Bill y Elliott or, Hexachordal subsets in Anderson & Carter

Carter took one abrupt turn, and much later, a gentle turn. His music from the '50s did not draw a hard line around scale degrees. Scale degree associations were not avoided like the plague. He drew the line in the 60s or late 50s. In the 80s, there began a wonderful softening, but without a return to scale degrees.

I began thinking of the banning of scale degree associations as a form of musical *partiality*. This notion came about while pondering Terry Riley's Y Bolanzero, where I see Riley enfolding some post-tonal moves into a soundworld that is also very *d harmonic minor*, not divorced from scale degrees, but still exploring other associations. It seems to come from his jazz background. In a nutshelll, Riley makes d harmonic minor and internal E hexachordal relationships work harmoniously together. I do this in my Poema armónico. The last historical figure to do that was Brahms of op. 88. Look at the Sarabande in the middle movements. It ties together local (within one "key") transpositions of the major 7 chord, with the proto-post-tonal relationships seen on the large scale--F major, C# (minor-major), A major. That, superimposed upon the inherited "natural" relationships--the keys of I and V, generates his surface material. F & Ab with F's dominant, C, for example. F & A, with A's dominant, E. These shapes abound in the Saraband, horizontally and vertically. Notice the missing pitch E# appearing at the end of the section.

My Poema is *soft PoMo*. No historical borrowings other than an erasure of the strict line drawn around scale degrees. Perhaps a vague Sicilienne. I don't mind it being called tonal, any more than Riley would object to hearing his Y Bolanzero as thoroughly d minor. For me, this state of affairs came about through a thorough impatience for any prolonged passages of pure symmetries--easy, complacent atonality.

There are "custom symmetries" that come from highly contextual configurations such as are seen in Schoenberg. Those are vastly preferable to octotonic drivel. Moreover, Schoenberg does land deliberately in a distinctly *other* space at telling moments, for example--when he lands in [ 0, 2, 4, 6 ] at the end of op. 27 #4. That 4/5ths of a dominant 9 chord erases the prevailing sound. The prevailing sound is so complex as to defy any easy label. It is a mash of 1 and 5 cycle, perhaps.

I noticed something about Poema. It "modulates" from the mitigated octotonic contexts for [ 0, 2, 5, 9 ] to [ 0, 4, 5 ]. Then it riffs on the "augmented scale"--014589, aka the E hexachord. However, later in the quasi-Sicilienne, various subsets of the E hexachord appear at phrase endings (landing places). That is a subtle change of modalities.

The complementary E hexachords are set off from each other by the exogenous [0, 2.5 ] or [ 0, 2, 7 ] suspensions between the two, memories of the opening "almost octotonic" material. I see that I am trying not to be OCD about anything. Relief from the E hexachord proceedings takes place in 2 episodes where 015 appears in diverse contexts in quick succession, 012678, chromatic, diatonic, 023457 before landing again in E--a bizarre *meta-extension* of E. As a different way of proceeding it breaks the prevailing harmonic rhythm.

Poema begs for a similar exploration of the all-trichord hexachord. In both cases--subsets erase the hexachordal context if they are landed strongly. This is why octotonic music can work--the 0, 4, 6, 10 subset scrubs away the octotonic scent. 045 is certainly a subset of E, but it is so strongly redolent of its diatonic contexts that it scrubs away the E sound. In Poema I notice phrases finding the E subsets that are distinct to the E hexachord. [ F, Ab, C#, E ] is an example. Babbitt lands entire E hexachords. Poema never does that, but it scares up the most E-scented subsets.

Mulling over subsets of a hexachord is very Cartereque. And yet there is here something that Carter did not do. Phrase endings & landings are not Carteresque, but he does come close to something similar as he moves between sections, perhaps. Phase endings are a feature of the common-practice era no less than scale degrees. Note also, that Babbitt & Schoenberg are among the very few high 20th C. modernists to *land* in a fashion that can be fairly said to be analgous to Haydnesque perioding phrasing. It is *precisely* this that got Schoenberg blackballed by Boulez. Babbitt got away with it by doing it in such a devilshly complex manner. Babbitt's way will be more clear to everyone when we get a more detailed definition of "super-array", a definition that explains what the counterpoints of arrays *do* especially with regard to *convergences*.

**The partiality that excluded the diatonic hexachordal context for 045 missed an important side of the ambiguity of 045.** The exclusion left one side of the trichord's ambiguity unexplored. Babbit stopped avoiding diatonic hexachords, eventually.

I declare the Boulez values utterly passé, and I claim to be allied with Terry Riley in that, among a few other like Dawe, Brickle, and Robert Pollock.

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