• Home
  • About
    • What’s going on here
    • Kyle Gann
    • Contact
  • AJBlogs
  • ArtsJournal

PostClassic

Kyle Gann on music after the fact

Nested 3:2 Addendum

For whatever reason, I was never much drawn to the type of nested 3:2 and 4:3 crossrhythms that I described in my last metametrics post, but I did use it once, and could have mentioned it. In 1985, on the verge of turning 30, I was under some psychological pressure to write something ambitous. I decided on a big set of variations for two pianos, somewhat inspired by the two-piano tradition of Busoni’s Fantasia Contrappuntistica, Wallingford Riegger’s Variations, The Art of Fugue, and such huge solo piano variations as the Diabelli and Brahms’s Handel. (This was before Larry Polansky wrote his Lonesome Road Variations, which dwarfed mine.) My I’itoi Variations was a set of eleven variations on the “Black Mountain” song from the I’itoi cycle of the Papago Indians. I was very involved in collecting, transcribing, and analyzing American Indian music in those days, because I was attracted to its, um, proto-totalist rhythmic character – specifically the way it shifted back and forth among tempos.

Another influence on I’itoi Variations (and on much of my music) was Beethoven’s Op. 111 Sonata – variations 1 through 6 were stormy and tense like Beethoven’s first movement, variations 7 through 10 were impersonal and calm like the second movement, and no. 11, in an attempted tour de force, went back through the first ten variations in reverse order. Variation 8 was based on a nested 3:2. The idea was simple. (I try to make all my ideas simple). There were two foreground lines, the bass line in piano 2 and the right-hand melody of piano 1, plus a line of quarter-note chords shared by both pianos. The bass was in dotted quarters, the treble in triplet quarters, for a 4:6:9 tempo resultant. I hoped the treble and bass would float in seeming unrelatedness to each other, though subtly mediated by the chords in between. Here’s a passage from the beginning of the variation:

I'itoi1.jpg

and another from the end, where the treble and bass lines have doubled in tempo:

I'itoi2.jpg

The bass line is the inversion of the theme, with the intervals doubled in size (a trick I picked up from Messiaen’s bird song music). I suppose it won’t much harm my reputation to admit that the changes of key are timed according to a descending sequence of Fibonacci numbers. Everyone who studied Bartok’s music had to try them once. This was back in 1985 when I had not yet heard of Mikel Rouse, Michael Gordon, or Art Jarvinen, and was blissfully unaware that they were using the same ideas.

Here’s the recording of Variation 8 from I’itoi Variations, played by the Double Edge duo – Nurit Tilles and Edmund Niemann, who premiered it at Cooper Union in New York circa 1990.

What’s going on here

So classical music is dead, they say. Well, well. This blog will set out to consider that dubious factoid with equanimity, if not downright enthusiasm [More]

Kyle Gann's Home Page More than you ever wanted to know about me at www.kylegann.com

PostClassic Radio The radio station that goes with the blog, all postclassical music, all the time; see the playlist at kylegann.com.

Recent archives for this blog

Archives

Sites to See

American Mavericks - the Minnesota Public radio program about American music (scripted by Kyle Gann with Tom Voegeli)

Kalvos & Damian's New Music Bazaar - a cornucopia of music, interviews, information by, with, and on hundreds of intriguing composers who are not the Usual Suspects

Iridian Radio - an intelligently mellow new-music station

New Music Box - the premiere site for keeping up with what American composers are doing and thinking

The Rest Is Noise - The fine blog of critic Alex Ross

William Duckworth's Cathedral - the first interactive web composition and home page of a great postminimalist composer

Mikel Rouse's Home Page - the greatest opera composer of my generation

Eve Beglarian's Home Page- great Downtown composer

David Doty's Just Intonation site

Erling Wold's Web Site - a fine San Francisco composer of deceptively simple-seeming music, and a model web site

The Dane Rudhyar Archive - the complete site for the music, poetry, painting, and ideas of a greatly underrated composer who became America's greatest astrologer

Utopian Turtletop, John Shaw's thoughtful blog about new music and other issues

Return to top of page

an ArtsJournal blog

This blog published under a Creative Commons license