The Sumer Aggregate Is a Cumin In

Four days into the summer, I’ve completed my first piece. Larry Polansky publishes an expanding book of rounds, and for years he’s been bugging me to write one, so I finally did. Dodecaphonically. [UPDATE: Larry’s put a better copy on the web here, and you can also see a lot of the other rounds in his collection.] [MIDI piano version here.]

It’s pretty singable if you don’t try the repeat. [UPDATE: It occurs to me that it would be more consonant and easier to sing if the repeat used P11 (down a half-step), the next repeat P10, and so on. Sort of like “12 Bottles of Beer on the Wall.”] [Still other versions could use P10 on the repeat and descend via whole-steps, or repeat with P6. It’s kind of amazingly flexible.]
I feel it’s also a nice mnemonic device.
I’m donating all royalties to the Society for Minimalism Music.


  1. says

    (And witty.)
    But what will Boulez do with *his* share of the royalties???
    KG replies: Thank you, I thought it was pretty clever, myself – I got the idea upon coming across a tone row in which every series of three consecutive notes created a triad (though one is diminished and one is augmented; I don’t think there’s one that works out all major and minor).
    But You’ve made me realize – if I register this with ASCAP, Boulez really WILL have to get half the money! He can’t say I never did anything for him. (Thanks for the great belly laugh.)

  2. Bob Gilmore says

    When I was a student a friend of mine used to reduce us all to hysterical laughter by improvising, at the piano, settings of passages from “Boulez on Music Today” in the style of Gilbert and Sullivan, or occasionally Rogers and Hammerstein, and singing in falsetto. I wish to God I had recordings.

  3. says

    I don’t think there’s one that works out all major and minor
    As I’m sure you figured out, the only way to try and construct this would be with interlocking major and minor triads, which won’t fill out the aggregate without repeating pitches (like C E G B D F# A C# E G# B D#/Eb Gb Bb D F).
    This row is just like the one in Chromatic Canon.
    KG replies: This row is [037]-generated like Tenney’s, but his – B D# G# G C E A# F# C# D A F – links the disjunct trichords with dissonances.