Polytonality and the maintenance of perceived tonal ambiguity in darius milhaud’s saudades do brasil by Ryan Thomas O'Connell

Ryan O’Connell MUS 197 May 11th, 2015

Polytonality and the Maintenance of Perceived Tonal Ambiguity in Darius Milhaud’s Saudades do Brasil Introduction Born in Marseilles and raised in Aix-en-Provence, France, Darius Milhaud has been widely recognized for playing a major role in the development of polytonality and the incorporation of jazz-based ideas in “classical” music. Though often exploratory and unconventional, Milhaud’s music maintains a consistent and unmistakable aesthetic and character. His impressive creative output includes many piano pieces, operas, and orchestral works, among other things. Milhaud was often influenced and inspired by places he visited, including Provence, London, Vienna, etc. Particularly notable for its influence on Milhaud is Brazil — he spent almost 2 years in the country, basking in its sounds and culture before returning to Europe in 1919. 1 In 1920, Milahud composed Saudades do Brasil (roughly translated to “Souvenirs from Brazil”), a two-volume collection of short dance movements for piano, which employ techniques of polytonality and polymodality, as well as tango rhythms and Brazilian-sounding (but original), lyrical melodies. Each movement depicts its own unique mood and is distinguishable from the rest, yet all twelve exist as a unified, cohesive whole. Part of what creates this unity (aside from the nearly perpetual, underlying tango rhythm) is Milhaud’s ability to place and keep the listener in a specific, relatively narrow sphere that lies at a certain point on the spectrum between traditional, 1

Darius Milhaud, Notes Without Music (New York: Alfred A. Knopf, Inc., 1953) 69–86.

triadic tonality and totally chromatic atonality. This is achieved in a variety of ways, which will be discussed at length.

The debate over polytonality Before exploring Milhaud’s own use of polytonality in Saudades any further, it will be useful to address the debate that has been ongoing among music theorists and composers on the topic of polytonality/polymodality in general. The basic disagreement that surrounds this debate stems from the challenging question of whether or not a piece of music that has been conceived of as being in two or more keys simultaneously (by the composer) can, in reality, be perceived as such (by a listener). Many assume that a piece of this nature will either 1) have essentially the same effect on the listener as a piece of atonal music, or 2) have — especially in pieces where specifically two key areas are being sounded (bi-tonal pieces) — one key area that “wins out,” and is heard more prominently than the other key.2 Since its first uses, music theorists and composers have struggled with and disagreed over how to think about music in multiple, simultaneous keys.3 Although Milhaud argues that the roots of polytonal thinking date back to the time of Johann Sebastian Bach4, some of the first real writing on the subject appears in the 1920s by the French composer and theorist Charles Koechlin,5 who discussed music 2

Dmitri Tymoczko, “Stravinsky and the Octatonic: A Reconsideration,” Music Theory Spectrum 24, no.1 (2002): 84. 3 François de Médicis, “Darius Milhaud and the Debate on Polytonality in the French Press of the 1920s,” Music & Letters 86, no. 4 (2005): 574 4 Darius Milhaud, “Polytonalité et Atonalité,” Revue musicale 4 (1923): 29–30. 5 Charles Koechlin, “Évolution de l’harmonie: Période contemporaine, depuis Bizet et César Franck jusqu’a nos jours,” Encyclopédie de la musique et dictionnaire du Conservatoire 2, no. 1 (1925): 591–670.

dating back to the early 1900s. Writings from Darius Milhaud6 and Alfredo Casella7 deal with slightly later music from the 1910s and the 1920s. Other, less pointed mentions of polytonality arose in the same period as well — Claude Debussy noticed it being employed in the works of Johann Strauss8, and it was spoken of at the premier of Igor Stravinsky’s Rite of Spring.9 Also a composer, Alfredo Casella crafted a piece in 1913 called Notte di maggio, which the critic Émile Vuillermoz saw as a reformulation of Stravinsky’s innovations into a more accessible form.10 The true debating on the issue began in France after the composer and critic Henri Collet wrote two articles in 1920 in which he coined the term “Les Six” (a clear reference to the Russian group “The Five”), denoting a group of French composers which included George Auric, Louis Durey, Arthur Honegger, Francis Poulenc, Germaine Tailleferre, and Darius Milhaud. In the first of these two articles, Collet, in addition to reviewing a piece of music and creating a new, now-famous term, explained that one of the things that united these six composers was their collective and deep sense of French nationalism.11 In the second, he went on to find more common ties between them, including the use of polytonality.12 He explained that all of these composers were not only like-minded in their nationalist goals, but that they also shared a common desire to

6 Milhaud, “Polytonalité et Atonalité. 7

Alfredo Casella, “Tone Problems of Today,” Musical Quarterly, 10 (1924): 159–71. Claude Debussy, Monsieur Croche et autres écrites (Paris: Gillimard, 1987): 138. 9 Truman C. Bullard, “The First performance of Igor Stravinsky’s Sacre du Printemps with Reviews of Sacre, 1913 in English Translation and Original French Texts of Reviews” (PhD. diss., University of Rochester, 1970). 10 de Medicis, 573–591. 11 Henri Collet, “Un livre de Rimski et un livre de Cocteau. Les cinq Russes, Les Six Français et Érik Satie,” Comoedia 16 (1920): 2. 12 Henri Collet, “Les Six français: Darius Milhaud, Louis Durey, Georges Auric, Arthur Honneger, Francis Poulenc et Germaine Tailleferre,” Comoedia 23 (1920): 2. 8

distance themselves from impressionism and the Schola cantorum. He cited these composers’ use of polytonality as being complexity in the pursuit of simplicity.13 Almost immediately after the publication of Coullet’s influential articles, heavy debating within the French press ensued (with those on the side opposite of Coullet’s often being anti-Les Six rather than necessarily anti-polytonality). Although voices from both sides of the argument were surely heartfelt, there remained a (perhaps unrecognized) state of terminological confusion, with no prior consensus having been reached on the true definition of “polytonality” or, for that matter, on “atonality, ” among others. Indeed, Koechlin used the term “polytonality” to describe music from both Wolfgang Amadeus Mozart and Arnold Schoenberg.14 Adversaries of Coullet, like Émile Vuillermoz, saw polytonality not as a good and artistic mode of expression, but rather as step backward in the historical development of music.15 The critic Alexis Roland-Manuel was among the first to call into question the basic existence of polytonality.16 Other arguments against the idea were based more on the promotion of a different brand of French nationalism and on anti-Semitism than on considerations of perceptibility and artistic merit.17 Still, the foreign sounds created by Les Six and other composers thinking in this vein were, for many, immediately objectionable — at the premier of Milhaud’s Suite Symphonique no. 2, the conductor was forced to stop the players mid-performance so he could turn around

Ibid., 201. Charles Koechlin, “Évolution de l’harmonie: Période contemporaine, depuis Bizet et César Franck jusqu’a nos jours,” Encyclopédie de la musique et dictionnaire du Conservatoire 2, no. 1 (1925): 699. 15 Emile Vuillermoz, Le Temps, 30 Dec. 1921. 16 Alexis Roland-Manuel, “Maurice Ravel,” Revue musicale 6 (1921): 1-21 15 de Medicis, 583. 16 Ibid., 587. 14

and instruct the vocal audience to keep their opinions to themselves until the piece was finished.18 In order to explain and defend his own position and new compositional way of thinking, Milhaud published an article in 1923 entitled: “Polytonalite et Atonalite.”19 In it, he gives his own definition for what polytonality is, and defends its existence by comparing it to atonality and pointing to its roots in early contrapuntal writing.20 He explains that we can think of polytonality as being derived from both the possibility of superimposing triads from different keys and of allowing oneself to not be constrained by an overarching key area upon the transposition of a melodic line (i.e. in a canon or a fugue, etc.). To corroborate this second generative option, he points to the second of J.S. Bach’s four Duetti, identifying a passage wherein a melodic line is transposed from D minor to A minor.21 He states that, although the left hand surely remains within the parameters of the key of D minor, it could be read, if extracted and played individually, as being in A minor, thus implying the existence — even in its original context — of a second key area. Milhaud claims that this theoretical implication came into being not just in this specific example, but rather at the moment when composers began admitting canons at intervals others than the octave. Milhaud provides the reader with more recent examples of (in his view) overt polytonality occurring in well-known music, including Stravinsky’s now famous “Petrushka Chord,” which can be interpreted as the superimposition of C major and F# major triads — each potentially implying its own tonality — and has itself been the 19

Milhaud, “Polytonalité et Atonalité.” 29–44. Ibid., 29. 21 Ibid., 29–30. 20

subject of much debate among music theorists.22 Milhaud also uses the extreme example of the superimposition of triads (each implying, in a hypothetical context, its own tonality) relating to all twelve key areas — or, total chromaticism.23 With the realization of this possibility, Milhaud admits that polytonality and atonality can sometimes merge, even fluctuating in and out of each other within a single piece. He concedes that this convergence can be successful, and stresses to the reader that what truly determines the character of a work is the melody that comes from the composer’s heart — that “absolute and organic necessity…”24 Whether the true origins of polytonality coincide with Milhaud’s explanation of them or not, the fact remains that, just as Schoenberg viewed himself and the furtherance of atonality as history’s natural extension from Beethoven and Wagner, Milhaud viewed polytonality and himself as history’s natural extension from Debussy and the French composers.25 Part of the reason for the aforementioned confusion regarding the term “polytonality” is the ease with which it can be confused with other, similar terms like “polyscalarity” and “polychordality” (even Milhaud did not address these differences enough in his article). In today’s terms when music is said to be “polyscalar,” it is an indication that there are notes from two different scales (i.e. notes from the G major scale and notes from the D minor scale) being sounded simultaneously in a single musical texture. The criterion for music to be “polychordal” simply involves the simultaneous layering or superimposition of triads from two different key areas, regardless of context. Neither of these situations necessarily means, however, that “polytonality” is occurring 22

Ibid., 34. Ibid., 39. 24 Ibid., 44. 25 Barbara Kelly, Tradition and Style in the Works of Darius Milhaud: 1912–1939 (Burlington: Ashgate Publishing, 2003) 145. 23

as well. Although there may be notes present from two different scale collections, those notes may not be implying the tonal center (for example, although they are from the E major scale, the notes A-natural and B-natural if, say, repeated continuously, do not inform the listener that there is an E major tonal center) of the key from which they are derived. Similarly, though a musical moment may be comprised of two distinct but combined triads, the resulting sonority will not necessarily imply two separate yet simultaneously hearable tonal centers (for example, a Cmaj7 chord is a popular sonority in jazz music, and is comprised of a C major triad and an E minor triad. It would be difficult to argue, however, that there is any pull towards or implication of an E minor tonality that results from that sonority). For music to be truly polytonal —as Saudades so often is — it must be made up of materials that are definitely suggesting/promoting more than one tonal center at a time. In other words, individual parts of a polytonal texture can be isolated and, when played alone, identified as belonging to one specific key, without question. In more recent years, the issue of polytonality continues to be discussed among active music theorists. Many figures prominent in the field including Arthur Berger and Peter van den Toorn deny the theoretical existence of polytonality altogether. 26, 27 In describing a colleague’s writing, van den Toorn is glad to announce that “’poly-‘ or ‘bitonality’ — horrors of the musical imagination — have widely (and mercifully) been dismissed as too fantastic (unreal) or too illogical to warrant serious consideration,”28 a stance with which he clearly agrees. Still, others like Richard Taruskin hesitate to dismiss 26

Arthur Berger, “Problems of Pitch Organization in Stravinsky,” Perspectives of New Music 2, no. 1 (1963): 11–42. 27 Peter van den Toorn, “Some Characteristics of Stravinsky’s Diatonic Music,” Perspectives of New Music 14, no. 1 (1975): 104–138. 28 Ibid., 105.

the notion, explaining that “To deny the possibility of existence to a phenomenon…a priori will no more prevent a composer (Ives, for example, besides Stravinsky) from employing that phenomenon than man’s theories of aerodynamics will prevent the bumblebee from flying.”29

“In Pursuit of an Analytical Approach”30 In 1982, Joseph Straus wrote about the state of music theory in regards to the style of Milhaud and his contemporaries, saying that: “A significant body of twentieth-century music — organized around tone-centers but not tonal in the traditional sense — continues to elude systematic analysis. While many important steps have been taken, no comprehensive theory for this music yet exists comparable to Schenkerian theory for tonal music or serial theory for twelve-tone music.”31 This statement is still essentially true in 2015 — neo-Riemmannian theory has emerged to assist in the analysis of much romantic music (some of which, chronologically, is aligned with Milhaud), but there is still not one set tradition of analysis dedicated to tonally-centric (but not totally tonal) or polytonal music. Rather than being a musical tradition that is built on identifiable expectations and tendencies (like music from the “classical” period, i.e. Mozart) or on a quantifiable system (like 12-tone music, i.e. Schoenberg), polytonal music is an adventurous extension of a pre-existing tradition (tonality), one that uses old concepts (adherence to key signatures) in a new way (using multiple keys at once), constantly 29 Richard Taruskin, “Chez Pétrouchka: Harmony and Tonality “chez” Stravinsky,” 19th-Century Music 10, no. 3, Special Issue: Resolutions I (1987): 283–4. 30 This is the title for the second chapter (pp. 18–56) of Deborah Mawer’s book Darius Milhaud: Modality and Structure in Music of the 1920s (Vermont: Scolar Press, 1997), and is — though not original — a fitting heading for this particular section. 31 Jospeh Straus, “Stravinsky’s ‘Tonal Axis,’” Journal of Music Theory 26, no. 2 (1982): 261.

bending and breaking rules that, in their original contexts, might otherwise be hard and fast. Polytonal composing is a practice that is more rooted in experimentation than in expectation, which makes it difficult to systematize. For this reason, we can allow ourselves to do two things in pursuit of an acceptable form of analysis for a piece like Saudades: 1) We can use the identification of the active bi/poly-tonalities and their relationships within each movement as an analytical foundation, and 2) we can borrow pieces and ideas from other music theorists’ works in order to supplement our understanding of the music. One concept that we can potentially borrow in order to aid our analysis is Allen Forte’s “set-theory” — a theory typically applied to music that is mostly or entirely chromatic, or atonal. In Forte’s system, sets of notes are catalogued and given specific numerical identities for quick reference. Referring to these sets in an analysis can be helpful (this analytical tool would potentially be most helpful in mvt. V of Saudades, which is arguably the least “tonal” of the movements — indeed, at least one analysis that employs this technique has already been performed for that movement (appendix 2)) because it helps the listener see how often certain sonorities or patterns occur, and gives insight into the composer’s method(s) of writing, especially when those sonorities or patterns are hard to point out or recognize in context.32 Another idea we can employ in dissecting Saudades is Joseph Straus’ concept of the “normative unit.” Straus uses this term in describing Stravinsky’s music, explaining that: … a certain unordered collection or set of notes…is established as a structural norm for the composition, pervading the surface of the music (both melodic and 32 See: Allen Forte, The Structure of Atonal Music (New Haven: Yale University Press, 1973)

harmonic) and governing the tonal motion at all levels of structure. Through repetition, this normative unit becomes so engrained in the listener’s consciousness that the sounding of part of the pattern creates an expectation for the completion of the pattern.33 As readers of Milhaud’s music, we can apply this theory not only to unordered collections of notes, but also to entire moments or sections of movements, and the unique tonal regions they exist within. We will see that Milhaud realizes that the listener will naturally get used to hearing whatever material he/she is presented with, and is for that reason sure to alter it whenever it returns. A third idea to keep in mind while looking at Saudades is Arnold Whittall’s notion of “confrontation.” Confrontation, according to Whittall, occurs when composers “…attempt to preserve essential features of an old system — especially, of course, tonality — in radically revised forms, yet in such a way that the music cannot be convincingly explained solely in terms of that preservation.”34 We can keep in mind while listening (and will be able to do so easily) that, though the music Milhaud is creating is not always tonal, it is based on the tonal system — a system that is, in a way, being used in a revised form. Whittall’s description of Stravinsky’s music can be applied to Milhaud’s as well when he says that the music “…actually reconciles its old and new components — if not by total synthesis, then by a harmonious balance of contrasts.”35 Milhaud cleverly reconciles the old (tonal) aspects of his music with the new (arrangement of tonalities simultaneously) to create his own, unique synthesis. Similarly, theorist Michael Russ writes: “Stravinsky’s music is very much the sum of its outwardly 33 Joseph Straus, “A Principle of Voice Leading in the Music of Stravinsky,” Music Theory Spectrum 4 (1982): 106. 34 Arnold Whittall, “The Theorist’s Sense of History: Concepts of Contemporaneity in Composition and Analysis,” Journal of the Royal Music Association 112, no. 1 (1986–1987): 2. 35 Ibid., 6.

contradictory, often divergent…parts.”36 We can think the same way about Milhaud’s compositions. Lastly, since the debate about Milhaud’s compositional technique of polytonality is so deeply rooted in questions of competing tonal perception(s), it is useful for us to take a look at some psychological studies that have been undertaken on this topic. Being aware of their findings can provide some insight into how Milhaud balanced, even if unintentionally, his competing and complementary tonalities to play in a particular way to our natural perceptual inclinations. In one pertinent study, two scientists at Cornell University conducted five experiments, all based on listeners’ perceptions of the aforementioned “Petrushka chord.” The research in this case found that listeners could certainly distinguish one tonic from another when the two competing triads (an F# major triad and a C major triad, each suggesting its own tonic if isolated) were sounded individually, but that the two implied tonalities could not be separated perceptually when they were sounded together, in the same range and rhythm and at the same volume.37 In another study, researchers found that when listeners are presented with a piece of music that is in two simultaneous keys they are sensitive to both keys and weight them according to each one’s perceived importance within the excerpt. In another experiment in the same study, wherein listeners were given a piano piece by Milhaud (one that presented different keys at simultaneously-sounding registral extremes), it was found that there was not a direct association between register and key area — instead, ratings for all three registers tested 36 Michael Russ, “Four Studies in the Analysis of Post-Tonal Music” (Ph.D diss., University of Ulster, 1985). 37 Carol L. Krumhansl and Mark A. Schmuckler, “The Petroushka Chord: A Perceptual Investigation,” Music Perception: An Interdisciplinary Journal 4, no. 2 (1986): 153–184.

only showed primary perception of the key area from the upper stave.38 This particular study also includes a general suggestion that “…listeners draw from long-term knowledge of tonal organization when listening to polytonal music.”39 We can assume that Milhaud understood at least some of these perceptual tendencies at some intuitive level, since the music in Saudades is consistently balanced in such a way that perception of key areas is vague or skewed. Register is always taken into account, with few extremes. Additionally, Milhaud is aware of listeners’ “long-term knowledge of tonal organization,” and therefore uses many formal and compositional techniques common to the tonal tradition in the writing of his polytonal piece (examples below). In any case, it is useful and interesting to keep the above findings in mind when listening to the kind of music on which these and other studies are based. As we begin to look directly at Saudades do Brasil, the terms “polytonality” and “bitonality” will be freely used in discussing the composition and interpretation of the music at hand. The reason for this is that “whatever one’s theoretical stance, Milhaud did compose by superimposing melodic strata of conflicting tonalities so that his polytonality is a result of contrapuntal encounter.”40 Even if a listener disagrees that polytonality is theoretically admissible, it was nonetheless the mindset of Milhaud when he wrote Saudades, and for this same reason an identification of which key areas are being presented simultaneously at any given time will be one of the most useful tools in an analysis of the piece.

38 William Forde Thompson and Shulamit Mor, “A Perceptual Investigation of Polytonality,” Psychological Research 54, no. 2 (1992): 60–71. 39 Ibid., 70. 40 Mawer, 19.

Overview Analysis of Saudades do Brasil As was previously mentioned, Milhaud strives, in Saudades, to keep the listener in a relatively narrow sphere of tonal perception, which lies at some specific point on the spectrum between tonality and atonality [fig. 1]. Tonality (i.e. J.S. Bach)

Milhaud’s Tonality In Saudades

Atonality (i.e. later Schoenberg)

Fig. 1

There are, of course, moments in the piece during which the music floats outside of this sphere, usually towards complete tonality (as in the conclusions of most of the movements), but in general the listener remains within its confines. Milhaud maintains this sphere in several ways:

1) Perhaps most obviously, Milhaud places each hand of the piano part in a different key area. While the left hand almost always expresses one clear tonality, using a perpetual I!V43 progression played in a tango rhythm, the right hand plays a melodic line that clearly promotes a (usually, though not always) different tonality. The characteristics that make Milhaud’s right hand melodies so suggestive of their respective tonalities (something that becomes especially important when bi-tonality is in play) include frequent arpeggiations, occurrences of scale segments, and the utilization of the independent tonic as a starting/ending point, or point of emphasis (for an example, see: Case Study — IV. Copacabana, appendix 1), the last of which is particularly indicative of a single, specific key

14 and helps clear up any pre-existing confusion resulting from the possibility of the presence of said key’s relative mode (i.e. the right hand in “IV. Copacabana” is, thanks to these characteristics, clearly identifiable as being in the key of B major, rather than in the relative mode of G# minor).

Below is a table that summarizes (for each movement where it is possible to do so — some movements are not in any recognizable key) the key areas each hand inhabits (Table 1):

Table 1: MOVEMENT/

HAND

A SECTION

B SECTION

D maj

G min (w/ added

INTERVALS BETWEEN KEYS I. Sorocaba

dissonance) M3, P1

Bb maj

G min

II. Botafogo

F# min

C maj

m2, M3

F min

Ab maj

III. Leme

E maj (w/ added

B maj (pentatonic)

dissonance) P1, P1

E maj (w/ added

“Dominant Hold”

dissonance)

(on B maj) w/ added

15 Â dissonance in chromatic passing tones

IV. Copacabana

B maj

White keys/Eb maj/Gmaj

M3, P1/m3/M3

G maj

White keys/C maj/ Eb maj

V. Ipanema

F maj

D maj

M2, A4 (tritone)

Eb min

Ab maj

VI. Gavea

White keys

C# maj

P1, M3

White keys

A maj

VII. Corcovado

D maj

Ab maj/C maj

P5, P1/M3

G maj

Ab maj

VIII. Tijuca

A min (w/ added

C maj (w/ added

dissonance)

A min (w/ added

C maj (w/ added

dissonance)

P1, P1

X. Paineras

C maj

Bb maj

M3, m3

Ab maj

G maj

XII. Paysandu

Ab maj (w/ added

C# maj

chromaticism) d3, A4 (tritone)

F# maj

G maj

We can see from this table that Milhaud is especially fond of writing in two keys that are a major 3rd apart (7 instances). Following are score examples of moments where the right hand is very clearly in a different key than the left hand:

(II. “Botafogo” — Right hand in F# minor, left hand in F minor)

17 (X. “Paineras” — Right hand in C major, left hand in Ab major)

During these extended moments of bi-tonality, Milhaud is careful to maintain a balance between the two key areas that avoids the over-powering of one by the other. Registral difference (as addressed in the above perceptual studies) between the music in the different keys is rarely large (the entire texture typically spans only 3–4 octaves, as in the examples above), and the bass voice’s perpetual tango-rhythm ostinati are counterbalanced by the right hand’s clear and prominent melodies. Typically, the only time in each bi-tonal movement that one key area will “win out” over the other is in the final measure (or measures), when the left-hand tonality will emerge as the dominant one:

[Conclusion of VII. “Corcovado”]

As we can see in the example above, although the right hand had inhabited the key of D major for the majority of the piece, it reconciles in the end with the left-hand key of G major.

2) Milhaud also maintains his unique sphere of tonal perception by keeping an awareness of the above-mentioned concept of a “normative unit.” He understands that a listener’s perception of any given musical material will vary upon the second hearing of that same material — specifically: even if the material in question is extremely dense or hard to follow or, as in Milhaud’s case, comprised of competing tonal regions, the listener will have become used to the material after having heard it once, and (at least subconsciously) have some idea or memory of what “should” come next. “…Polytonal counterpoint tends to create its own polytonal norm of consonance.”41 Milhaud employs an ABA form for each movement of Saudades, meaning that the material that was presented at the opening of each movement is presented again at the end of the same movement. Although the “A” section may be tonally and perceptually interesting/confusing because of its bi-tonality, it will feel less confusing and more acceptable to the listener upon its return. Subsequently, Milhaud is careful to always change the material the second time around, to keep the listener engaged and to better maintain a sense of tonal ambiguity, just as that listener might be getting used to the new bi/poly-tonal space. Observe, for example, the opening measures of Mvt. III. “Leme”:

41 Jeremy Drake, The Operas of Darius Milhaud (New York: Garland Pub., 1989) 210.

Both hands, in this case, agree upon the key of E major, but Milhaud adds chromatic dissonance in both parts to keep the tonality a step away from being entirely tonal (in perception, if not function). As dissonant as this material is, Milhaud understands that the listener will have become accustomed to it by the time it comes back, and so he adds even more dissonance to the texture during its return (noticeable in the “C!B!A#!B” counterpoint in the left hand):

This concept of altering previously heard ideas to make them lean further towards chromaticism is also viewable on a macro scale: as we can see from table 1, most of the movements are bi-tonal and simply rely on the pairing of two separate keys to create a tonally interesting space. By the end of the piece, however, Milhaud realizes that the

listener has become used to hearing bi-tonality after so many movements, and subsequently adds more chromaticism and dissonance to an already bi-tonal texture in the final movement.

3) A third way in which Milhaud maintains his specific tonal sphere is by placing dissonance and chromaticism in those sections of the piece wherein polytonality is not being used. Theorist Jeremy Drake noticed this technique in Milhaud’s operas, explaining: “What seems to be polymodality in these operas is usually either an example of polyvalency (1) or of “black” against “white” combinations (2)…”42 An example of this can be seen in Mvt. VIII. “Tijuca” — though it is not bi-tonal (the left and right hands generally agree upon A minor), Milhaud makes a point to include C-naturals and C-sharps, as well as G-naturals and G-sharps, to create a sense of uneasiness in regards to the listener’s conscious or sub-conscious decision as to whether the sounding key area is major, minor, or either of the two:

42 Drake, The Operas of Darius Milhaud, 228.

4) Even though this is largely music that is leaning away from traditional tonality, Milhaud still employs many functional and formal techniques from the tonal tradition in the composition of these dances. It has already been mentioned that each dance uses a rounded binary (ABA) form. It has also been mentioned that a I ! V motion is constantly referenced, especially in the left hand’s tango ostinati (which tends to follow, more specifically, a I ! V43 motion). The movement to a V area can also occur on a larger scale, as is often the case in tonal music — indeed, Mvt. III. “Leme” contains a B section that consists entirely of a prolonged V, a sort of “dominant hold” that eventually returns to the tonic with the return of the A section.

22 We, as listeners in 2015, have a leg up on those listeners who would have been

hearing this music and struggling with it in the 1920s. We have been exposed to both music that is solidly grounded in tonality, and music that is as far removed from tonality as possible. For this reason, our expectations can be different and we can perhaps have less of an inherent, historical bias that might pull our ear towards a specific tonal region when it is implied or — as in Milhaud’s case — when it exists as part of a whole, as one ingredient in a unique and multi-faceted tonal language or idiom. We can more easily pull ourselves away from the side of tonality, away from the spectrum altogether, allowing ourselves to “float” in the tonal sphere Milhaud has created, enjoying being in that space without the frustration that comes from wanting to go somewhere else.

23 Appendix 1

CASE STUDY — IV. “COPACABANA” Below is a closer investigation of a single yet characteristic movement from Saudades. The music is broken down into individual moments, each explained in detail. Special attention is paid to the compositional techniques mentioned above (i.e. the ways in which Milhaud maintains his characteristic sphere of tonal ambiguity).

(mm. 1–20)

As is typical in Saudades, this movement follows an ABA form. Also typical is the variation in dynamics — each A section is gentle and quiet, while the B section is raucous and loud. This particular movement is clearly bi-tonal, and we can safely identify what two key areas are being employed to create this new, unique tonality by as early as the fifth measure. The left hand arpeggiates a G major triad in the first measure, and moves to a V43 (D7) chord in the second measure (though the F# in the right hand acts primarily as scale-degree 5 in its own independent tonality, it is strategically placed on the downbeat

of m. 2 to lend credence to the hearing of the left hand note collection as a V43 chord in the key of G major). The continual repetition of this two-bar pattern allows us to safely consider the left hand’s music to be firmly in the key of G major. The right hand also follows a continual I ! V two-bar pattern, but is more importantly outlining a melody, though in the key of B major instead of G major. We can be sure that the notes being used in this melody are in the key of B major (rather than the relative mode of G# minor, or in any other similar mode) not only because it does so closely follow the V ! I pattern in that key, but also because it consistently sounds scale degrees 5 ! 1. Additionally, the greatest durations are given to those notes that are members of the B major pentatonic. Finally, there are some obviously scalar passages (i.e. system 2, 6th measure), and the entire melodic line begins (m. 1) and ends (m. 21, see below) on B-natural. It is worthwhile to point out before continuing that, although each hand of this piano part is in a different key, there are many interesting moments (similar to the above description of the F#’s role in m. 2) in “Copacabana” during which an agreement on one single tonic (G major) feels possible, even likely. The possibility of this agreement only comes to fruition, however, at the conclusion of the movement. The first 3 beats, for example, are entirely comprised of notes that belong to the G major scale. It is not until we hear the clash between C-natural and C# in the second beat of m. 2 that we become aware of the existence of more than one tonality at play. Similarly, m. 8 can be initially thought of as a typical descending melodic line (in G major, scale-degrees 7–6–5) being played over the expected V ! I progression. Our memory of the right hand being in B major, however, should lead us to anticipate the D# on the downbeat of m. 9 rather than a

potentially initially expected D-natural, and to consider that melodic line as actually being comprised of scale degrees 5–4–3. It is also worth mentioning that Milhaud so immediately achieves a successful balance of tonalities due to the texture he creates. As described above, there is careful weighing by the composer of the impact of each tonic pole on the overall sound, and for this reason the right hand’s melodic line is clear and explicit — using all of the techniques previously listed — giving it the power to elicit as much of an aural pull towards its B major tonality as the left hand’s perpetual I ! V tango has towards G major. Neither hand is much more active or texturally dense than the other, and the dynamic levels are the same. All these considerations allow for the natural development of a new tonal space, one that is a combination of G and B but that does not favor either.

(mm. 21–38)

Beginning in m. 21, one hand’s (the right’s) texture does change density and begin to dominate the music. Though the left hand is still following its I ! V pattern, it has been texturally reduced to half-notes, giving it less impact (interestingly, although the tango rhythm is gone from the left hand, the syncopation in the right hand provides the sense that it is still lurking somewhere in the music). For this reason, Milhaud combines the two tonalities in the right hand, the upper-register notes belonging to G major and the lowerregister notes belonging still belonging to B major. The listener’s initial perception of this moment may be that there is finally one tonic being agreed upon, since the top and bottom voices both adhere to the key of G major. The members of B major that are almost hidden in the middle, however, maintain the unsettling tonal ambiguity Milhaud has already created. Though the overt melodic line that was present in the first 20 measures is no longer present, there is still a sense of melody here, particularly in the very top voice of the texture (the reader will recall that, according to one of the perceptual studies discussed above, the top voice is the one that has the greatest impact on the listener’s perception of tonality), which is now in G major instead of B major. The result is that — fascinatingly — although the tonalities Milhaud is using have not changed, the downbeat of m. 21 has the feeling of, if not a key change, something very closely related (the other new element that helps facilitate this feeling of slight change and newness is the subtle movement, for the first time, away from the I and V43 chords — VI7 chord in m. 30, ii chord in m. 31, etc.).

(mm. 39–51)

At the section marked “animez un peu” (the beginning of the B section), there is an abrupt shift not only to a ff dynamic, but also to a surprising unison C major tonality. This is momentary unity proclaimed through two measures (mm. 44 and 45) of “hunting calls.” What follows are pairs of 16th-note tetrachords (which form 8-note sonorities) moving in parallel stepwise motion and comprised of only white keys. The first of these sonorities (pc set 4-20 in the right hand, 4-27 in the left — interestingly, the second sonority places 4-27 in the right hand, and 4-20 in the left…) contains all the notes of the C-major scale. These tetrachords spread out from each other, reaching an apex on beat two of m. 47, and collapse in on each other by the end of m. 48, where they meet on a C9 chord. Measure 50 sees a return to the “horn call” rhythm, now extended to last for 8 measures before returning to the quick 16th-note tetrachords in parallel motion. In the same measure, the left hand remains in C major, while the right hand modulates to Eb

major. Immediately afterwards in m. 51 everything is shifted up by a third, as the left hand is given to the key of Eb major while the right hand gets G major. (mm. 52–65)

Measures 54–58 are a transposition of mm. 44–48, this time based on G major rather than C major. The rallentando in m. 59 marks a transition back to the “Mouvt du début,” or the A section, and the melody we heard at the beginning of the movement returns. The reader will notice, however, that there is now more chromaticism than there was before — the result of a thickening (and, interestingly, a quieting down — to ppp) of the original texture. Though the left hand still employs a (more dense/active) version of the I ! V tango rhythm in G major, it is supplemented by more voices, which make complete triads. The right hand also includes additional notes from the key of B major — these extra notes in the right hand combined with the more obvious G major and D major triads in the left hand make for a musical surface that is more clashing (more opportunities for dissonance), hectic, and confusing than before, one that could potentially be difficult to interpret were it not for our previous hearing of the basic material at the beginning. This

trend continues into the second part of the repeating “A” section, wherein the right hand is given bigger chords to play than before. (mm. 66– end)

This alteration of that material to be more perceptually challenging is an example of Milhaud’s awareness of the fact that the listener will become used to music he/she has heard, even if it is initially polytonal. In other words, the “norm” has been developed, and now it must be altered in order to keep the listener unsure of and engaged in the tonal space being created. As is the norm for the movements of Saudades, the conclusion includes a tonal agreement favoring the left hand tonality (in this case, G major).

30 Appendix 2

Deborah Mawer and Keith W. Daniel show that Forte’s set-theory can be a useful supplementary tool in an analysis of some of Milhaud’s more chromatically dense music. In the case of Saudades, the most appropriate application is to Mvt. V. “Ipanema.” Though a few interesting facts can be gleaned from this set-theory based approach, the most illuminating investigation into this and the other movements comes from identifying the tonal regions being employed, and the relationships between them.

— Mawer, pp. 321–327.

32 BIBLIOGRAPHY

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*All score excerpts used are public domain and taken from imslp.org