Machaut estructura y contrapunto

Line, 'Contrapunctus' and Structure in a Machaut SongAuthor(s): Sarah FullerSource: Music Analysis, Vol. 6, No. 1/2 (Mar. - Jul., 1987), pp. 37-58Published by: WileyStable URL: http://www.jstor.org/stable/854215 .Accessed: 07/01/2014 13:27

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SARAH FULLER

LINE, CONTRAPUNCTUS AND STRUCTURE IN A MACHAUT SONG

Enough has been written about structural plan and order in the songs of Guillaume de Machaut to establish the prolific poet as a composer of formidable skill and, in Wolfgang D6mling's phrase, 'reflective awareness'.1 Nevertheless, there is much still to be learned about Machaut's compositional practice, not only as embodied in his musical oeuvre as a whole, but also as expressed in individual genres, in specific chronological strata (insofar as these can be determined), within groups formed by particular vocal scorings, or in any other natural subset of works. Indeed, detailed study of the oeuvre leads more often to recognition of heterogeneity and variety than to limpid visions of standard procedures.2

Musical structure has been at the forefront of discussion: motivic, rhythmic or harmonic associations between phrases or sections of a song; contrapunctus foundations of florid polyphony; design of individual lines; middle- and background linear progressions. Amid the plethora of contributing factors, one may well ask how the image of essential structure in a composition is conveyed, and what is thereby revealed about the techniques and habits of its creator. The present focus for these questions is an early two-part ballade by Machaut,J'aim miex languir (No. 7 in the modern editions of Machaut's musical works).3 Besides furnishing an occasion for contemplating design and structure in a supposedly representative song, J'aim miex also raises analytical issues pertinent to the repertory as a whole.

I A first necessary observation, indeed a guiding axiom, is that J'aim miex is a setting of a poetic text and that its structure cannot be comprehended adequately apart from the text. This is not simply a claim about the creative process, a declaration that Machaut doubtless started with his ballade before him, and that his choices about where to begin and end phrases, where to position main tonal nodes and what syntactical units to articulate musically

MUSIC ANALYSIS 6:1-2, 1987 37


SARAH FULLER

should be understood as his considered response to the text.4 It is a critical assertion about the analytical process to be employed. Quite apart from the question of how Machaut proceeded, any analysis of the song's structure cannot but depend on textual factors that affect perception of principal articulations, accentual emphases and main phrase components. Relations between poem and music are reciprocal. Rhythmic caesurae and cadential progressions delimit textual segments. But at the same time, textual syntax, verse structure and sense modules demarcate basic musical units. They can, moreover, significantly shape the music, weakening a phrase ending with a bridge of ongoing textual syntax, or obscuring parallel pitch structures positioned athwart a poetic division.5 The two partners are inextricably bonded in that composite which we receive as the song. The course of both influences our analytical judgments. An introduction to the text, however slender, is an essential step in the analytical process.

J'aim miex consists of three strophes (the standard number for a Machaut ballade), uniform in layout and sung to the same music. They sound the familiar courtly-love themes of ardour unrequited, honour, steadfast constancy and painful longing. Only the initial strophe need concern us at present, for it is the one to which the musical setting adheres most tightly:6

I J'aim miex languir en ma dure doleur II Et puis morir s'Amour le prent en gre III Qu'avoir mercy se ce n'est a l'onnour IV De vous dame que j'aim sans faussete. V N'onques en moy n'ot autre volente VI Ne ja n'avra pour peinne que j'endure VII Et mefussies cent millefois plus dure.

Rather would I languish in my harsh pain and then die, if Love so please, than receive relief, if it is not to your honour, Lady, whom I love without dissemblance. Never have I wished otherwise, and never shall, whatever pain I endure, were you a hundred thousand times more severe.*

This strophe consists of seven lines, each ten syllables long, rhymed a b a b b c c. The final line is a refrain which recurs unchanged in subsequent strophes. Syntactically, the strophe consists of two long sentences. The first comprises lines I-IV and juxtaposes the lover's agony with his dedication to the lady's honour. The second spans lines V-VII and affirms the sufferer's willingness to endure even harsher treatment from the lady. (Does he protest too much?) This bipartite division well suits a musical convention of AoAcB form ('o' and 'c'

* I am indebted to Leslie Morgan of the State University of New York at Stony Brook for help with the translation.

38 MUSIC ANALYSIS 6:1-2, 1987



stand for ouvert and cldos cadences respectively). The first sentence coincides with the AoAc section and ends emphatically with the cldos cadence. The second corresponds with the B section. Textually, the fusion of lines I-II and III-IV by enjambement gives rise in the musical setting to phrases spanning syllables 1-10 and 1-4 of lines I and II respectively, and syllables 1-10 and 1-4 of lines III and IV respectively. Lines V and VI are separate syntactically, but Machaut takes advantage of the balanced N'onques en moy . .. Ne ja avra . .. construction to link them in the same way as I-II and III-IV (Ex. 1).7

The consistent pattern produced jointly by verbal units and musical phrase cuts across the uniform poetic lines defined by rhyme and creates asymmetrically divided couplets responsive to verbal syntax. Phrasing separates each even-numbered line into 4 + 6 syllables and joins the first segment to the preceding line. It sustains each odd-numbered line in an unbroken unit, and also elongates each by four additional syllables. Only the climactic refrain line stands independently, neither subdivided nor fused with part of another line. Just as this hyperbolic declaration brings each stanza to an apex, so it blocks off the final stages of linear and tonal closure accomplished in the last musical phrase.

II In approaching the music, two fundamentally different perspectives may be imagined. One is that of an individual performer learning or practising his or her part alone, apart from the other strands of the polyphony.8 Another is that of a listener attuned to contrapunctus, sensitive to a firm framework of consonances between the participating voices.9 The two modes of perception - one tracking the single line, the other reacting to the polyphonic entity - are not to be understood as antitheses. A skilled composer can be assumed to have kept both in mind to some degree; an experienced listener to react to both. They are simply different standpoints from which images of the song may be formed. Not only the images themselves but also the convergences and divergences between them contribute information about the shaping of the music and its fundamental structure.

Because it offers the most direct initiation into the song and is closest to the initial impression of the performer, the single-line perspective makes an appropriate starting-point.10 Example 2 plots the essential structure of the cantus alone as I interpret it at a middleground level. To facilitate comparison with the song text, the breve count is indicated above the staff, the distribution of poetic lines below.

The melody is characterised by registral balance about c' and sharply chiselled phrase units, each of which closes on a sustained breve. Two melodic processes dominate. One is direct linear motion, mainly downward, as is established in the first long breath (bs 1-8). The other is disjunctive motion, followed by the closure of gaps created by melodic discontinuities. Either the



SARAH FULLER

Ex. 1 J'aim miex languir

2 4 6

SIF Jaim miex lan guir en ma dure do

n

leur

[III

Et puis mo -

[III Qua- - - -voir mer cy se ce nest a Ion nour [IV]De vous da -

8i 1 10 12 - rir sA- - mour le prent en

-me que j'aim sans faus- - se-

-OP

14a 15a 14b 15b 1618

8 gre [V] N'on- - ques en - te.

20 22 24

moy not autre vo-len- te [VI] Ne ja n'a- vra pour pein-ne que j'en-

A26 28r- 1 30 . 32

du- -re[VIII Et me fus- sies cent

du- .re

344 36 38 40 mil-le fois plus du- - -re. mil-le

fois

plus du- -re.

?*IL 40 MUSIC ANALYSIS 6:1-2, 1987



Ex. 2

Phrase (Da 8 2 Breve 6 8 , 10 12 14a 6 8 10 12 15b

rf.. *

.--

Text I 1-1() II 11-4 5-10( III 1-o0 IV -4 5-10

17 21 23 , 24 29 31 34 35 37 40

V -l1() VI 1-45-( VII 1- 9- 1()

KEY

an important structural pitch

S a significant adjunct to a structural pitch

(e) a pitch of equivocal status

* registral disjunction between structural pitches, as in bs 1()-12 between g'and c'

consecutive linear motion between structural pitches

S / Interrupted linear motion, as in bs 24ff., where a line rising from c' is interrupted by a leap to g'

subsequent resumption of a line previously left hanging



SARAH FULLER

line converges from both outer boundaries to some pitch within the gap (as in bs 9-14a, where lines from g' and from c1 converge on el), or it returns conjunctly to the point at which the interruption occurred (as in bs 35-7, subsequent to the leap in b.34). These two processes of melodic motion complement each other, for the continuity of the stepwise movement acts as a foil to the disjunctive motion and, moreover, arouses expectation for the closure of melodic gaps. Alternation between the processes can be said to govern the melodic design. The first phrase is uniformly stepwise in its course, while the second commences with a spectacular leap and is later cut by a sharp registral disjunction. The second couplet (bs 17-30) repeats the juxtaposition. Its first phrase unwinds smoothly and predictably through adjacent pitches, but the next (bs 24-9) is a series of interrupted fragments. Its erratic character is confirmed by an inconclusive ending on e1, an audible parallel to the ouvert phrase (2a), which is also disjunctive in nature. The refrain reconciles the opposing tendencies by combining them in a single extended period. In this extended phrase, a single medial gap (b.34) is closed by two smooth lines which converge from the registral extremes, gI and g, onto c'.11 This interpretation regards the melody as embodying an active process whereby conjunct and disjunct middleground motions, contrasted in alternating phrases, finally coalesce in terminal synthesis (Fig. la).

Fig. 1

a) Melody: Process

conjunct I disjunct

I 1-10 II 1-4 I 115-10

III 1-10 IV 1-4 IV 5-10

'V 1-io VI 1-4 'VI 5-10

VII 1-10

b) Melody: Association

ouvert clos

SI-II III-IV

ouvert clos

V-VI VII 42 MUSIC ANALYSIS 6:1-2, 1987



Fig. 1 (cont.)

c) Tenor

G G SI-II

,, C

III-IV

C G V

C G VI-VII

C

d) Contrapunctus *

systematic X 51 I 1-1o II 1-4 I1 5-10 voice leading I III 1-10 IV 1-4 IV 5-10

V 1-10 VI 1-4 VI 5-10 unsystematic voice leading

VII 1-10o

* Rxx i-,,,I1 indicate motivic correspondences



SARAH FULLER

From a more conventional angle, the melodic design can be described in terms of two parallel blocks. The first block consists of the first section with its repetition, which together constitute a coherent unit with an ouvert couplet (phrases la and 2a, ending on e') answered by a clos couplet (phrases lb and 2b, ending on c'). The second section forms a parallel, foreshortened block whose successive open (b.29) and closed (b.40) cadences echo the preceding syntactical group. Not only is the sequence of cadential pitches identical (e' ouvert, c' clos), but the f'-el-f'-d' motive which appears before each of these cadences (and nowhere else in the melody) enhances the association. The motivic link between the two clos endings, a musical 'rhyme' three breves long, is especially pronounced. This interpretation views the melodic construction as essentially passive, based on flat sectional balances (Fig. ib).

These two accounts of the melodic action - the one a threefold juxtaposition of conjunct/disjunct motion followed by synthesis, the other an essentially passive, architectural balance between the settings of lines I-IV and of V-VII - suggest different options for hearing and performing the song. Common to both is a conception of the tune as an integrated whole possessed of its own internal integrity. This is not to imply that the cantus was conceived as a monophonic entity to which another part was added. Indeed, various features, such as the rests in bs 9, 12 and 35 and the elongated f'-el in bs 28-9, seem to assume the presence of another voice. It is simply to observe a significant trait of the melodic line.

Compared with the texted cantus, the tenor is decidedly restricted in rhythmic figures and in melodic activity. It moves mostly in breves and spends much time within the upper half of its six-note range, on f, g and a. The absence of textual signals complicates decisions about main musical segments when the line is taken in isolation. Because the cantus phrases do ultimately impinge upon the tenor, they are indicated in the sketch of essential linear motion (Ex. 3). Just as in the case of the melody, the reduction reveals two sorts of tenor activity: movement within f-g-a with g as its central axis, and direct linear descent from g to c. These two activities alternate in orderly fashion. The g-centred plateau always stands at the beginning of a formal unit (as defined by sections and phrase breaks); the descent to c at the end. In the first section of the song, the alternation coincides with the melodic design, the motion about g corresponding with conjunct, the move to c with disjunct process. But in the second section it cuts across the melodic design. Whereas the melody groups lines V-VI against VII (in both process-orientated and associative interpretations), the tenor completes a pattern within line V and groups VI and VII in another pattern (Fig. Ic).

Figure 1 shows three different formal groupings which emerge from consideration of the individual lines. Each involves aural associations over somewhat different temporal spans and confers precedence on different musical elements: linear process (a), motivic and cadential parallelism (b), pitch succession (c). The disparities among the groupings create a subtle web of formal tensions within the song.




Ex. 3 Linear Motion of Tenor

Phrase Breve 3 8 , 1() 12 14a 3 8 , 10 12 15b

17 23 , 25 28 31 36 40

-- - U

III Another sort of structural depth is apparent in the interplay between line and contrapuntal framework. Once cantus and tenor join together, impressions of each individually are subject to modification by the context of primary consonances they produce. The succession of consonances, the contrapunctus structure, can confirm and reinforce certain linear features, alter or efface others. In this particular case, the intervallic framework substantially modifies impressions of pitch relationships within the opening phrase of the tenor. If the tenor is considered in isolation, g is the stable axis in bs 1-10, due to its extended duration and centrality in relation to f and a (Ex. 3). In the contrapunctus structure, however, the f and the a are the pitches associated with stable perfect intervals in the first phrase (Ex. 4). The g receives an unstable imperfect third and is thereby defined as tonally subsidiary to the f and the a. Not until breve 9, when a cantus f# ' pushes the tenor a down to g is the g-centring proposed in the tenor line acknowledged at the contrapuntal level. But even this is short- lived, as the voices move directly on to a C octave. Line and contrapunctus are here linked in a subtle play between the potential and the actual. The forces of imperfect-to-perfect consonance in the first phrase override a plausible g focus in the tenor line, but that potentiality to some degree prepares the sudden move to a G octave which inaugurates the second phrase, as well as the subsequent predominance of the G octave in the composition (bs 17, 31).

The tenor is not alone in being shaped by the polyphonic context. Contrapuntal elements also significantly colour the c' in the opening cantus phrase. Although plainly the goal of the line down from fl, the c first makes a third, then an extended dissonant fourth with its partner.12 Only at the end of the poetic line (doleur) is it allowed the support of a perfect consonance, and even then the memory of its prior instability is fresh enough for the phrase to slip



SARAH FULLER

Ex. 4 Contrapunctus Framework

* = Cantus * = Tenor

2 4 6 8

J'aim miex languir en ma dure doleur Et puis morir Intervals 8 5-(4)-3- 5 (4) +3 5 5- (4) -3-- -1

10 1,2 _ 14a

s'A- mour le prent en gre +6- -8 5 6- +6-- 8 5-6 8- 6 +6

12 A

.

14b

faus- se- te --8 5-6 8- 6 6 +6 - 8

17 17 20 22

N'onques en moy n'ot autre volente Ne ja n'a- vra 8 5- (4)- 3 +6 5 1 3 +6 8

28 24 26 30

8 Pour peinne que j'en- du - - -re 5 1 5 6 - 8 8 -6 6- 5

0( 32 34 36 38 40

Et me fus - sies cent mille fois plus du - - - - - -re 8 6-5 6 8 5 1 3 5-6 8-10 5-6 8-6 6 +6 -8




discreetly down to a. Because of such intervallic shadings, a distinct cantus pitch focus does not really emerge until the second section. This phenomenon is intimately connected with aspects of tonal organization to be discussed below.13

These observations naturally propel attention towards the song as a whole and its contrapunctus structure. The contrapunctus framework of consonant sonorities, the idealized core of the polyphony, must be abstracted from the skilfully worked surface of the piece. Because the premises guiding realization of the contrapunctus condition the construct and the conclusions based on it, they require brief summary here. Particular details of execution may be discovered by comparing Exs 1 and 4.14 1) The accepted structural intervals are unison, fifth and octave (the perfect

consonances), major and minor thirds, and sixths (the imperfect consonances)."

2) Consonance quality takes precedence over relative duration: for example, in b. 10 the g' is chosen as the structural pitch even though the f, sounds longer.

3) The main consonant interval may change during a sustained pitch: for example, in b.2 the tenor a bears both a fifth and a third.

4) Textual syntax, rhythm and voice-leading progressions establish the primary phrase modules of the contrapunctus, numbered 1 to 5 in Ex. 4.

5) The chief mensural units (in this case breve and semibreve) define the temporal grid within which contrapunctus relationships are heard.

The contrapunctus sketch of Ex. 4 shows both textual coordination and mensural units, for they affect the relative weight of individual intervals and progressions. It also indicates some dissonances (represented by x's in the cantus) that have motivic or linear significance.

As was observed with the melody of J'aim miex, the design of the contrapunctus can be considered from two separate perspectives, those of process and association. The former has to do with the course of voice-leading and interval progressions, the latter with referential connections between individual moments or gestures. From the perspective of process, two opposite modes of proceeding are evident, one premised on regularity and standard voice-leading progressions, the other free from constraints of pattern, seemingly spontaneous and unsystematic. The more ordered approach prevails in the opening section (phrases 1 and 2), the less systematic one in the second section (phrases 3-5). To the extent that process becomes loose and unpredictable in the second section, associative links between phrases increase. Both the third and the fifth phrases make explicit surface references to cardinal elements in the first section and to each other. The two facets of design - process and association - thus stand to some extent in a complementary relationship.

The opening is a model of contrapuntal clarity. Over the large span, the octave contracts to a unison via fifths and thirds. Over the small span, series of fifths and thirds propel a linear return to perfect consonance on f, the initial tenor pitch. The fifth-third motive comes three times (see brackets in Ex. 4), always with a characteristic intervening fourth. The underlying sequence is easily perceptible, even though surface features mask the repetition, saving it



SARAH FULLER

from too mechanical an aspect. The first 5-(4)-3 progression occurs within the span of one breve, the second extends over three breves, while the third unexpectedly ends on a unison instead of the anticipated fifth.'6 In its confinement to adjacent consonances and its regular successions of imperfect to perfect intervals, the phrase as a whole is a textbook example of fourteenth- century contrapunctus teaching.

The second phrase also holds to standard contrapunctus progressions, but concentrates on the succession sixth-to-octave instead of third-to-fifth. With the clos ending (phrase 2b), it falls into two parallel segments, each of which starts with a 6 -- 8 progression and proceeds to a C octave through a series of sixths (bs 9-12, 12-15b). With the ouvert ending (phrase 2a), the second segment becomes stranded on a sixth whose resolution prompts the return to phrase 1, complementing the verbal continuity that motivates it textually.

No such obvious patterning controls the third contrapunctus phrase. It is, rather, an amalgam of gestures from the first two phrases. The very opening recalls the first phrase, but the parallel lasts only two breves (17-18). Instead of the previous smooth succession of imperfect to adjacent perfect intervals, the sixth g'-e' (b. 19) is left hanging as an 'open' or unresolved interval. The overall octave-to-unison framework of bs 17-21 also relates to the move of the first phrase from F octave to a unison, but the sense of the gesture is quite dissimilar here. The progression is compressed within the text line, not expanded over the full phrase, and the unison is not the goal of contrapuntal motion but a point of departure for the approach, by contrary motion, to the C octave. The final d6 -- c8 cadence recalls the characteristic sounds of phrase 2 in general, and the clos ending in particular.

Contrapuntally, the fourth phrase is the most 'disordered' of the five, just as it is the most disjunct melodically. The succession of intervals neither follows contrapunctus norms nor exhibits regular internal patterning. Its tentative ending - a neutral progression to a perfect interval - leaves the listener suspended uncertainly in tonal space.'7 The fifth phrase restores order to some degree, by taking up the thread of discourse from the third phrase. The contrapuntal parallelism between its first progression g8-a5-g6 and the opening of phrase 3 is reinforced by melodic resemblances in both voices (Ex. 1, bs 31-3, 17-19). The G unison at b.34, although rhythmically displaced, recalls the medial G unison of phrase 3. The last half of phrase 5 expands the reference to phrase 2 introduced at the end of phrase 3, closing with the literal quotation of breves 13-15b.

The contrapunctus structure, then, suggests yet another design than those projected in the individual voices (Fig. Id). The general dynamic is from a controlled exposition, bound by standard contrapunctus progressions, to loose combinations and recombinations of familiar elements, a free commentary upon prior material. The referential elements are so arranged as to link the beginnings of the first, third and fifth phrases and the ends of the second, third and fifth phrases. In effect, the initial and the terminal gestures of the first section are taken up at the phrase level in the second section. This parallelism of odd-




numbered phrases matches the special couplet grouping of the text lines so that contrapuntal and textual segments are in phase. In standing apart, the fourth phrase intensifies the sense of return and summary in the refrain.

An even more schematic abstract of the contrapuntal structure shows how deeply the parallelisms cut (Ex. 5). Both first and third phrases begin with a

Ex. 5 Abstract of Background Voice Leading

II - I I 4 5 1

V 1- 1 VI 1- 4, VI 5- 10

VIII -

stable and tonally static unit framed by perfect consonances on a fixed pitch (f8-5 and g8-1 respectively). Each closes with a directed progression to an interval situated on another pitch degree. This partitioning into 'initial' and 'terminal' elements is fostered by the verse structure. The first and final syllables of the odd-numbered lines coincide with the perfect consonances delimiting the settled initial element. The four syllables of the conjoined even- numbered lines bear the directed cadential progression. Metric position also plays a contributing role, for each of the critical intervals is situated at the beginning of a breve. The fifth phrase follows the same trajectory, but is shaped quite differently, for its constituent parts are placed so as to avoid any pronounced interior articulation. The single text line blocks any sharp break between initial and terminal elements of the phrase. Neither the fifth nor the unison on g (candidates for forming a tonal unit with the initial G octave) coincides with a natural verbal subdivision or with the inception of a mensural unit. The first move to the C octave (b.36) lacks cadential weight, for the cantus melisma continues right through it, and a strong dissonant adjunct overshadows



SARAH FULLER

the upper c'. The phrase flows in one unbroken span from its starting-point, the G octave, to the final cadential descent. Not only is it the longest phrase in actual duration, it also projects the most spacious contrapuntal arch, for its opening is fused directly with the cadential progression, not detached from it as in phrases 1, 2 and 3. The contrapuntal continuity gives force to the climactic refrain line and also accomplishes a tonal purpose, explicitly binding the separate pitch nodes of the song.

IV The contrapunctus framework is, of course, more than a string of local interval progressions and the seat of harmonic associations between phrases. It also embodies broad tonal emphases and pitch relationships. Putting aside the temptation to attribute hegemony to the terminal pitch and claim C automatically as the controlling centre of the music, a triangle of relationships can be seen to dominate the tonal scheme. This triangle consists of F, G and C, the three pitches favoured consistently with transparent octave sonorities. Beyond their consonance degree, the three owe their prominence especially to position - to strategic placement at the beginnings and ends of phrases and sections. They are cornerstones tonally because they stand at critical boundaries of syntactic units.

F and G assume initial functions. They are points of departure, places from which motion elsewhere is initiated. Not only does every phrase but the fourth begin with a prominent F or G octave, but the first and third phrases (and to a lesser degree, the fifth) make firm medial articulations on their starting tenor pitches. As remarked above, the initial segments of all these phrases are stabilized tonally within an area circumscribed by the opening octave and a subsequent perfect consonance on the same tenor pitch, F or G. These stable initial areas stand out prominently at the structural level reached by a second reductive sweep (see Ex. 5).

C is alone in fulfilling a significant terminal role. It is a point of arrival, the place towards which the principal contrapunctus units move. (The case of A, its only possible competitor, will be considered below.) The two main sections both close on C, preparing the arrival with their series of imperfect consonances. The third phrase is also directed toward C and helps to reinforce the C closure of the first section.

Relationships within this triangular partnership are not fixed and static but fluctuate over the course of the song. The initial orientation is towards F, the foundation of the octave-fifth unit that encompasses the first text line. Within the context provided by the first set of voice-leading progressions, the A cadence at breve 8 seems but a temporary deflection, an unanticipated departure from the F focus which provides a fitting analogue to the unexpectedly drastic future foreseen by the suffering lover.'" Whatever its affective qualities, the a, joined by a bright cantus f# ', also sparks a new orientation towards G.19 This, however,




is short-lived - a suggestion rather than an achieved goal - for the G octave is blurred by a prominent seventh, and the tenor moves promptly to a new pitch area. By the time the tenor g is regained, at the end of phrase 2a, it is linked with an unstable major sixth that inclines back to the initial point of orientation, the F octave. The cadence of b. 14a is ouvert not just in resting elsewhere than on the ultimate point of repose, but, even more pointedly, in its active tendency towards resolution. In preparing a return to the F octave it strengthens F as an aural reference point and relegates G to a secondary plane. The first effective challenge to the status of F comes in phrase 2b, where the previous weak medial gestures toward C (bs 10-12) develop into a definite cadential move to a stable C octave.20 The F, instead of being granted terminal as well as initial position, launches a directed descent by sixths to C.

The balance of forces is otherwise in the second section. G definitely assumes the initial position, C the terminal one in its two principal phrases (3 and 5). F recedes from the forefront of action. In phrase 4 the F intervals engage in no very pointed progressions, while in phrase 5 a medial F octave again heads a descent to C. The overall scheme of relationships can be seen in Fig. 2. The two main sections of the piece constitute one axis of the F-G-C triangle, bisecting it symmetrically; the dichotomy of initial and closing positions (or functions) makes another axis, bisecting the triangle asymmetrically.

The two sections of the song are not be regarded as belonging to separate tonal spheres, even though different pitches hold the initial position in each. For one thing, both sections share the same final point of closure. For another, each explicitly acknowledges the pitch with initial status in the other. As already observed, an obvious feint towards G occurs between the initial F and the terminal C of the first section. In the second section, the F octave surfaces in phrase 4 and again in phrase 5 where it links the G and C octaves. In each section, then, the opening referential pitch of the other receives some medial exposure (recorded within parentheses in Fig. 2). Relationships among F, G and C shift, but the group is intact in both sections.

In addition to these general parallels, specific tonal details bind the two sections of the song together. The unusual A closure of phrase 4, for example, relates back to the singular A cadence of phrases la and lb. Once again, although less spectacularly, a close on A precedes a move to the G octave. Phrase 4, which stands apart in the general associative scheme (see Ex. 5), would seem to perform two not insignificant functions. One is to recall a special detail from the first half of the song, the 'odd' A cadence of breve 8. The other is to create an area of tonal contrast before the refrain where the final disposition of primary pitch relationships finds its decisive formulation. The tentative quality of the A ending - a neutral octave-fifth progression mediated by a hanging sixth - is an effective foil to the goal-directed character of phrase 5. By repeating the A gesture immediately within the context of the G octave and fifth (bs 31-4), Machaut formally absorbs it within the contrapuntal framework.

Another significant detail common to both sections ofJ'aim miex is the g-e' sixth. This sonority first comes to the fore at the ouvert ending, where it



SARAH FULLER

Fig. 2 Tonal Scheme

Initial Final Position Position

FI

(G) First Section +Second Section - - - C-

Second Section

G

functions to reinstate the F orientation and, concomitantly, to deny the turn towards G initiated at the beginning of phrase 2a. Subsequent striking recurrences revive the memory of an unstable G. A first telling reference is at b. 19, where an obvious disjunction in voice leading leaves the g-e' openly suspended (Ex. 4, phrase 3). The sixth is all the more exposed as it occurs just when the parallelism with phrase 1 breaks off (bs 1-2/17-18). The g-e' sonority persists in phrase 4, still without being satisfactorily resolved. Not only is it separated from its natural goal, the F octave, by a G octave (b.26), but the e' sticks in the cantus voice and in fact becomes the main structural pitch in that voice (Ex. 6). First the sixth over g, then the seventh of f, the el finally finds a stable context as the fifth over a. The two secondary details of the pitch




Ex. 6 Contrapunctus, bs 24-9

b. 19) -

g 5 5 6 8 8(7) 6 5

structure, the unstable g-e' and the terminal a, are clearly brought together at the end of the phrase.

The final phrase deals with the g-e' in two ways. It leads the e' down to d', in emulation of the preceding 6-5 progression over a (Ex. 7), and it allows the sixth to proceed directly to its 'natural' resolution (bs 37-8). Neither of these voice leadings necessarily constitutes the definitive resolution of the issue. Both together contribute to the perception that the g-e' has been taken care of contrapuntally.21 In retrospect, it is as though the ouvert ending continued to play a role beyond its local context.

Ex. 7 Contrapunctus, bs 28-34

6- 5 8 6- 5 6- 5 L~ L L. L

V The tonal design of J'aim miex exhibits a remarkable degree of integration and coherence both on the surface and at inner structural levels. Rather than exhibiting the characteristics of a tonic-centred, or even a tonic-directed, system, it presents a carefully adjusted web of primary and secondary relationships among the pitches and intervals.22 The main functions are defined by initial and terminal positions in phrases and sections. Changes in position, reinforced by adjustments in the force of contrapunctus progressions, permit fluid shifts in balance among the chief referential pitches. Motion from one area of orientation to another where closure occurs appears to be a central generative premise. Details of voice leading, line and rhythm are so constituted that final closure is reserved to the last phrase where various threads cast forth previously are finally woven together.



SARAH FULLER

Even though it is possible to abstract a central tonal core (Fig. 2), there is no reason to believe that this core was an a priori generative element. The manner in which the whole scheme of pitch and intervallic relations unfolds over the course of the song speaks more for an intuitive process, a contextual development of associations and connections. This position finds some degree of support in the lack of similar structures in other Machaut songs that have been discussed in print. The first section ofJe ne cuit pas (Ballade 14), anchored on one interval (not, incidentally, the final resting-point of the song), proposes but a single pitch axis.23 The rondeau Rose lis (No. 10) has been said to be founded on 'a sequence of octave intervals . . . descending through the hexachord towards the final'.24 Casting further afield, De desconfort, the ballade copied adjacent to J'aim miex in the principal Machaut manuscripts, shares many surface features with it, but does not possess a comparable tonal core;25 it is far looser in pitch structure and voice leading than its companion. Dame ne regardes pas (Ballade 9) comes closer in concept with its confrontation of a-e1 (the true axis for most of the piece) with g-d' (which accumulates the main terminal positions). But these are simply examples culled at random. Much more comprehensive investigation of tonal structures in Machaut songs is necessary before any solid judgment on his practice can be made and any clear sense of its systematic or non-systematic character obtained. It is very possible that further study will show J'aim miex to be not a model of Machaut's habitual practice but an individual example of one manner in which he shapes a piece tonally. To a mind attracted to coherence and unity as artistic values, it may seem especially successful in realization, but it does not necessarily represent a chosen path for Machaut.

Just as striking as the intricate interplay of pitch relationships and flexible tonal orientation is the complexity of groupings and associations within the short span of J'aim miex. The individual lines, the contrapunctus framework and the tonal network all produce perceptible patterns of association or process, but these patterns do not converge to form a one-dimensional, sharply-stamped image of the piece. For example, both melodic process and tonal action concur in placing the refrain phrase apart and conferring an important role of synthesis upon it, but the one locates the preceding phrase (the setting of syllables 5-10 of line VI) within an established pattern, while the other sets it apart as an area of contrast (compare Figs la, Id). More associative ways of hearing which give priority to motivic relationships and formal parallelisms group the refrain with other phrases (Figs lb, Ic) or emphasize its kinship with prior syntactic units (Fig. Id). Other elements pointed out above (shifts in tonal orientation, voice- leading processes etc.) suggest differently shaded conceptions of the work. One could choose a single facet - basic tonal scheme, for instance - to represent the structure of J'aim miex, but to do so would be to conceal an intriguing quality of the song, the intersection of multiple planes of action within the whole. Rather than assuming a neat single-track sort of structure, it might be preferable to admit the possibility of a messy, multi-faceted structure, a sort of cubist construct with intersecting planes of reference, association, process. Some




planes are doubtless more prominent than others, but all would be accepted as components of that elusive inner core, the musical structure.

This, at any rate, is what I would like to argue for J'aim miex: that its structure, as embodied in concrete properties of lines, contrapunctus, voice- leading progressions and tonal orientations, is a complex of intersecting planes that do not naturally align themselves hierarchically to form a one-track linear core. The metaphor of planes is an attempt to communicate the multiplicity of levels and temporal spans on which significant relationships operate. Whether or not one wishes to subscribe to such a position, the level of technical control and artistic skill exhibited in J'aim miex remains undiminished. The design of the individual voices, the integrity of the contrapunctus, the coherence of tonal relationships, the closed web of internal references - all testify to a highly accomplished compositional technique which can be comfortably accepted as yet another link in the tradition of complex, well-reasoned Western polyphony. Yet in the wider context, one may well ask whether such rational and cultivated musical discourse is a pervasive aesthetic, or whether it is only on occasion or with increasing maturity that the various elements of Machaut's craft coalesce into so convincing a whole.26 In presenting this analysis of J'aim miex I do not claim that the song represents a norm of practice, but rather propose it as a marker to guide future efforts towards tracing the configurations of Machaut's musical art.

NOTES

1. 'reflektierende Bewusstheit': Die mehrstimmigen Balladen, Rondeaux und Virelais von Guillaume de Machaut, Muinchener Ver6ffentlichungen zur Musikgeschichte, Vol. 16, 1970, p.85. D6mling's monograph is a pioneering work. Other notable contributions to the study of Machaut's compositional technique are Wulf Arlt, 'Aspekte der Chronologie und des Stilwandels im franz6sischen Lied des 14. Jahr- hunderts', Forum Musicologicum, Vol. 3, ed. Hans Oesch and Wulf Arlt, 1982, pp.193-280, especially Parts 3 and 4; and Daniel Leech-Wilkinson, 'Machaut's Rose, Lis and the Problem of Early Music Analysis', Music Analysis, Vol. 3, 1984, pp.9-28.

2. See Arlt, 'Aspekte der Chronologie', p.228. 3. This ballade is early, being among the works transmitted in the first part of the

manuscript Bibliothbque Nationale, fonds franqais 1586 (commonly cited as C), which represents the state of Machaut's oeuvre around 1350. But if Machaut was born c. 1300, as is usually supposed, this still leaves a period of some thirty years during which the song might have been composed. On the dating of f.fr. 1586 see F. Avril, 'Les Manuscrits enlumin s de Guillaume de Machaut', Guillaume de Machaut, Actes et Colloques, Vol. 23, 1982, pp.117-24, and Ursula Giinther, 'Contribution de la musicologie a la biographie et A la chronologie de Guillaume de Machaut', ibid., pp. 101-6.

4. On the evidence for claiming a pre-existent text, see Sarah Jane Williams, 'Vocal



SARAH FULLER

Scoring in the Chansons of Machaut', Journal of the American Musicological Society, Vol. 21, 1968, p.256.

5. For an example of the first situation, see Esperance qui m'assure (Ballade 13), breve 4, where text sense bridges a musical articulation (shown by a dotted line in the incipit). For an example of the second, see Arlt, 'Aspekte der Chronologie', pp.234-5.

6. This is normal in Machaut's ballades: see Arlt, 'Aspekte der Chronologie', pp.235-6, and D6mling, 'Aspekte der Sprachvertonung in den Balladen Guillaume de Machauts', Die Musikforschung, Vol. 25, 1972, pp.301-7.

7. The version presented in Ex. 1 is edited on the basis of MSS. B.N. f.fr. 1586 (C), f. 160v, and f.fr. 1584 (A), f. 457. It differs in some details from the standard edition of Leo Schrade (PMFC, Vol. 3), particularly in text underlay and in including the pause before the refrain line. Parentheses enclose accidentals that could carry through the line. Both manuscripts provide blank staves for a triplum, but no a3 version is known from any source.

8. Machaut's songs were, of course, notated in separate parts, which are copied adjacently in the sources.

9. On contrapunctus, see Klaus-Jilrgen Sachs, Der Contrapunctus im 14. und 15. Jahr- hundert, Beihefte zum Archiv fiir Musikwissenschaft, Vol. 13, 1974. I discuss problems of relationship between contrapunctus teaching and composed music in 'On Sonority in 14th-Century Polyphony', Journal of Music Theory, Vol. 30, No. 1, 1986, pp.39-40.

10. In starting voice-by-voice I do not mean to suggest a successive mode of composition, although the successive/simultaneous dichotomy is often raised in conjunction with this repertory (Arlt, 'Aspekte der Chronologie', pp.253-61, and Leech-Wilkinson, 'Machaut's Rose, Lis', nn. 6, 9, pp.24-5). The procedure is simply a device for homing in on differences in analytical judgments which result from the stance adopted by the observer.

11. Note that on a large scale this convergence reflects that of phrase 2a. 12. I proceed as though at this stage the fourth was considered in contrapunctus circles

to be a dissonance. However, it should be noted that the earliest documentary evidence, from Petrus of Amiens (Petrus dictus palma ociosa), dates from 1336 (Richard L. Crocker, 'Discant, Counterpoint and Harmony', Journal of the American Musicological Society, Vol. 15, 1962, p.7). Treatises outside the contrapunctus sphere express a range of opinions. Writing in the 1350s, Nicholas of Oresme cites the fourth along with the fifth and the octave as representative of symphonic or consonant proportion (Nicole Oresme and the Medieval Geometry of Qualities and Motions, ed. Marshall Clagett (Madison: University of Wisconsin Press, 1968), pp.312-13). Johannes Boen (Musica, 1357) places the fourth among the consonances per accidens, those granted consonant status only when sounded with an independent consonance (consonantia per se). His conditions are met only in textures of three or more voices (W. Frobenius, Johannes Boens Musica und seine Konsonanzenlehre, Freiburger Schriften zur Musikwissenschaft, Vol. 2, 1971, pp.74-6).

13. Leech-Wilkinson notes cases of tension between line and contrapunctus functions in




the four-part rondeau Rose, Lis ('Machaut's Rose, Lis', pp. 19-20). 14. I consider the contrapunctus to be a first level of structure which lies just below the

surface of the piece and is to a considerable degree, especially in retaining a mensural dimension, still closely connected with that surface. Further reduction levels become increasingly abstract and artificial (though by no means uninformative) as they depart from the contrapunctus (e.g. Ex. 5). Retention of the Latin term is intended to prevent confusion between levels and emphasize the concreteness of the contrapunctus reduction. For background to the premises articulated here, see Sachs, Der Contrapunctus, especially pp.24-74, and my article 'On Sonority in 14th-Century Polyphony', pp.35-63.

15. Just when the minor sixth was formally invested with consonant status cannot be determined. Using Petrus of Amiens (for whom it is still non-consonant) as a reference point, Crocker suggests c. 1350 ('Discant, Counterpoint and Harmony', p.7). Because in actual usage it seems to function as a consonance early in the ars nova (especially in parallel series of sixths), I admit it to the contrapunctus reductions.

16. Should the b at breve 7 be sung as b-rotundum (i.e. flattened) to produce the preferred progression minor third-to-unison? Petrus of Amiens would encourage such an inflection (Johannes Wolf, 'Ein Beitrag zur Diskantlehre des 14. Jahr- hunderts', Sammelbande der Internationalen Musikgesellschaft, Vol. 15, 1913-14, pp.509, 513-14), but the Machaut manuscripts offer no concrete supporting evidence for it. The case would seem to admit of two possible solutions, and executants must choose between two quite dissimilar aural effects.

17. In my definition, a neutral progression is one in which the first sonority has no particular inclination (produced by imperfect intervals) to move towards the second. Its opposite is a directed progression in which a sonority prepares and proceeds to its natural resolution. For more on the subject, see my article 'On Sonority in 14th-Century Polyphony', pp.50-5.

18. A textual connection is not unlikely in the context of recent investigations of text/ music relationships in this repertory: see D6mling, 'Aspekte der Sprachvertonung in den Balladen Guillaume de Machauts', and Arlt, 'Musik und Text', Die Musikforschung, Vol. 37, 1984, pp.272-80.

19. In the first couplet, this reorientation coincides with, and underscores, a significant textual turn away from the speaker himself to a personified external force.

20. The earlier approach (b. 11) is weakened by prominent sevenths which cloud the parallel sixth progression to the octave. Although contrapunctus pedagogy views dissonance as inessential and merely decorative, Machaut seems not infrequently to employ dissonance functionally (see Leech-Wilkinson, 'Machaut's Rose, Lis', pp.18-19, and my 'On Sonority in 14th-Century Polyphony', pp.42, 55).

21. By this remark, I mean to dissociate myself from a position according to which one of these moments would have to serve as 'the' structural voice leading. The abstract resolution of the g-el is not necessarily to be attached to only one concrete detail of the piece.

22. Nor is the song modally controlled. I take issue with the position that mode was a pre-compositional factor for Machaut, a position argued by Richard H. Hoppin



SARAH FULLER

('Tonal Organization in Music Before the Renaissance', PaulA. Pisk: Essays in His Honor, ed. John Glowacki [Austin: University of Texas, 1966], pp.25-37) and by Gilbert Reaney ('Modes in the Fourteenth Century', Organicae voces: Festschrift Joseph Smits Van Waesberghe [1963], pp.137-43; 'La Tonalit6 des Ballades et des Rondeaux de Guillaume de Machaut', Guillaume de Machaut, Actes et Colloques, Vol. 23, 1982, pp.295-300.

23. Arlt, 'Aspekte der Chronologie', pp.231-2. 24. Leech-Wilkinson, 'Machaut's Rose, Lis', p.23. Rose, Lis is a four-part song, but the

comment applies to an essential two-voice reduction. Although it is possible to construct an octave descent in J'aim miex, I do not think it central to the piece in terms of voice leading or of tonal relations.

25. The similar features include a decided break between the first and second phrases accompanied by a fresh tonal orientation, a 6-5 interval progression over a held tenor pitch just before the refrain, and, on breve 8, the f'-e'-f'-d' motive that serves as a cadential marker in J'aim miex.

26. Other Machaut songs display similar compositional procedures (see the studies cited in n.1 above), but the density of organisation seems especially marked in J'aim miex.



Article Contentsp. 37p. 38p. 39p. 40p. 41p. 42p. 43p. 44p. 45p. 46p. 47p. 48p. 49p. 50p. 51p. 52p. 53p. 54p. 55p. 56p. 57p. 58

Issue Table of ContentsMusic Analysis, Vol. 6, No. 1/2 (Mar. - Jul., 1987), pp. 1-204Front Matter [pp. 1-2]Methods of Analysis in Musicology [pp. 3-9+11-36]Line, 'Contrapunctus' and Structure in a Machaut Song [pp. 37-58]The Two-Voice Framework and Its Harmonization in Arcadelt's First Book of Madrigals [pp. 59-88]The Rhetorico-Musical Structure of the 'Goldberg' Variations: Bach's 'Clavier-bung' IV and the 'Institutio Oratoria' of Quintilian[pp. 89-131]A New Model for Pitch Motion in Tonal Music [pp. 133-167]ReviewsReview: untitled [pp. 169-179]Review: untitled [pp. 179-192]Review: untitled [pp. 192-196]Review: untitled [pp. 196-202]

Back Matter [pp. 203-204]

Machaut estructura y contrapunto

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