Flat Earth & Aggregates
(wonky, for musicians, but not wonky enough for theorists)
In the early 16th Century Magellan circumnavigated the globe. At around the same time, musicians navigated the circle of fifths. During the few moments when the US was culturally upwardly mobile, when the US was sending people into orbit and launching them to the moon, composers were speeding through the chromatic space at shocking speeds. At those fast speeds, the aggregate of all twelve pitches starts asking to be treated as a harmonic unit.
Charles Wuorinen told me he didn’t think the aggregate is a meaningful harmonic entity. Dina Kioston agreed. Aggregates could be a thing, or a heuristic. Pragmatically, the aggregate can be useful or moot. Consider three works by Robert Pollock before you decide.
Upcoming on Furious Artisans
Robert Pollock Five Decades
In another blog from just a few days ago–
– Robert Pollcok Five Decades –
I mention Pollock’s quest for control of harmony, a major postwar and Cold War project, now sidelined as musical coherence has become unfashionable. I suggested that we compare the pre-war and post-war modernisms of Antheil and Pollock.
I now want to dig down into aggregation in three pieces from the upcoming Pollock CD–
Metaphor for guitar solo(1995)
Proposing for this progression of works, each six years apart:
1–that they are coherent, they hold together nicely
2–they hold together differently from Antheil’s structures
3–the later two pieces diverge from Schat’s vision of tidy aggregates
Through these three works, I propose we see aggregation gradually moving to the background while still providing a spine, a ground , gravitational system holding together as various tune/harmonies develop (as interval context evolves).
I’m guilty here of projecting my structural understanding, with all its limitations, onto Pollock’s music. Robert commented on this:
Krishnamurti had a prosaic but profound expression:
The observer is the observed. By extension, the listener is the listened. What you hear in my music is part of your musical universe.
–Click Here for Metaphor (1995) –
Metaphor for guitar solo opens with two phrases, both palpable aggregates–Megallanic Aggregates.
–The first three descending tetrachords
–Four ascending trichords and a bridge into development of the material.
This piece was a direct result of Pollock’s first meeting with Peter Schat in Ship Bottom, NJ. Schat was concerned with very tidy aggregation.
–credit to Jenny McCloud for the tone clock illustrations–
Each of the 12-trichords creates an aggregate, with no redundancies, through a “steering interval” that is not present in the focal (thematic) trichord. For example, 5 steers 048.
 +5 =  +5= [t26] +5= [37e]
Compare Metaphor with Entertwined and Romance-Fantasy.
In Entertwined, at 3:38 on youtube, the “slow movement” lays-in (instates) an Eb, leaves it briefly, returns to it. The next phrase begins the story about venturing further away from Eb. This is Haydnesque common sense. I sympathise with Wendell Berry when he points out that modernisms generally lose something with each new thing they bring. Pollock holds onto Haydnesque principles.
In 2020 there is in the air a contention that 12-EDO has been surpassed. My question is, will X-EDO or other alternatives to 12-EDO lead to a bridge-burning, non-Euclidean music, or will it enfold the old into the new, imbricate Haydn & Pollock into a new paradigm? Mario Davidovsky remarked, “It’s almost as if the young composers are giving up any attempt at syntax and semantics.” Davidovsky & I share Wendell Berry’s concern.
Metaphor for guitar solo is almost a minimalist experiment while the later two works realize a highly fleshed-out middle ground development. If Metaphor is a village, Entertwined and Romance-Fantasy become a town, a city.
An aggregate of 12 notes starts to be a thing when music starts blasting through chromatic space fast enough. We hear such a speed in the first three chords of Pollock’s Metaphor for guitar. Schat parsed the twelve trichords for precisely such neat aggregation.
The aggregation in the latter two works becomes slower, pushed further into the background.
The development of the foreground (foreground intervalic content) is steered by targeting the return to the main theme (the 0279 theme), transposed and completing background aggregates in accord with tone clock principles, but over longish times spans. In each of these three works, the harmony of the main theme is 0279. In Schat’s poetics, 0279 is steered by 4.
 +4 = [46e1] +4 = [8t35]
The opening phrases of Entertwined are already a compounding, an enrichment and expansion of tone-clock principles. The aggregate is no longer so geometrically straightforward.
Romance-Fantasy explodes the intervals between 0279 collection boundaries as the 0279s complete over longish time spans. Pollock no longer cares about tidy aggregate completion? One leg of a 2-step completion becomes sufficient, the last leg of the symmetry is implicit? Robert responded to these questions:
True. Aggregate completion can work so long as other harmonic aspects of harmony such as balance, A-B-A, chord rotations, do not supercede…
It makes me very happy to hear landings on 0279 displacing foreground collections from various interval cycles that emerge in the mid phrase. 0279 is not a subset of the octotonic scale, not a subset of the whole tone scale, not a subset of the augmented scale (E hexachord). We land in 0279 as if entering a space with fresh air.
0279 is ‘tonal’. It’s a very familiar sound. Some riffs in Pollock can be imagined in a work by Antheil, Honneger, Stravinsky, or prog rock–Yes’ Perpetual Change–
–but Pollock’s riffs are in motion, even when they seem to stand alone. This is a stand alone riff, solid-seeming until the material that follows reveals the commitment to the work’s harmonic revolutions.
I take this proposition from Romance-Fantasy:
Even very deep background attention to aggregation provides foundation, provides spine for interval content evolution.This because aggregation will preclude some capricious turns in the interval content trajectory. The price paid is that the large scale form will be a symmetry like Brahms op. 88 or Beethoven Diabelli Variatons.
The aggregate question is a long forgotten story reaching back into the last century. Pollock lived a long and fruitful creative life, and the release of this first all-Pollock CD gives us an excuse to examine things that have been off of our radar for a long, long time.
Call this–wither the aggregate–a buried musical value, a musical value on ice. It was controversial even then.
It’s a very special thing to live long enough to see things ferment into an intense, rare pugency. Sometimes you find a hazel nut that’s partly fermented, but not rotten,and the complex volatiles have an extraordinary effect on the nervous system; the more ancient olfactory apparatus touches the deepest part of our being.
CD Cover Art by Esther Pollock - Jongeneelen