Dave Brubeck and Polytonal Jazz

Abstract

Dave Brubeck has incorporated polytonality into his jazz compositions throughout his long career. Like his composition teacher Darius Milhaud, Brubeck defines polytonality as the combination of distinct triads, and this technique forms the definition of the term as used in this article. This approach avoids the insoluble problems of chord spelling and perception inherent in polytonality; it also allows for a grey area between simple polychords and the projection of multiple tonal centers (and Brubeck exploits both procedures in his compositions).

This article introduces a method to compare the relative dissonance between polychords in order to reveal the logic behind Brubeck’s incorporation of polytonality into the standard jazz vocabulary. Brubeck’s use of polytonality helps to project a general decrease or increase in relative dissonance, thereby clarifying the formal structure on both the small‐ and large‐scale. The comparison with tonal theory extends to include pivot chords; with Brubeck, such chords simultaneously serve as the final chord in a polychordal passage and as the first and most exotic chord in a tonal passage.

The final goal of this article is to trace Brubeck’s influences. Milhaud is the most obvious of these, but certain Stravinskian features are also found in Brubeck’s music, including rhythmic practices first identified by the theorist Pieter van den Toorn.

Notes

¹ Richard Wang, “Dave Brubeck,” vol. 4, The New Grove Dictionary of Music and Musicians, 2nd ed., ed. Stanley Sadie (London: Macmillan, 2001), 452.

² George T. Simon, liner notes to Dave Brubeck: Greatest Hits, Columbia 32046, 1967, LP. Brubeck discussed this subject on the radio show Piano Jazz. In this broadcast, the show’s host, Marian McPartland, mentioned that she “was interested to hear you [Brubeck] say that you approach jazz from the classics. You know a lot of people who don’t believe that, do they? They think, ‘jazz and classics: never the twain shall meet.’” Brubeck responded “never shall they part,” to which McPartland agreed. Marian McPartland’s Piano Jazz with Guest Dave Brubeck, Jazz Alliance 12001, 1993, compact disc.

³ This is a topic that has received little attention despite the fact that Brubeck has mentioned his use of polytonality repeatedly in interviews, including those for television. See, for example, Brubeck’s October 17, 1961, appearance and interview on Ralph Gleason’s Jazz Casual, Wea Corporation DVD B00006RJCR, 2003.

⁴ François de Médicis points out that questions over the definition of this term date back to the origins of this technique. See François de Médicis, “Darius Milhaud and the Debate on Polytonality in the French Press of the 1920s,” Music & Letters 86 (2005): 576.

⁵ See Allen Forte, Contemporary Tone Structures (New York: Teachers College, Columbia University, 1955), 137.

⁶ See Benjamin Boretz, Meta‐Variations: Studies in the Foundations of Musical Thought (New York: Open Space, 1995), 243, and Pieter van den Toorn, The Music of Igor Stravinsky (New Haven: Yale University Press, 1983), 63.

⁷ Stravinsky spoke of the second act of Petrushka as being written “in two keys.” See Igor Stravinsky and Robert Craft, Expositions and Developments (New York: Doubleday, 1962), 162. Ravel provided an analysis of a passage from his Valses nobles et sentimentales, demonstrating that polytonality can be formed by unresolved appoggiaturas. See René Lenormand, A Study of Twentieth‐Century Harmony (London: Joseph Williams, 1915), 62–63. See also Darius Milhaud, “Polytonalité et atonalité,” La Revue Musicale 4 (1923): 29–44; Alfredo Casella, “Tone‐Problems of To‐day,” Musical Quarterly 10 (1924): 159–71; and Charles Koechlin, “Évolution de l’harmonie: Période contemporaine depuis Bizet et César Franck jusqu’à nos jours,” vol. 2, Encyclopédie de la Musique et Dictionnaire du Conservatoire, edited by Lavignac and La Laurencie (Paris: Delagrave, 1925), 591–760, and Traité de l’harmonie (Paris: Eschig, 1927–30).

⁸ All writers on polytonality make a distinction between harmonic and melodic polytonality. The former is the more common version involving polychords, while the latter is composed of a polyphonic texture, with each line written in a distinct tonality.

⁹ Milhaud, “Polytonalité et atonalité,” 30–31.

¹⁰ Koechlin, Traité de l’harmonie, 252.

¹¹ For a discussion of how these two terms were used synonymously in the 1920s, see de Médicis, “Darius Milhaud,” 574.

¹² For other recent attempts to define polytonality, see Daniel Harrison, “Bitonality, Pentatonicism, and Diatonicism in a Work by Milhaud,” in Music Theory in Concept and Practice, eds. James M. Baker, David W. Beach, and Jonathan W. Bernard (Rochester, NY: University of Rochester Press, 1997), 393–408; Deborah Mawer, “In Pursuit of an Analytical Approach,” in Darius Milhaud: Modality & Structure in Music of the 1920s (Aldershot, UK: Ashgate, 1997), 18–56; Peter Kaminsky, “Ravel’s Late Music and the Problem of ‘Polytonality’,” Music Theory Spectrum 26 (2004): 237–264; and Barbara Kelly, “Polytonality, Counterpoint and Instrumentation,” in Tradition and Style in the Works of Darius Milhaud, 1912–1939 (Aldershot, UK: Ashgate, 2003), 142–168.

¹³ Harrison, “Bitonality, Pentatonicism, and Diatonicism,” 394.

¹⁴ Darius Milhaud, My Happy Life: An Autobiography (London: Marion Boyars Publishers, 1995), 201.

¹⁵ Brubeck’s octet included several other performers and composers who would later establish their own significant reputations, including Paul Desmond, Cal Tjader, David van Kriedt (tenor saxophonist and composer of “Fugue on Bop Themes”), and Bill Smith (clarinetist and member of Brubeck’s current quartet).

¹⁶ Milhaud, My Happy Life, 146.

¹⁷ This was related to the author in a March 2003 conversation with Dr. Katherine Warne, a former student of Milhaud (she is also currently president of the Milhaud Society). Milhaud, “Polytonalité et atonalité,” cited above.

¹⁸ This meeting was undoubtedly arranged by Brubeck’s older brother, Howard, who was one of Milhaud’s first teaching assistants. Howard eventually substituted for Milhaud at Mills College during the latter’s semiannual leaves to teach at the Paris Conservatoire.

¹⁹ Even more tellingly, Desmond recalls that by 1949 he sometimes had to ask Brubeck to simplify his playing since Brubeck would often accompany Desmond’s solos in three keys at once. See Marian McPartland, “Perils of Paul,” in All in Good Time (New York: Oxford University Press, 1987), 59.

²⁰ Marian McPartland’s Piano Jazz with Guest Dave Brubeck. Transcription of the example by the present author.

²¹ There is a similarity between minor‐third related triads/keys and Hindemith’s concept of indefinite third relation. The similarities between Hindemith’s theory and polytonality are discussed in greater depth below.

²² Specifically, the three notes from G major that are not found in Bb major (F#, B‐natural, and E‐natural) introduce upper chromatic clashes with the dominant, tonic, and subdominant scale degrees, respectively.

²³ Kaminsky, “Ravel’s Late Music,” 238–248.

²⁴ “I readily admit, however, that in many of the harmonically polytonal examples cited above, it is quite difficult to determine which is the primary tonality in them!” Italics in original. Koechlin, “Évolution de l’harmonie,” 723. Koechlin’s belief that one key in a polytonal combination was generally more strongly projected (mentioned above) is implied in his comment on the exceptional nature of the excerpts he references here.

²⁵ Stravinsky’s ballet Petrushka (1911–1912) features a polychord that is associated with the main character. The polychord is composed of both C and F# major triads. These six notes belong to a single octatonic (diminished) scale, which serves as the recurrent, associative harmony for Petrushka. For more information on the rich history of Russian harmonic characterization, see Richard Taruskin, “Chernomor to Kashchei: Harmonic Sorcery or Stravinsky’s ‘Angle’,” Journal of the American Musicological Society 38 (1985): 72–142. For more information on Stravinsky’s varied use of octatonic harmony throughout his long career, see Pieter van den Toorn, The Music of Igor Stravinsky (New Haven, CT: Yale University Press, 1983).

²⁶ Arthur Berger, “Problems of Pitch Organization in Stravinsky,” Perspectives of New Music 2 (1963): 11–43.

²⁷ This example is a piano reduction made by the present author from the performance found on Dave Brubeck, Dave Brubeck Octet, Fantasy OJCCD – 1012, 1999, compact disc.

²⁸ This was related to the author by Brubeck in a personal conversation from July 2003. In this same conversation, Brubeck referred to his Stravinskian influence as a “bag” from which he could pull things from when composing and performing. In context, the “things” to which Brubeck referred were the Stravinskian techniques he had learned over his long years of study of this repertoire. Stravinsky’s influence on Brubeck will be more fully documented in the discussion below relating to the latter composer’s late works.

²⁹ A later work to reveal the same influence in both style and name is History of a Boy Scout, modeled on Stravinsky’s L’histoire du soldat.

³⁰ Milhaud, My Happy Life, 65.

³² This example is adapted from Figure 2.1 in Mawer, Darius Milhaud, 20.

³³ For more information on pitch‐class set theory, see: Allen Forte, The Structure of Atonal Music (New Haven: Yale University Press, 1973); John Rahn, Basic Atonal Theory (New York: Schirmer Books, 1980); and Joseph N. Straus, Introduction to Post‐Tonal Theory, 2nd ed. (Upper Saddle River, NJ: Prentice Hall, 2000).

³⁴ Among the many articles critical of pitch‐class set theory, the most important include: William Benjamin, “Ideas of Order in Motivic Music,” Music Theory Spectrum 1 (1979), 23–34; George Perle, “Pitch‐Class Set Analysis: An Evaluation,” The Journal of Musicology 8 (1990), 151–172; Richard Taruskin, “Revising Revision,” dual review of Kevin Korsyn, “Towards a New Poetics of Musical Influence,” and Joseph N. Straus, Remaking the Past: Musical Modernism and the Influence of the Tonal Tradition, in Journal of the American Musicological Society 46 (1993), 114–138; and Ethan Haimo “Atonality, Analysis, and the Intentional Fallacy,” Music Theory Spectrum 18 (1996), 167–199.

³⁵ Paul Hindemith, The Craft of Musical Composition, vol. 1, Theoretical Part, trans. Arthur Mendel (New York: Associated Music, 1942), 115 ff.

³⁶ Harrison, “Bitonality,” 401. The theoretical terminology here again requires a bit of explanation. Harrison is referring to the transposition of pitch‐class sets, and in this case, the pitch content of a Milhaud melody. The letter T refers to the transposition that relates two melodies with the same pitch content together, and the numbers 1 and 6 refer to the number of semitones of this transposition (the semitone and tritone, respectively).

³⁷ Since tritones are self‐inverting, their weighting will appear to be twice of that of the other interval classes.

³⁸ A second possible method for calculating relative dissonance involves applying a dissonant weight to each interval class, including the consonant interval classes 3–5. Yet difficulties arise with interval class 5 since the perfect fourth could be either a consonance or a dissonance based on context. Because of this (and other difficulties in the assignment of dissonance weights to consonant intervals), only the dissonant intervals are considered in the method of calculating the dissonant quotient in this study. It is further possible to divide the dissonant quotient of a chord by the number of intervals it contains, thereby using an average of the dissonances rather than their sum. While this averaging method seems mathematically sound, it produces skewed results. For example, Milhaud’s chord type IV/VIII would have a dissonant quotient average of 4 and chord type VI an average of 2.1. Such results are possible since chord type IV/VIII has no entries for interval classes 2/10 and 6. Thus, the process of averaging the dissonance quotient incorrectly identifies the former chord type as the most dissonant from Example 4 above.

³⁹ The motion from relative dissonance to consonance, or vice versa, is similar to Fred Lerdahl’s relaxing and tensing branches. While Lerdahl has explored this analytic territory in tonal and post‐tonal music, he has avoided the analysis of polytonality. See Fred Lerdahl, Tonal Pitch Space (Oxford: Oxford University Press, 2001).

⁴⁰ The Brubeck performances used for the discussion of these works are as follows: “Strange Meadowlark,” from Dave Brubeck Quartet, Time Out, Columbia CK 40585, 1990 (orig. rec. 1959), compact disc; and “The Duke” (orig. rec. 1954), from Dave Brubeck, Dave Brubeck: Greatest Hits, Columbia 32046, 1994, compact disc; and “In Your Own Sweet Way,” from Brubeck Plays Brubeck, Columbia 065772, 1998 (orig. rec. 1956), compact disc. This article’s transcriptions from these works are by the author, with reference to the published transcriptions by Howard Brubeck that appear in The Dave Brubeck Anthology (Van Nuys, CA: Alfred Publishing, 2005).

⁴¹ For an attempt to accommodate these high tertian sonorities within a traditional Schenkerian framework, see Steve Larson, “Schenkerian Analysis of Modern Jazz: Questions about Method,” Music Theory Spectrum 20 (1998): 209–41.

⁴² This example has been shortened from the published version for reasons of space. Only minor differences between the two versions have been omitted: the final chord of m. 1 is not arpeggiated when repeated; and the first chord of m. 8 is an open fifth rather than octave when repeated.

⁴³ Indeed, jazz theory frequently conceptualizes chords as being composed of superimposed elements. For instance, Mark Levine discusses the “sus” chord as a subtonic triad superimposed over the dominant scale degree, and he defines “slash” chords as follows: “the note to the left or above the slash represents a triad and the note to the right or below the slash represents a bass note, or, as in the next example, another triad. This last example shows a B triad over a C triad, usually notated B/C.” Mark Levine, The Jazz Piano Book (Petaluma: Sher Music, 1989), 23 and 142, respectively.

⁴⁴ Before leaving this work, the hidden complexity of its first theme must be mentioned since it reveals the extent to which Brubeck was influenced by the Second Viennese composers. This eight‐bar passage begins and ends in C major, but easily moves through a number of keys in between, including D, Eb, Db, Bb, and Ab major. In fact, chords with roots on all twelve chromatic pitches appear in the course of this theme. Brubeck did not discover this for himself, but was told by a fan years after he wrote the work. It is for this reason that Brubeck jokingly said that the work should be renamed “The Duke Meets Darius Milhaud and Arnold Schoenberg in the Bass Line.”

⁴⁵ See, for example, the performance of this work on Dave Brubeck, Time Signatures: A Career Retrospective (Columbia/Legacy 66047, 2000, compact disc boxed set), that was recorded shortly after its composition.

⁴⁶ This was related by Brubeck to the author in a personal conversation from July 2003.

⁴⁷ The analysis of this work in Example 8 is from the performance on Brubeck’s Time Signatures CD anthology. The transcription of this work is by the author.

⁴⁸ Dave Brubeck, liner notes to Brubeck, Time Signatures, 24.

⁴⁹ This was related by Brubeck to the author in a personal conversation from July 2003.

⁵⁰ “Struttin’” was composed earlier than the other movements and was originally entitled “Polly,” which is an allusion to the name of a family friend as well as the polytonal language of the work.

⁵¹ This is not to imply that rhythmic complexity is lacking in any of Brubeck’s jazz influences (including the influences of Cleo Brown, Art Tatum, and Duke Ellington), but only that the rhythmic complexities found in Brubeck’s late works most closely represent those found in Stravinsky’s scores.

⁵² Van den Toorn, “Rhythmic (or Metric) Invention,” in The Music of Igor Stravinsky, 204–51.

⁵³ The first two traits mentioned above are clear in this example, while the second two are more difficult to see (although they are obvious to the ear). The rhythmic immobility is seen in the inner voice motive, in which the note A3 is consistently notated as an anacrusis. The change is concerned with rhythmic placement and is heard in the two appearances of this same note, which, when renotated, appears first as an anacrusis and then as a downbea.

⁵⁴ This was related by Brubeck to the author in a personal conversation from July 2003. In fact, Brubeck remembers stopping dead in his tracks as he was walking across campus as an undergraduate and heard the university orchestra rehearsing Stravinsky’s Symphony of Psalms (this was this first time he had heard the work). This event happened at approximately the same time as Brubeck first read Milhaud’s article on polytonality, so he was introduced to both these composers at roughly the same time in his musical development.

⁵⁵ The standard use of this scale in jazz—as a descending scalar run over a dominant seventh chord—appears prominently in “Eleven Four” from 1962, although this tune was written by Paul Desmond.

⁵⁶ See, for instance, the passages (m. 27 and mm. 39–41) labeled as octatonic in Example 9.