Outagraphic #1

Scored for Clarinet, Bassoon, Trumpet, Trombone, Violin,
Bass, & Percussion (Glockenspiel & Xylophone)

Duration: 4’20”
PDF Score here.

Dedicated to Theodore “Ted” Joans (1928 – 2003), the inventor of Outagraphy.

LIE Scale used: G0 < > C8 Outagraphic
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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
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The OUTAGRAPHIC of G0 – C8 (the Orchestral range) is 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).
Quantity of IC’s: 11 – 13 – 15 – 13 – 11
Consecutive sequences/collections (quantity of PC’s) =
3 – 3 – 5 – 4 – 5 – 7 – 7 – 5 – 4 – 5 – 3 – 3 – (2)
D1-E1, G1-A1, B1-Eb2, G2-Bb2, C3-E3, G#3-D4, F4-B4, Eb5-G5, A5-C6, E6-G#6, Bb6-C7, Eb7-F7, G7-G#7

  • The first 11 intervalic classes (IC’s) at either end of this scale 2, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1 correspond 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).
  • OEIS A118914 is the only sequence that corresponds to 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, 2Concatenation of the prime signatures (sorted lists of exponents of distinct prime factors) of the positive integers.

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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
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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
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The unused pitches within range constitute the complete outagraphic scale.