Many Worlds Interpretation

(for Dorothy who danced)

Scored for Flute, Bb Clarinet, Violin, Cello & Piano
Duration: 5′ 0″ (or 10′ 0″)
PDF Score here.

LIE SCALE = Chromatic Scale with Linear Intervallic Expansion (LIE)
The primary Scale used in this piece is the Orchestral Outagraphic derived from the Orchestral range (Tuba G0 to Piccolo C8).

LIE SCALE (Ascending):
G0 (+1) G#0 (+2) Bb0 (+3) C#1 (+4) F1 (+5) Bb1 (+6) E2 (+7) B2 (+8) G3 (+9) E4 (+10) D5 (+11) C#6 (+12) C#7

OUTAGRAPHIC SCALE (Ascending):
A0, B0 – C1, D1 – E1, F#1 – A1, B1 – Eb2, F2 – Bb2, C3 – F#3, G#3 – Eb4, F4 – C#5, Eb5 – C6, D6 – C7, D7 – C8

LIE SCALE (Descending):
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

OUTAGRAPHIC SCALE (Descending):
G1 – F2, G2 – E3, F#3 – D4, E4 – B4, C#5 – G5, A5 – D6, E6 – G#6, Bb6 – C#7, Eb7 – F7, G7 – G#7, Bb7

LIE SCALE COMPLETE (up + down = 26 fixed field PC’s):
(G0, G#0), Bb0, C#1, F1, F#1, Bb1, E2, F#2, B2, F3, G3, Eb4, E4, C5, D5, G#5, C#6, Eb6, A6, C#7, D7, F#7, A7, B7, C8

Ascending and descending Intervalic Sequence = 1 | 2, 3, 4, 1, 4, 6, 2 | 5, 6, 2, 8, 1, 8, 2, 6, 5 | 2, 6, 4, 1, 4, 3, 2 | 1 2, 3, 4, 1, 4, 6, 2

(2, 3, 4, 1, 4, 6, 2 = OEIS A104567)

OUTAGRAPHIC SCALE COMPLETE:
A0, B0, C1, D1-E1, G1-A1, | B1-Eb2, F2, G2-Bb2, C3-E3, F#3, G#3-D4, F4-B4, C#5, Eb5-G5, A5-C6, D6, E6-G#6, Bb6-C7, Eb7-F7, G7-G#7, Bb7

The first 11 intervalic classes (IC’s) at either end of this scale 2, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1 corresponds to the OEIS integer sequence A280509 (only 1 OEIS result found).

For the next 13 IC’s 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2 – (up to F#3, & down to C#5), the only matching OEIS sequence is A001179, the Leonardo logarithm (a function related to Fibonacci numbers).

The remaining 15 central IC’s = F#3, G#3-D4, F4-B4, C#5 = 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2 relates to OEIS A118914.

The OUTAGRAPHIC of G0 – C8 (the Orchestral range) is therefore comprised of 3 mirrored & symmetrical intervalic/integer sequences:
A0 – C#2 (A280509) | C#2 – F#3 (A001179) | F#3 C#5 (A118914) | C#5 – F#6 (A001179) | F#6 – Bb7 (A280509)