Scored for: fl, cl, vln, vc, pf, & perc
(percussion: Glass harmonica, 2 x toms & snare)
PDF Score here.
LIE SCALES (Chromatic Scales with Linear Intervallic Expansion)
From Nicomachus of Gerasa’s “Manual of harmonics” via Partch, Cowell, & Riemann et al – pitch has been derived from and defined by numeric ratios; undertones and overtones are symmetrical extensions of the fundamental.
Lie Scale principles (see): lie scales & the outagraphic
A0^ + C8v (the pf range) = a 24-tone row (fixed field) dispersed across 7+ octaves:
A0 ^: A0 (+1) Bb0 (+2) C1 (+3) Eb1 (+4) G1 (+5) C2 (+6) F#2 (+7) C#3 (+8) A3 (+9) F#4 (+10) E5 (+11) Eb6 (+12) Eb7
C8 v: F#1 (+12) F#2 (+11) F3 (+10) Eb4 (+9) C5(+8) G#5 (+7) Eb6 (+6) A6 (+5) D7 (+4) F#7 (+3) A7 (+2) B7 (+1) C8
A0, Bb0, C1, Eb1, F#1, G1, C2, F#2, C#3, F3, A3, Eb4, F#4, C5, E5, G#5, Eb6, A6, D7, Eb7, F#7, A7, B7, C8
F4^ + E4v = a 16-tone row (fixed field) dispersed across 7+ octaves:
F4 ^: F4 (+2) G4 (+3) Bb4 (+4) D5 (+5) G5(+6) C#6 (+7) G#6 (+8) E7
E4 v: F1(+8) C#2 (+7) G#2 (+6) D3 (+5) G3 (+4) B3 (+3) D4 (+2) E4
F1, C#2, G#2, D3, G3, B3, D4, E4, F4, G4, Bb4, D5, G5, C#6, G#6,E7
(A0 ^ + C8 v) + (E4 v + F4 ^) = 40-tone row (fixed field)
A0, Bb0, C1, Eb1, F1, F#1, G1, C2, C#2, F#2, G#2, C#3, D3, F3, G3, A3, B3, D4, Eb4, E4, F4, F#4, G4, Bb4, C5, D5, E5, G5, G#5, C#6, Eb6, G#6,A6, D7, Eb7, E7, F#7, A7, B7, C8
Symmetrical IC pattern = [123 2115 15251 32223 11111 32223 15251 5112 321]