Philosopher Roger Scruton describes "Erbarme dich" from J. S. Bach's St. Matthew Passion:
"Here
all boundaries are weak, and the melody can be subdivided in countless ways, to
permit multiple elaborations in the course of the aria. Yet it involves melodic
thinking of the highest order. It is
neither a theme nor a tune, but an unbroken melisma, which throws out spores
around itself as it grows [italics mine]."
But couldn't he also be describing Coltrane's Interstellar Space?
The melismatic vocal line that traveled from western Africa to the American blues (which most likely shares a common ancestor with Bach's) becomes permeated harmonically with the rise of jazz and is apotheosized in this last recording by Coltrane. Here is another philosopher discussing Interstellar Space.
The brilliant video below documents Lee Konitz and Dan Tepfer on the road in Europe. Its musical focus is on Jerome Kern's "All the Things You Are" of 1939, a longtime staple in Konitz's repertory.
The timeless popularity of this tune among jazz players is often remarked upon. Common explanations for this include the step-wise descent of parallel thirds between the bass and upper voice, mediated by a progression of chords through the cycle of descending fifths. Also, the tune notably features chord roots on each of the twelve chromatic tones. The resulting harmonic saturation provides ample fodder for improvisers. I suspect that there is more to the story, however, as the kind of musical fecundity offered by "All the Things You Are" can never be so easily explained. One question that strikes me as more difficult than it would appear at first is that of the tonic: what key is this tune in? The obvious answer is A-flat, the key in which the song concludes. The opening phrase tonicizes A-flat (as well as C), and the next phrase tonicizes the dominant, E-flat (as well as G). As Milton Babbitt suggests, the bridge tonicizes G and therefore acts as an "extended leading-tone" to the tonic A-flat. The non-tonic opening is described by analysts influenced by Schenker as an "auxiliary cadence," which means, as Michael Buchler explains, that "from a Schenkerian perspective, [the] refrain opening [does not] actively participate in its overall fundamental structure." But does this interpretation underestimate the role of F minor? F minor is metrically accented, appearing as it does in bars 1 and 25, and is prepared in both cases by its dominant. Also, the first eight-measure phrase could be heard as a rather typical prolongation of F minor through its relative major (A-flat) to its dominant (C). This i-III-V prolongation is then repeated at the fifth in the second phrase. An F-minor hearing is bolstered by the hyper-metrical "strong-beat" bass descent of F-E-flat-D-flat-C, supporting melodic tones A-flat-G-F-E. If the bridge's G harmony represents an "extended leading-tone" to A-flat, could we not also say the same of the bridge's E harmony vis-a-vis F? If we posit an F-minor tonic, the G and E harmonies of the bridge could suggest upper and lower neighbor tones. Finally, the D-flat7#9-C7#9 riff used by performers like Charlie Parker as both "intro" and "outro" points strongly to F minor as a gravitational locus.
A-flat undoubtedly has a strong claim to the tune's tonic, as the last sixteen bars clearly outline vi-(I)-IV-ii-V-I in A-flat. But the first twenty-four bars seem to make more sense as prolonging an F-minor tonic, where the E major at the end of the bridge behaves as a third-related substitute for the dominant: i-V-v-V/V-VII-(V). (E major and F minor are of course also related by SLIDE transformation since they share the same third.)
Could a case be made here for the "double-tonic complex" as described by scholars like Robert Bailey and Deborah Stein? Developed as a tool for analyzing nineteenth-century lieder and other music, the double-tonic complex is characterized by, among other things, a sense of oscillation between the two equally-weighted tonics. Jazz performances of "All the Things You Are," with their repeating improvised cycles through the tune's harmonic form, certainly seem to oscillate between F minor and A-flat. This feeling of tonal ambiguity -- supported by both "auxiliary cadence" and "double-tonic complex" interpretations -- helps to illustrate the sense of the tune's lyrics. The lyrics are hopeful, longing, anticipatory, future-oriented. The tonic goal is continuously withheld, just as love is withheld in the song's lyrics. It is important to stress that jazz performances of American Songbook pieces resist categorization along the standard teleological lines of Western music theory due to their cyclic and thus perpetually unfinished nature.
It is widely understood that
counterpoint played an important role in the musical thinking of Lennie
Tristano. His improvised piano solos occasionally exhibit the contrapuntal
interaction of two independent lines (or more, as in the case of the
multi-tracked “Turkish Mambo”), and his ensembles frequently engaged in “collective
improvisation,” in which multiple players simultaneously improvise melodies
(i.e., polyphony).
Perhaps less widely discussed, however,
is the technique guiding such improvised counterpoint. How do the independent
voices relate to each other? For performances of compositions from the American
Songbook, a given chord sequence will obviously circumscribe the harmonic
content of the improvisation (unlike purely free-improvised pieces like
“Intuition” and “Digression”). But is that the full extent of the musical
coherence, or can we discover other significant relationships between the
voices in Tristano-school counterpoint?
A chorus of simultaneous improvisation
by Lee Konitz and Warne Marsh on Burton Lane’s “How About You?”, recorded live
at the Half Note in 1959, provides an example for analysis. (My transcription can be found here.)
In the second bar of the form, Marsh
introduces a motive which outlines a four-note stepwise ascent. Following by
one beat and before Marsh’s statement is completed, Konitz answers with the
retrograde version of the motive. Konitz repeats the retrograde form of the
motive in bar 4, this time transposed down a diatonic step, and he follows in
bar 5 with a varied form of the descending motive which foreshadows later
motivic developments. The original ascending form of the motive returns in
Marsh’s line in bar 6, where it is roughly played twice in succession. Finally, Konitz answers in bars 7 and 8 with an
elaborated statement of the ascending motive, outlining G-A-B-flat-C, plus the
falling third (B-flat-G) as when we first heard the motive from Marsh. Konitz’s
final sounding of the motive is put into relief by the fact that it clearly
outlines G minor, anticipating the formal harmonic arrival of this chord by a
measure and a half.
In addition to its motivic coherence, this
passage is also interesting for its elegant higher-level voice-leading. In the
first four measures, Konitz embellishes a descending stepwise line of F(bars 2–3)-E-D-C(bar
4)---an instance of the motive in retrograde---while Marsh in contrary motion ascends by step from F (bar 2, heard in the
upper octave) through G (bar 3) to A (bar 4). Konitz and Marsh seem to
simultaneously anticipate the F chord of bar 5 by placing chord tones (C and A,
respectively) on the final beat of measure 4. Measure 5 finds the two players
exchanging voices, C for neighbor-note embellished E, and another
voice-exchange in the following measure switches F and D-flat (C-sharp) on beat
one and the upbeat of three. Konitz and Marsh reach a unison E-flat, from above
and below, respectively, in bar 7. The prevalence of consonant thirds and
sixths between the two voices in these bars is noteworthy.
Another period of imitative cohesion
arises in measure 12 beginning with Konitz’s stepwise “down-up” motive (which
at least in terms of its initial pitch content seems related to the original
motive of measure 2). After stating the motive, Konitz repeats it four times
at different pitch levels through measure 15. Marsh follows behind by a bar,
imitating the “down-up” motive in measures 13 and 14. Note the contrary-motion
3-6 progression onto the strong beat 3 in bar 13 and the parallel thirds on the
first two beats of bar 14. Konitz’s phrase-ending ^3-^1 descent in bar 15 is
inverted and lengthened to two measures as Marsh responds with the ascending
sixth in bars 15–16.
The start of the second half of the form
finds Konitz reactivating the preceding motive, this time in inversion (“up-down”)
at the same pitch level as in bar 12 and immediately elided with a form of the
original (“down-up”) at the third below. Konitz returns to this motive in its full
form in bars 19–20, and then isolates the “down-up” fragment in bar 21. In
measures 22–24 Konitz reverses the order of the motive fragments for two
statements of “up-down + third descent / down-up,” with the first half of each
accelerated rhythmically as sixteenth notes. Marsh’s imitation, meanwhile,
consists of a two-fold answer to the “up-down” motive segment with descending
third in bar 18, which then spins off a chromatic ascent of the minor third
dyad to bar 21.
It is during this phrase that subtly imitative rhythm also comes to the fore. Marsh plays a four-note eighth-note rhythm on beats 3 and 4 of bar 22, in which the final note represents an anticipated downbeat of 1 (that is, the eighth-note on the upbeat of 4 is tied over the bar to beat 1.) When Marsh repeats this rhythm in bars 23–24, Konitz plays the same rhythm in unison, and it is sounded again by Marsh in bars 26–27. This unison rhythm has the effect of propelling the music towards the coming conclusion of the form, an effect heard to even greater impact with the rhythmic and melodic unison in measure 28 (which begins with an instance of the “up-down” motive fragment) in approach of the final turnaround.
Finally, the technique of voice-exchange
heard earlier returns in bars 31–32, where two chromatic instances of it, first
exchanging C for A and then F for A, outline the chromatically-inflected tonic triad. This final passage also includes an example each of the chromatically-ascending minor third dyad and the falling third, both of which are motivically salient due to their earlier appearances in the music discussed above.
It is clear from the nature of improvisation that the relationships described here are subtle, inexplicit, and emergent rather than planned, but they nonetheless contribute to the audible integration of two otherwise fully independent voices and suggest that Konitz and Marsh possess a remarkably heightened sense of musical hearing.
"... I even tried a bit of twelve-tone composition and struck up a correspondence with the pianist Lennie Tristano, the most 'advanced' jazz musician of that time [the early 1950s], in which I helpfully pointed out that the twelve-tone method obviously also held the key to the future of jazz. (Tristano gently replied that I seemed not to have too much acquaintance with jazz improvisation, and was kind enough to invite me to come and talk with him. We shared a turkey sandwich one Thanksgiving evening.)"
William H. Youngren, "Schoenberg, Rosen, and the Common Listener," 1978.
Jazz is a syncretistic music, and I therefore believe that it requires a heterogeneous approach to analysis. In a previous post, I discussed Coltrane's chromatic major third cycles in terms of harmonic implications derived from the principles of tonality. Scholars like William Rothstein, Matthew Bribitzer-Stull, and David Kopp have traced the history of the chromatic major third full cycle (I-bVI-III#-I) back to examples in Schubert and Rossini, and they demonstrate how such chromatic mediant relationships abounded throughout nineteenth-century music. It is apparent that Coltrane's application of the major third cycle belongs in this lineage, perhaps as mediated by Slonimsky. It would be an obvious mistake, however, to neglect to have an ear to the blues when analyzing jazz music, especially the music of an artist like John Coltrane. In his book Origins of the Popular Style, Peter van der Merwe persuasively describes the melodic practice of the blues as consisting partly of a "process of piling up thirds" (124):
"In short, the blues mode takes the form of a ladder of thirds, but it is a flexible ladder that can be extended up or down at will." (125)
Listening to any of his improvisations on "Impressions" reveals that what is typically misconstrued as "Dorian modality" is instead Coltrane's version of just such a blues-derived, "ladder-of-thirds" melodicism. The so-called "mode" is most often a six-note scale abstracted from the stacks of thirds on top of and below the tonic: i.e., D-F-A-C and D-B-G. There is, then, a sense in which it might be appropriate to think of Coltrane's emphasis on chromatic (major and minor) third relations and cycles as a translation into harmonic terms of the "ladder of thirds" melodic concept that Van der Merwe finds central to blues practice. When Coltrane prolongs a harmony with digressions through third-related keys, I suggest that he is "composing-out" the pendular or stacked thirds of a higher-level blues melody. Another element of blues melody comes to the fore in conjunction with Coltrane's mediant-based harmony: the variable third. According to Van der Merwe,
"...[in] genuine blues tunes there will be no question of a clear-cut contrast such as we find between the classical major and minor... major and minor or neutral thirds may be juxtaposed throughout." (120).
When Coltrane moves from a minor tonic to the major mediant, for example, or from a major tonic to the major submediant, the major third and minor third of the tonic key will be intermixed. As just one example from Coltrane's playing, this excerpt from the eleventh and twelfth bars of "Countdown" illustrates:
Here Coltrane is in the act of traversing from D major to B-flat major via F7, but in these five beats one hears only the collection (D E F F# G A). These are simply scale steps 1-2-3-4-5 in D, where scale step 3 includes both the major and minor variants.
When taken all together, the pitch classes of the three triads contained in a chromatic major third cycle (I-bVI-III#-I) yield the hexatonic collection, set class (014589). This collection consists of two augmented triads a semitone apart. Coltrane used two hexatonic scales as a basis for his composition "One Down, One Up," for instance.
Notably, the hexatonic collection contains major and minor triads built on shared roots. Thus a possible non-discrete tetrachordal subset of the hexatonic collection is set class (0347), shown in the example above. Bearing the intervals of a minor third, major third, and fifth, an example of this set class is (D F F# A). This is a "triad" with the variable third that Van der Merwe describes as a hallmark of blues melody. It appears therefore that the hexatonic collection and the blues have a certain affinity, which John Coltrane succeeded in making audible.
It is interesting to note that Coltrane’s chromatic major
third cycle was applied compositionally and improvisationally (too sharp a
distinction should not be drawn) in both the ascending and descending directions.
Ascent and descent have accordingly different musical effects. “Giant Steps”
and an excerpt from “Venus” may serve as examples.
The first seven bars of “Giant Steps” feature two incomplete descending chromatic major third cycles which are paired with descending melodies. The remainder of the composition reverses that direction for an ascending major third cycle with rising melody.
This excerpt from “Venus” (1:33-1:57 in the video below) illustrates an instance of the
ascending major third cycle complemented by an ascending melody, followed by a major third harmonic descent with descending melody.
In both cases, the ascending third cycle is accompanied by
the feeling of an increase in tension, while the descending third cycle brings
about the feeling of a dissipation of tension. This is partly due to the rising
and falling melodies, but there is also a harmonic component to the effect of
accumulating or lessening musical tension.
In Coltrane’s music, the chromatic third cycle has harmonic
implications inherited from the principles of tonality. The ascending major third
cycle (I-III#-bVI-I) moves each harmony four ticks in the sharp-key direction
along the circle of fifths (C-G-D-A-E...). In tonal music, harmonic
movement in the sharp-key direction is associated with an increase in tension. Conversely, the descending major third cycle (I-bVI-III#-I) moves each
harmony four ticks in the flat-key direction along the circle of fifths (C-F-B-flat-E-flat-A-flat…). Shifts to the flat-key area are generally associated with
the relaxation of musical tension. In addition, the III triad contains the
leading tone and (raised) fifth, and is therefore related to the dominant chord;
whereas the bVI triad contains the tonic and (flatted) sixth, thus relating it
to the subdominant chord.
The sense of building and releasing tension in these
examples, then, is overdetermined: both melodic contour and the harmonic implications
of the third cycle play important roles in creating the effect.
A friend who is a brilliant trombonist as well as a medical doctor draws my attention to two outstanding excerpts from John Coltrane's solo on "Take the Coltrane." These turnaround phrases start in measures 9 and 8 of the blues form and can be heard in the video below at 1:49 and 2:10, respectively.
We hear Coltrane going "outside the changes" in a fashion not at all untypical of his playing in this period. It is clear, however, that there is no merely mechanical superimposition of "Giant Steps" or "Countdown" harmonies, as is so often and so glibly asserted. Rather, what we hear in these two examples is a fluid and spontaneous chromatic prolongation of a particular governing harmony. The term "prolongation" is borrowed from Schenkerian theory and is meant to suggest that the chromatic harmonies heard in these excerpts represent not simple substitutions but an elaboration of a single higher-order harmony that obtains over the course of four and five measures. To illustrate this I have verticalized Coltrane's melody, adjusted note register to idealize the voice-leading, and used Schenkerian symbols to highlight higher-level relationships. (In the graphs below, the bass voice is derived from the implied root movement of the melody. Accidentals apply only to the pitch immediately following.)
In Example A, the foreground cycle of chords (C-B-E7-A-C7) prolongs a C chord, the dominant to the tonic harmony of this blues in F. Prolongation of the dominant is appropriate since this phrase begins in the ninth measure of the form. The sense of orderly departure from and return to the governing harmony gives the phrase a kind of centripetal logic. Coltrane uses a chromatic upper-neighbor motion to prolong the conceptual top voice C while the harmony moves through the chromatic lower mediant, itself preceded by secondary dominants. The conceptual bass voice returns to C via the subdominant minor, creating a III-IV-V ascent that effectively prepares the subsequent arrival of the tonic. The phrase illustrated in Example B begins in the eighth measure and prolongs an F-sharp seventh chord, which is the "tritone sub" of the dominant or the Phrygian II, spelled enharmonically.
In this phrase, Coltrane pivots from the F-sharp seventh to a local resolution on B, followed by an incomplete cycle of chords whose roots descend by major thirds (B-G-E-flat). The cycle is related to "Giant Steps," although in this case the major chords are not mediated by intervening dominant chords. Through this prolongation the upper voice C-sharp descends by step to B-flat/A-sharp. Here the F-sharp harmony returns and is additionally expanded, this time by a lower neighbor tone in the conceptual upper voice and a passing tone in the conceptual inner voice. The melodic tones of the last measure can be heard as 6-5-2-3 in F-sharp or as 4-3-7-1 in B-flat minor, the subdominant to the tonic F which returns at the top of the form in the following measure. The latter hearing suggests a particularly grave sort of plagal cadence, and the leading-tone transformation of F-sharp major to B-flat minor reflects the type of major-third relation that Coltrane explored to great effect in this period. This rising third also inverts the falling third from earlier in the phrase. It is worth noting that in both examples, the goal chord reached before the return of the chord of the governing harmony is the chromatic lower mediant (A in Example A, where the prolonged harmony is C, and E-flat in the F-sharp prolongation of Example B.). Also notable in Example B is the stepwise descending third motive, heard twice at the foreground level in the inner voice (F-sharp-E-D-sharp, then E-D-sharp-C-sharp) and once at the middleground level in the upper voice (C-sharp-B-A-sharp). The descending third motive is also suggested by the bass movement from F-sharp to E-flat on the middle ground level and more loosely (in augmentation) by the foreground cycle, B-G-E-flat. In my view, these excerpts offer evidence of hierarchical structure in Coltrane's improvisations, inviting analyses that make use of Schenkerian concepts like prolongation.
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.
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.
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.
"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.
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.
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:
"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(?)"
