Permutahedra by David Victor Feldman published on 2015-04-09T05:04:25Z Honestly, this essentially is the piece that got me thrown out of music composition graduate school 37 years ago. "Essentially" because then and until now it existed only as a "head chart." My teacher asked me what I planned to do next, I started to describe my design. Before long he'd heard enough, stopped me, denounced what I'd described as indicative of everything wrong with what I'd been doing lately. "Your music is not eidetic"; at the time I didn't even know the word "eidetic." Though I didn't stop composing when I left school (quite the contrary I entered a very productive time), I just never made time to write down this piece, but I never forgot about it either. The basic idea is simple enough: to try to make total serialism safe for ear-training dunces like myself. So pitch classes play absolutely no role here. The atoms of this music consist of short conjunct musical fragments, not unlike Baroque ornaments. The mathematical abstraction that underlies these fragments then controls everything: timing, register, duration, dynamics, articulation and instrumentation. Doubtless the overall structure does not seem transparent, but at least maybe one feels the presence or trace of structure. About the title: a permutahedron is a polyhedron whose corners correspond to all the permutations of a certain length. The permutahedron corresponding to permutations of length 5, the length of the musical fragments here, lives in four-dimensional space. So a linear map from four-dimensions into eight-dimensions generates enough data to determine all the parameters. Then ten different linear maps general ten "variations," the scare quotes because the variation stand to one another more as multiple views of the same sculptural construction than as conventional musical variation on a theme. Genre Total-serialism