"Brasilia": Octatonicism, Self-Similarity, and Blues

In a previous post I looked at twelve-tone elements in the composition “Brasilia.” Another remarkable feature of that piece is the octatonic collection OCT1,2 embedded within the full chromatic set that makes up its first phrase. After the initial E-flat minor triad, all eight members of OCT1,2 are stated in (almost uninterrupted) succession, and the prepenultimate B-flat links OCT1,2 with the returning statement of E-flat minor.

Of the four pitch-classes excluded from OCT1,2, E-flat and G-flat comprise the tonality-defining beginning and ending gestures of the first phrase. The middle portion of the phrase can be considered OCT1,2 if non-members C and A are heard as subordinate embellishments to melodically predominant members of OCT1,2. From one possible voice-leading perspective, C is a neighbor-passing tone to B, and A is a neighbor tone to B-flat.

The use of the octatonic collection here is significant insofar as it can be conceived as a substitute for B-flat7, the dominant of the governing E-flat minor tonality of the piece. Jazz musicians sometimes use an octatonic scale over a dominant seventh chord when improvising, and theorists like Schoenberg, Berger, and others have shown the derivation of the octatonic collection from the double-semitonal transformation of a cycle of seventh chords whose roots are separated by the interval of a minor third. “Brasilia” manifests this melodically, stating the octatonic collection with pitches from B-flat7 (F, D), G7 (F, D, G, B), and E7 (B, G-sharp, E) as well as C-sharp minor sixth or B-flat half-diminished seventh (G-sharp, E, C-sharp, B-flat).

This means that the first phrase of the composition can be heard with reference to tonality: a statement of tonic E-flat minor, a move to an expanded dominant B-flat, and a return to tonic E-flat minor. Simply, i-V7-i, a bedrock progression of tonality.

As I point out in the previous post, the B-phrase of this piece seems to prolong the dominant harmony of a tonic E-flat minor. Thus, like much tonal music, “Brasilia” is hierarchically self-similar: the tonic-dominant-tonic structure of the A-phrase is reflected on a higher level by the tonic-dominant-tonic (ABA) form of the whole piece.

For one final thought, notice how the register of melody notes in the A-phrase can be rearranged to depict the entire phrase as a long and almost unbroken string of falling thirds. This brings to mind the "ladder of thirds" which Peter van der Merwe argues is the underlying form of what he calls the "blues mode." It is crucial to recognize that the application of twelve-tone technique in "Brasilia" does not thereby jettison the norms of tonal music and the blues.

The Golden Ratio in Improvised Music

Analysts such as Ernő Lendvai and Roy Howat have claimed to discover signs of the golden ratio in compositions by Bartók and Debussy, respectively. It has also been discussed with regard to Mozart's piano sonatas, and elsewhere. But is the golden section strictly an architectural principle, or could it be a natural, emergent property of music? If the latter is true, one might expect to find it in purely improvised music. 

This improvisation by trombonist Ben Gerstein is approximately 115 seconds long. The ostensible climax occurs on G3, the note with the highest pitch, greatest intensity, and longest duration of the entire piece, at roughly 71 seconds in. The ratio of the duration of the whole improvisation to the duration preceding the climax, then, is 115/71, or 1.6197... This is very close to the golden ratio value of 1.6180... The ratio of the duration of the piece preceding the climax to the duration following the climax is 71/44, or 1.6136... Since the ratios of the larger and smaller durations are not exactly equal, they do not precisely represent the golden proportion. Nonetheless, the climax of Gerstein's improvisation is a remarkably close approximation of the sectio aurea. 

Is this example a solitary coincidence, or is it often the case that a proper sense of balance in a piece of music will spontaneously approximate the golden ratio? 

A more extensive analysis of Gerstein's improvised music can be found here.

Music and Brains

Evidence from recent brain studies suggests that the pleasure in listening to music is derived at least partly from "pattern recognition and prediction," which would seem to lend support to Leonard Meyer's theory of musical expectation. 

Does this have critical implications for non-developmental or non-teleological music? For music that is effectively static, or without recognizable patterns? Or for ad hoc music of the type which bears no relation to an established tradition or corpus, for which it is impossible for the listener to make any kind of prediction? 

In The Aesthetics of Music, philosopher Roger Scruton points out one of the problems with thinking about music in terms of pattern recognition and prediction, expectation and frustration: "The pattern of expectations and fulfilments would change from hearing to hearing, to the point where, knowing the piece by heart, we should assign probability 1 to every event in it, and therefore cease to distinguish it from other pieces in the repertoire." (332) 

"As an unfamiliar piece unfolds in time, our brains predict how it will continue to unfold," says Valorie Salimpoor, the neuroscientist who authored the study linked to above. Ostensibly it is the satisfaction of these predictions that gives us pleasure. Unfortunately, this tells us nothing about our understanding and enjoyment of a piece of music that we already know note for note, of which for musical Kenner as well as Liebhaber there are many. 

Furthermore, the conclusions of this study suffers from a certain circularity. The study tells us that listening to music releases dopamine in the brain. The brain releases dopamine when we like something. So this study confirms that we like listening to music. This might strike some as less than earth-shattering news. 

While Pinker's notion of music as "auditory cheesecake" may well explain its biological origins, it remains to be seen whether neuroscience will succeed in explaining our experience of music and its subjective meanings. Scruton expounds on his skepticism in this regard here.

Who Wrote "Brasilia?"

"In conversations with Eric, Schoenberg is a name that will come up frequently." 

Robert Levin, quoted in Eric Dolphy: A Musical Biography and Discography by Vladimir Simosko and Barry Tepperman, p. 12.

 In the course of writing an analytical paper on the tune "Brasilia," I have begun to speculate on the possibility of an alternative provenance than that which is usually assumed. 

"Brasilia" (sometimes spelled "Brazilia") was first recorded live at the Village Vanguard by the John Coltrane Quartet featuring Eric Dolphy on November 1, 1961. It was initially released as "Untitled Original" (Impulse! AS 9325). Coltrane later recorded a quartet version of "Brasilia" (Imp A-85) at Rudy Van Gelder's studio on May 17, 1965. On all releases, John Coltrane is listed as the composer. The two performances can be heard below. 

Though perhaps not immediately apparent upon listening due to its strong tonal allusions, analysis of "Brasilia" reveals that the composition incorporates dodecaphonic elements. Below is a transcription with pitch-classes numbered 0 through e. (Pitch-class will hereafter be abbreviated "pc".) Parentheses indicate consecutively repeated pc's, and brackets indicate pc's repeated after the row has been exhausted.

The first phrase, labelled "A," consists of a complete statement of the twelve-tone row, (t 6 3 5 2 7 0 e 8 4 9 1). The concluding three notes of the phrase repeat the first three notes of the row and serve to establish an Eb-minor centricity. The row is quasi-derived from the subset set-class (0 3 7): note the prevalence of minor and major triads and their constituent interval-classes. 

The second phrase, labelled "B," does not exhibit full chromatic saturation. Eleven pc's are heard before any are repeated: (1 8 e t 7 9 0 5 4 3 6). Unlike the A-phrase, repeated pitches at the end of the phrase do not instantiate a repetition or another form of the row, but like the A-phrase they serve to establish triad-centricity---in this case, Db minor. 

Notably, the fourth and final subphrase of the B-phrase, (1 3 4 6), is a T7 transposition or an I2 inversion of the first subphrase, (8 t e 1). (The I2 operation is inversion about Db, which happens to be the first and last pitch of the B-phrase and the root of the minor triad on which the end of the phrase "cadences.") The third subphrase, (1 3 4 6 8), is an I1 inversion of the second subphrase, (5 7 9 t 0). The complete B-phrase, then, consists of a palindromic statement of two set-classes: (0 2 3 5) (0 2 4 5 7) (0 2 4 5 7) (0 2 3 5). This is illustrated below:

The nonstandard row at "B" is not a transformation of the row at "A." Notice, however, the ways in which the second phrase organically mirrors the first. Both feature a pair of shorter antecedent-consequent phrases. The first subphrase at "A" contains a leap up, a minor third down, and a step up---the first subphrase at "B" is roughly inverted, with a leap down, a minor third up, and a step down. Similar parallels obtain between the remainders of the two phrases as well.  The last subphrase at "A" exhibits a falling minor third, for instance, while the last subphrase at "B" embellishes the upward leap of a sixth; and so on.

Interestingly, the 11-member set (by definition) and the B-phrase overall are not dodecaphonic: pc (2), or (D), is missing. Here one can perhaps venture an apophatic interpretation: what is the significance of this absence? (D) is the leading tone in Eb minor, the key established melodically by the A-phrase and used as the basis for improvisations. The key areas manifested in the B-phrase strongly suggest the dominant of Eb. We hear Bb minor, F major, and Db minor, or Eb: v - V/v - vii. These key areas compose out the minor dominant triad in Eb (sc [0 3 7], again!). Db minor, or vii, receives special emphasis as the final harmony of the phrase. The triad on the seventh scale step is in many cases accepted as a kind of substitute for the dominant; note also that much folk music features a i - VII - i oscillation in place of the dominant-tonic polarity. Here the subtonic triad has a minor quality, however. Diminishing the expected major third changes F to Fb. I argue that, in addition to having expressive purposes, this harmonic alteration mimics the behavior of the first two long notes of the melody at "A": notated above as F and E, the latter an enharmonic spelling of what is actually a Phrygian II, or Fb in the key of Eb. At any rate, the leading tone, (D), would conflict with this minor dominant-minor subtonic harmony and is therefore left out; yet in the conspicuousness of its absence it nonetheless points the way back to the tonic Eb. 

It is clear that "Brasilia" applies twelve-tone techniques within the context of a quasi-tonal (because hierarchical and triadic) jazz composition. (Obviously the aesthetic goals of its composer are not those of Schoenberg.) In this respect, "Brasilia" is very similar to "The Red Planet," another rare piece in the jazz repertory that takes advantage of the dodecaphonic method. Coincidentally, both pieces were debuted at the same Village Vanguard performance in 1961 of the John Coltrane Quartet featuring Eric Dolphy (and both were later recorded by the Quartet without Dolphy). As the quotation that began this post indicates, Eric Dolphy's affinity for the music of Schoenberg and the Second Viennese School is often commented upon. His improvisations reflect the influence of the angular, atonal sonorities of that style. Indeed, we now know that it was Dolphy, not Coltrane, who composed "The Red Planet." 

Coltrane's style, on the other hand, does not readily suggest the influence of twelve-tone atonality. His improvisations, even in his most "experimental" later period, reveal smooth voice-leading, diatonic fragments, cyclic symmetries, dominant-tonic gravitation, and functional hierarchies. Coltrane's later compositions, too, belie any presumption of influence by Schoenberg or his followers. To the contrary, they are generally cellular or scalar in their construction. Even Joe Goldberg's tantalizing and unreferenced suggestion that Coltrane "expressed a desire to write in the twelve-tone system" is weakened by the rest of his discussion of Coltrane's influences at the time, which mostly involves Indian music, ragas, and modality. 


Considering all of the above, then, I would like to argue for the possibility that "Brasilia" was either co-written with Eric Dolphy, or that it is the work of Dolphy alone. As with "The Red Planet," Coltrane has perhaps been credited as its composer simply because he was the leader of the session in which it was first performed. 

I welcome any documentary or other evidence that either supports or contradicts this hypothesis. 


Update: 

I have included some additional thoughts on octatonicism, self-similarity, and the blues in "Brasilia" here. 

JMac's Vibrato

Speaking of the operatic impulse in jazz, listen to Jackie McLean's dramatic use of vibrato in this recording from 1973. Perhaps more than any other alto saxophonist, McLean was able to “widen” or “enlarge” the “size” of the instrument’s natural tone (these terms are all metaphorical, of course). The use of heavy vibrato is but one instance of this ability.

"Monk's Dance," Ode to Super (with Gary Bartz)

While McLean's approach to playing is undoubtedly singular, a general increase in the use of vibrato and other, more extreme timbral effects accompanied the reemergence of Dionysian energies in jazz after the end of a classicizing, Apollonian interim in the 1940s and 50s. 

Konitz's "Silent Improvisation"

Having played with the Claude Thornhill Orchestra in 1947-8, Lee Konitz can thus be added to the list of those---including Alphonse Allais, Erwin Schulhoff, and Yves Klein---who beat John Cage to the punch:

Wittgenstein's Music of the Future

"I shouldn't be surprised if the music of the future were in unison. Or is that only because I cannot clearly imagine several voices? Anyway I can't imagine that the old large forms (string quartet, symphony, oratorio etc.) will be able to play any role at all. If something comes it will have to be---I think---simple, transparent.  

In a certain sense, naked. 

Or will that hold only for a certain race, only for one kind of music(?)" 

Wittgenstein, 1930

John Coltrane, Interstellar Space (1967):