (American Institute of Mus~cology,1967-72); translated hy Philip Gossett as Treatise on Harnlorzy (New York: Dover, 1971). Iv.
Other theorists, such as Descartes and Mersenne, certainly influenced Rameau greatly. Rameau always returns to Zarlino's texts, however, when arguing for change. In the first footnote of the Trait&, Rameau reveals the importance that he attributes to Zarlino's writings as opposed to those of later authors: "Zarlino was a celebrated author on music who wrote approximately 150 years ago. We find only feeble restatements of his works in later writings on the same subject."' COMPOSITIONAL CANONS
The first two books of the Traite' abound in direct references to Zarlino. I will begin this investigation of Zarlino's influence on Rameau, however, by looking at Book 111. It comes as a bit of a surprise after Books I and I1 that Zarlino's name is completely absent from Books 111 and IV, titled "Principles of Composition" and "Principles of Accompaniment" respectively. And yet Rameau hardly neglects his precursor in the discussion of practical music. In fact, I believe that Rameau's most acute awareness of Zarlino's shadow, and his most powerful attempt to distance his readers from his predecessor, occurs near the conclusion of Book 111. At this point one finds-with some shock-that for his culmi'"Zarlino, Auteur celehre en Musique, qui a ecrit a peu-pre~depuis 150 an\. & dont on ne trouve que de tr2s-foihles Copies. dans les Ouvrages qui ont part apr6s les siens, sur le m@mesujet." Trait4 ile l'harmonie, Preface, second page; Treatise on Harnlon?: xxxiv. All translations of Rameau given here are by Philip Gossett.
Rameau and Zarlino: Polemics in the Traite de l'harmonie 45
nating compositional tour de force, his last word in compositional technique, Rameau presents two strict canons. The shock occurs because, having followed Rameau's harmonic agenda for three books now, one hardly expects him to cap off his composition lesson with a strict contrapuntal form. An explanation is suggested by the fact that the culminating compositions of Book I11 of Zarlino's Istitutioni harmoniche are also a pair of canons. These two authors' similarly placed canons, which have been almost completely overlooked, turn out to be summaries of their respective theories on music. Furthermore, Rameau's compositions can be seen as a powerful demonstration of the inadequacies of the traditional contrapuntal explanations offered by Zarlino. A close examination of Zarlino's two culminating canons, and the methods by which Zarlino constructed them, will help one recognize exactly how Rameau's two canons in the Traite' are a response to his precursor. In the Istitutioni, Zarlino makes it clear that advanced musicians show their talent and knowledge by taking on and solving challenging problems of canonic writing. When Zarlino is just beginning to describe canons, he says that he is most impressed by canons which are not garden-variety, two-voice compositions whose voices are separated by a short distance. He writes, "Constant practice of this close imitation has resulted in such a common idiom that a fugal pattern cannot be found that has not been used thousands of times by various comp o s e r ~ . "In~ demonstrating advanced canonic techniques, Zarlino intends to teach his readers to "apply all our ingenuity to write fugues that are fresher."'
'". . . ma il troppo continuare cot a1 vicinita fece, che si casch in un certo mod0 commune di comporre, che a1 presente non si ritrova qua si Fuga, che non sia stata mille migliaia di volte usata da divers1 Compositori." Gioseffo Zarlino, Le Istitlctlon~harnloniche, reprint of the 1573 Venetia edition (Ridgewood, N.J.: Gregg Press, 1966). 258; Gioseffo Zarlino. The Art of Counterpuirzt, trans. Guy A. Marco and Claude V. Palisca (New Haven: Yale University Press, 1968), 127. All translations of Zarlino given here are by Marco and Palisca. '". . . & cercaremo con ogni nostro potere di fare delle Fughe. che siano piu nove." Le Istitlctioni hannonicrhe. 258: The Art of Counterpoirzt, 127.
Zarlino often relies on canons to demonstrate the practical applications of his contrapuntal rules, and by exploring different canonic types, he shows his preference to seek out less common varietiesh Example 1 lists the many different canonic techniques in the Istitutioizi in their order of presentation, which roughly corresponds to their compositional difficulty. The final three canon types are all in four voices, and in the last two, each of the voices takes part in the canon. The final two compositions of Zarlino's counterpoint text appear in Chapter 66, and they are meant to be the most ingenious of his canon types. Both are pieces with two pairs of parts in canon by contrary motion. They are reproduced in Examples 2 and 3. These canons display two of Zarlino's important lessons about composing in three or more parts. When earlier discussing threevoice compositions in Chapter 59, Zarlino writes, Composition may be called perfect when, in every change of chord, ascending or descending, there are heard all those consonances whose components give a variety of sound. Where such consonances are heard, the harmony is truly perfect. Now these consonances that offer diversity to the ear are thg fifth and third or their compound^.^
hA similar tendency to explore can be found in Zarlino's discussion of douhle counterpoint. He writes, "Though there are many ways of writing such counterpoints, as I have said, I shall demonstrate only those that seem most difticult and most elegant. This mill avoid boring the reader, who can readily infer the other procedures for himself." The Art of Counterpoint, 205. ("Ma ancora che molti siano li modi di comporre tali Contrapunti: come ho detto: porrb solamente quelli, che mi sono paruti piu difticili & piu elegant]: accio non sia tedioso a i let tor^: da i quali ciascuno ingegnoso potra comprendere, come ai haveri da reggere in qualunque altra maniera di simili compositioni." Lr Istitlctioni harnloniche, 297.) -"Quells compos~tionesi puo chiamare Perfetta: nella quale in ogni mutatione dl chorda, tanto verso il grave, quanto verso I'acuto, sempre si odono tutte quelle Consonanze. che fanno varieti di suono ne i loro estremi. Et quella 6 veramente Harmonia perfetta, che in essa si ode tal consonanze: ma li Suonl, o Consonanze, che possono fare diversita a1 sentimento sono due, la Quinta & la Terza. over le Replicate dell'una & dell'altra." Le Istitlctioni harmoniche, 287: The Al? of Counterpoint, 186.
Music Theory Spectrum
46
Example 1. Canon types found in L'lstitutioni hannoniche, Part I11 1. Canon at the distance of three to five minims (Exs. 88/89 at 8ve, 94/95 at 3rd, 98/99 at 5th) 2. Canon in contrary motion (Exs. 90/92a, 91/92b, 96/97)
4. Adding three parts, two of which are in canon, to an existing tenor (Ex. 161) 5. Composition with two pairs of parts in canon by contrary motion (Ex. 162) 6. Perpetual composition with two pairs of parts in canon by contrary motion (Ex. 163)
3. Adding a two-part canon to an existing tenor (Exs. 154 and 155)
Example 2. Zarlino, Ijtitutioni, Part 111, Chapter 66, Composition with two pairs of parts in consequence by contrary motion
plus minor third a b m c
[p; &
-
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Ha$\, and consequent of the soprano
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Rameau and Zarlino: Polemics in the Traite de I'harmonie 47
Example 3. Zarlino. I.rtit~ltiotli,Part 111, Chapter 66, Perpetual composition with two pairs of parts in consequence by contrary motion
Soprano, and p ~ d of e the h ' ~ \ \
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Tenor. and consequent of the alto
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Zarlino's melodies are masterfully constructed to maximize the number of perfect harmonies despite the strict contrapuntal form. Almost every verticality is a 2 chord. In each example. Zarlino is particularly careful that the canon's frame. which I define as those chords that fall at the time interval of the canon, do not spiral into imperfection. The time interval of the canon in each cxample is two bars in the modern realization. Example 3 lists the chords in the odd-numbered measures of Examples 2 and 3. The list starts with m. 3. because at that point enough voices have entered to create a perfect harmony. Except for the end of Example 2. at which
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time Zarlino rnakes an adjustment to provide n Phrygian cadence, the canonic frame of both examples simply alternates two different perfect triads. The conditions of composing a double canon by contrary motion. interesting in their own right. also demonstrate that Zarlino's choice of canon type was motivated by the lessons of the I.stitlltioni. By closely examining this presentation, one can see the contrapuntal mastery with which Rameau is competing. In a contrary(notion canon, although the dlrx and comes could be inversionally symmetrical around any pitch. Zarlino decides in both canons that
48
Music Theory Spectrum
Example 4. Triadic roots at the time interval of the canon in Zarlino's contrary motion canons Triadic Roots in Measure
Examule 2 a C ( l st inv.) a C F (I st inv.) E
Examule 3
z4 D
z4 D a o
etc
the note D will be the inversional center. This arrangement fits in with the intervallic make-up of the "white notes" as is shown in Example 5. The chromatic notes Bb and F# are also included because Zarlino uses them in both pieces. Example 6 shows that the alternating chords (cf. Ex. 3 ) are also, as one would expect, those that are symmetrical around D. The first column shows the inversional mappings between notes of the A and C triads. These chords alternate throughout most of the first canon. The second column shows the mappings between the G and D triads. These chords alternate in the second canon. For Zarlino. however, the mere presence of perfect harmonies does not assure variety. He stresses throughout his text that there are distinctive types of perfect harmonies. For example. in Chapter 3 1 of Part 111. Zarlino writes: The variety of the harmony in auch situations does not consist solely in the variety of the consonances that are found between two voices. but also in the variety of the harmonies-which [variety] is determined by the position of the note that makes a third o r tenth above the lowest voice of the composition. Either these [intervals] are minor, and the harmony that arises is determined by o r corresponds to the arithmetical proportion or division. o r they are major, and such a harmony is determined by or corresponds to the harmonic mean. O n this variety depends a11 the diversit) and perfection of harmonies. . . . For as I have said elsewhere, when the
major third is below, the harmony is cheerful, and when it is placed above. the harmony is sad.8
Zarlino did not just happen to choose to write a canon in contrary motion as a contrapuntal challenge. Rather, he utilized the special features of that form to highlight the inversional relationship of major and minor chords. This can be observed by looking at the role of each pair of canonic voices separately. In Example 2, the dux of the canon between the alto and tenor begins with E. This maps to a C in the tenor in nl. 3. which is set by another E in the alto. This again maps to C in the tenor in bar 5 and again is set by an E. The pattern continues until In. 13. For almost the entire piece, the innervoice canonic frame consists of the major third from C to E. Zarlino has the choice of whether to place a minor third above or below this fixed major third. His choice will result in a major or minor triad respectively. By taking advantage of the inversional pair G-A, which provides the notes a minor third above and below the fixed major third C-E. Zarlino is able to alternate between C major and A minor chords. In m. 3. the dux of the outer-voice canon sounds a G. thus combining with the inner voices to form C major. The G maps to the bass A in ni. 5, thus sounding A minor. The G is found again in the dux of m. 7, again forming C major." ""Conciosia che la varieth dell'Harmonia in simili accompagnamenti non consi\te solarnente nella varieth delle Consonan7e. che i i troia tra due parti: rn'i nella iarieti anco delle Harmonie. la quale con\iste nella positlone della chorda. che fh la T e r n , over la Dccima wpra In partc gra\e della cantilenu. Onde. overo che cono minor1 & I'Harmonia che nasce. C ordinata. 0 \i a\\imiplia alla proportlonalith, o mediations Arithmetica: overo bone ~nagpor-i& tale Harmonla 5 ordinata, over si a s \ i ~ n ~ g l alla i a mediocrith Harmonica: & da questa varieth dipende tutta la diver\iti & la perfettione dells Harmonie . . . percioche (como hh detto altro\e) cluando \ I pone la T e r n mappiore nella parte grave. I'Harmonia \ i fh allegra: & quando ci pone nell'acuto si S ~ me\ta." I LC, I ~ t i r u r ~ ohcir-r~ic~~~ic.I~c~, ~i~ ? 10-1 I : The 4rt of Cour~rc~ipoi~it. 69-70. "Because of the utrict cond~tionsfor con\tructing triad\ in a double controrq motion canor:. it is clear that Zarlino i i adding a single note ( A or C;) to a pitct, pairing that i \ set ( C and E). Bq this method. mm. 3. 7. and I I are C rnajor triads. What is interehng is that the chord in m. 7 ic a C major triad In fir\[ in\t.rsion. Ba\ed on his theoretical text. Zarlino would not have recopnired a relation
Rarneau and Zarlino: Polemics in the Traite de I'harmonie 49
Example 5 . Inversional mapping of notes in Zarlino's contrary motion canons D-D c-E B W F Bb t-,F# A W G Notes: A Distance (steps):
C
B I
112
D 1
E 1
F 112
G 1
Example 6. Inversional mapping of triads in Zarlino's contrary motion canons Chord Root$ C -A G-A E t , C C-E
D-G A -G F# t , B b D-D
F C A F
-E -E -G t , B
The alternating pattern continues until the last bar of the piece when a G # is substituted for the Gh as part of a Phrygian cadence. The canonic frame in Example 3 alternates between major and minor chords using a slightly different method. Instead of adding up thirds as in Example 2, Example 3 divides a perfect fifth. The perfect fifth is found in the soprano-bass canon. Two inversional pairs are found in the odd-numbered bars starting in m. 3: the D-D pair first mapped between mm. 1 and 3, and the A-G pair first mapped between mm. 3 and 5. Thus m. 3's outer-voice twelfth between a C chord in root position and a C chord in first inversion. Rather, one would be a chord with a third and a fifth, and the other would be a chord with a third and a sixth. In the practical context of this composition, however, Zarlino is pressed to recognize the equivalence of the two sets of notes. Therefore, the demands of canonic writing lead to an early instance of inversional thinking. Pursuing this subject could easily generate another essay.
from D to A maps to m. 5's outer-voice twelfth from G to D. This fifth is mediated by one of the notes from the inversional pair F#-Bb in the inner voices. Since each of these notes is a major third from D, and D is found in both of the fifths, it is clear that one fifth (D-A) is divided with the major third on the bottom, forming D major, and the other fifth (G-D) is divided with the major third on top, forming G minor. The simple alternation of two chords at the canonic frame of Examples 2 and 3 makes such a complicated canon easier to compose. More importantly, however, it directs the reader's attention to the structures recommended in Zarlino's text-perfect chords that demonstrate the diversity of harmony. In Example 3, the duxof this composition is only seven notes, but the piece gains considerable length because it is a perpetual canon. This is striking, because it is Zarlino's only perpetual canon. In some sense, Zarlino's final compositional statement of Part 111 is meant to linger in the reader's head forever. As has been suggested, it seems more than coincidental that Rameau also includes, as his final compositions in the Trait&, a pair of four-voice perpetual canons. In these pieces Rameau provides his own commentary on issues raised in Zarlino's canons about which type of chord to privilege, and how to obtain diversity in harmony. Rameau's canons constitute a carefully designed response to Zarlino, with the intention of revolutionizing musical thought and, in many ways, turning music theory away from its contrapuntal explanations. Although Rameau's canons are not introduced with enormous fanfare, they may well be the first pieces specifically designed for harmonic analysis. Rameau's four-part canon at the fifth is reproduced in Example 7. This piece is what I have termed a stacked canon, because the tenor and alto, each of which is an imitative voice, also each plays the role of dux for another part entering later.'"hus Rameau 'Osee Alan Gosman, "Stacked Canon and Renaissance Compositional Procedure," Journal of Music Theor) 4112 (1997): 289-3 17.
50
Music Theory Spectrum
Example 7. Kameau, Trait6 de l'han?iorzie, Book 3, Chapter 44, Canon at the Fifth
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Rameau and Zarlino: Polemics in the Traite de I'harmonie 51
Example 7 [continued]
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52
Music Theory Spectrum
revives Zarlino's practice of displaying canonic acumen by straying from a straightforward model.I1 But Rameau's four-voice canon is not merely a demonstration of compositional technique. He also intends to remind the reader of what he considers a fundamental mistake by Zarlino, a mistake that the "Zarlino" entry in the Truircs Table of Terms specifically criticizes: "The errors found in his rules arise partly because he envisaged only two sounds at a time."'? While Zarlino did in fact compose some fourpart canons. the fourth voice in these pieces is almost always a doubling. Zarlino exhibits no great desire to build up chords with four different notes.13 Rameau ventures into the realm of four-voice canonic writing not only because Zarlino did, but also because the exploration relates closely to the Trrrite"~teachings. Significantly. the four-voice texture aswres the possibility of a complete seventh chord once all of the voices have entered. This is consistent with Rameau's preference for the seventh chord as a means of harmonic propulsion, particularly when used on the dominant. In Book 11. Chapter 2. Ra~neauwrites of the seventh chord. T h e dibersit) that this chord brings . . . b! introducing a certain tartness which si~nultaneouslyenhances the sweetness of the perfect chord, ~ n a h e s us desire its presence, not reject it. We must thus place it among the fundamental chords, since it in no way destroys the source which subsists in the lowest sound of the perfect chord.!' "Ranieau crroneou\ly proclaim\ h~mselfto hc the tint to h a ~ cconipo\ed a four-part canon of thlh type (Trrurite or7 Hcrr.~jro~i\:370). ""Les erreurs q u ~sr trou\ent dans Ir\ Rcglrs de Zarlin proLienncnt cn pnrtle dr ce qu'il n'en\isagroit que deux Sons i la fois." Trr~itisrlr /'i~rir~?~orjir, xxi\: Tretrrite or! Hrirrriorr); I\. l'ln Zarl~no'\four-\oice canons hy in~ersion.only two \e\rnth chord\ occur. The\e are in Example 1 , on the last quarter note of mm. 8 and 13. I n each case, the \e\enth has a clear pabsing function. ""La d~\ersitCque crt accord y cause en y introduisant unr crrtalne aniertunic. qui relc\c en nitnir tcnips la doucrur de I'accord parfait. doit nous Ir f'111e .
souhalter, hicn l o ~ nde le rejrtter, ne p o u ~ a n tnous dl\penscr pour lors de la mettre au nomhrr dea accords fondamentaux. puisqu'il ne dCtru~tpolnt le princ~pequi subaistr toC?jouu dans le Son gra\e de I'Accord parfait." TrfiitP rlu 5 2 , T r ~ a t i on ~ r Harmorn, 61 l'hc~rn~orlir,
In the canon of Example 7, once all four voices have entered in m. 6, every vertical sonority (senzufine) is a complete seventh chord. Before m. 6, where complete seventh chords are impossible, one is aware of their approach as the imitative voices are added. In m. 2 the parts suggest a C7 chord (V3IIV) as the notes Bb and G are embellished by an eighth-note upper-neighbor C in the bass. In In. 4 the piece inches closer to stating a full seventh chord with G, D. and F sounding as half notes or longer. Finally. in m. 6. the seventh chord (D7) is complete. While it may look as if the harmony is a byproduct of melody, the extraordinary features of this canon make it clear that Ra~neaucarefully planned the harmonic progression first, and allowed it to guide his melody. He thereby provides compositional evidence for one of his principal assertions, that harmony is prior to melody. The natural fit between the structure that Ra~neaucreates ( a four-voice canon) and his penchant for seventh chords suggests to his audience that the contrapuntal devices of the past have actually been in service of more basic harmonic principles, with the phenomenon having gone unnoticed before Rameau. Although the canon goes on perpetually, because it transposes each eight bars up a major third. three cycles through the melody are required before the dll.r which begins on C (now technically B# ) is repeated in In. 24. This brings up interesting tuning issues. although these will be avoided at the present time. Example 8 shows that these three passes through the ~ L L . Yare exactly how long i t takes fot- the even-numbered measures (the canonic frame) to present a dominant seventh chord on each of the chromatic scale's twelve notes. In addition to displaying all possible dominant seventh chord^ Rameau takes very seriously how they are connected. Relying on his explanation in Book 11. progressions of funda~nental bass notes follow the findings based on the divided string. In particular. they demonstrate the desired progression by fifths. In this respect, the canon in Example 7 succeeds masterfully as a pedagogical tool. Beginning an analysis at the repeat of the melody in the bass voice at m. 8, where all four voices are present, it is easy to see that harmonically the piece moves in two-measure fragments (the
Rameau and Zarlino: Polemics in the Traite de I'harmonie 53
Example 8. Chords at each time interval in Rameau's Canon at the Fifth m. 8 m. 10 m.12 m. 14
A; E?; B7 F#;
m. 16 m. 18 m. 20 m. 22
C#: G#: D#' A#?
m. 24 m. 26 m. 28 m. 30
E#J = F ; B # j =C?; Fx7 = G 7 Cx; =D;
time interval of the canon) related by ascending fifth (the imitative interval of the canon). The ascending-fifth sequence can be seen in the major-minor seventh chord arrivals in mm. 8, 10, 12, and 14. which proceed through different inversions of A7, E7, B7, and F#7. Each of the fragments within these two-bar divisions consists of its own descending-fifth sequence. In m. 7 there is a B i going to an E7 which resolves to an A$ in m. 8. In mm. 9-10 the fundamental bass progression of mm.-7-8 is transposed by a fifth: F/i B?, and Ei. Rameau must have been proud that his canon so spectacularly displayed his preferred method of fundamental bass movement by fifths, both ascending and descending. The manner in which Rameau builds up these chords can be gleaned from the shape of the dux. From a harmonic point of view. the main task of the d ~ l xis to introduce each degree of the seventh chord, the root, third, fifth, and seventh. Once introduced, the degree remains constant when it reappears in each cornex. This is shown by the line in Example 7 connecting mm. 8, 10, 12, and 14: the chord degree contained in the dux at m. 8-the fifth-remains the fifth of the chord when it is imitated in the tenor, alto, and soprano voices. Since the initial appearance of a chord's fifth in the dux assures that the fifth will be found in the upper voices two, four, and six bars later, the dux can introduce other chord degrees at these points. In m. 10, the bass melody introduces the seventh of the chord. with the result that this chord degree is locked into the chords at the succeeding three even-numbered measures. The root of the seventh chord is found in the bass of
2,
m. 12, and the bass completes the cycle of four notes by sounding the third of the chord in m. 14. Because Rameau designs each pass through the dux to be eight bars long before its transposition, there is exactly the required time to introduce systematically all four of a seventh chord's degrees. In contrast to Zarlino, who presented the diversity of harmony by alternating major and minor chords, Rameau demonstrates diversity by displaying each of the inversions of a seventh chord within each pass through the dux.'Wnce again, the canon in Example 7 vividly portrays a melody's dependence on harmonic principles. Like Zarlino, Rameau utilizes a second canon, reproduced in Example 9, to convey his theoretical ideas in practice. In his first ~ s canon, the four entrances related by fifth resulted in the d ~ being repeated up a major third every eight bars. In the second one. the du.u is repeated up a minor third every six bars. Therefore four cycles must take place before the dux returns to its starting pitch E. now spelled as an Fb (m. 24). Since the time interval of the canon is again two bars, the canonic frame of this piece also presents a chord built on each of the twelve pitches. Because the canon has only three voices, however. Rameau has to work harder to show the common occurrence of seventh chords. For example, from the middle of m. 6 to the middle of m. 7, a G minor chord ends up as a G7, having moved through a passing chord on the downbeat of m. 7. In m. 8, the G7 resolves to a C minor triad, preparing the listener for a chain of dominant to tonic relationships that will continue until the performers have the good sense to stop. It is obvious that Rameau's decision to conclude the T~aite' with two canonic compositions was not motivated merely by a desire to engage a topic that had not been mentioned until that point. His decision to end with two canons seems inspired by the similar conclusion of Zarlino's Part 111, and more importantly by Rameau's belief that Zarlino failed to express important theoretical '
