OTC 12L 12s

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Omnitetrachordal MOS and MODMOS scale


24 tones (10+4+10)

catler, compton; 3 forms

Form 1 (MOS) has some unusual properties:

  • it has only two modes
  • either mode may be split in any of the three possible omnitetrachordal ways (9/8-4/3-4/3, 4/3-9/8-4/3, 4/3-4/3-9/8)
  • it is its own dual (changing all L to s, and vice versa, gives the same scale)

See also OTC 5L+5s (blackwood) and OTC 7L+7s (whitewood), which have similar properties.

For all 3 forms:

  • the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio

Forms 2 and 3 are duals.

P = undefined (-1?)

Q = 24.5754362493 (4/3 = 5L+4.5s)

L = 50.00 to 100.00 cents (96.09 cents @ Q)

s = 0.00 to 50.00 cents (3.91 cents @ Q)

9/8 = 2L+2s (200.00 cents, for any L/s)

4/3 = 5L+5s (500.00 cents, for any L/s)

MOS generator = s (0.00 to 50.00 cents)

MOS period = 1/12 octave (100.00 cents)

notable EDOs: 36, 48, 60, 72, 84

LsLsLsLsLsLsLsLsLsLsLsLs (OTC form 1, MOS)

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ssLsLLssLLssLsLLssLLssLL (form 2, MODMOS) - gc 3,3,3,2,3,3,2; 5o ;; pc 12,2,2; 8o

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ssLLsLssLLssLLsLssLLssLL (form 3, MODMOS) - gc 3,3,3,2,3,3,2; 5o ;; pc 12,2,2; 8o

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LsLsLsLsLsLsLsLsLsLsLsLs (form 1)

all modes, form 1:

LsLs LsLsLsLsLs LsLsLsLsLs LsLsLsLsLs LsLs LsLsLsLsLs LsLsLsLsLs LsLsLsLsLs LsLs
sLsL sLsLsLsLsL sLsLsLsLsL sLsLsLsLsL sLsL sLsLsLsLsL sLsLsLsLsL sLsLsLsLsL sLsL

all modes, form 2:

ssLsLLssLL ssLsLLssLL ssLL
sLsLLssLLs sLsLLssLLs sLLs
LsLLssLLss LsLLssLLss LLss
sLLssLLssL sLLs sLLssLLssL sLLssLLssL sLLssLLssL LssL
LLssLLssLs LLss LLssLLssLs
LssLLssLsL LssL LssLLssLsL
ssLLssLsLL ssLL ssLLssLsLL
sLLssLsLLs sLLs sLLssLsLLs
LLssLsLLss LLss LLssLsLLss
LssLsLLssL LssL LssLsLLssL
ssLsLLssLL ssLL ssLsLLssLL
sLsLLssLLs sLLs sLsLLssLLs
LsLLssLLss LLss LsLLssLLss
sLLs sLLssLLssL sLLssLLssL sLLssLLssL LssL sLLssLLssL
LLss LLssLLssLs LLssLLssLs
LssL LssLLssLsL LssLLssLsL
ssLL ssLLssLsLL ssLLssLsLL
sLLs sLLssLsLLs sLLssLsLLs sLLssLLssL sLLssLLssL sLLs
LLss LLssLsLLss LLssLsLLss LLssLLssLs LLssLLssLs LLss
LssL LssLsLLssL LssLsLLssL LssLLssLsL LssLLssLsL LssL
ssLL ssLsLLssLL ssLsLLssLL ssLLssLsLL ssLLssLsLL ssLL
sLLs sLsLLssLLs sLsLLssLLs sLLssLsLLs sLLssLsLLs sLLs
LLss LsLLssLLss LsLLssLLss LLssLsLLss LLssLsLLss LLss
LssL sLLssLLssL sLLssLLssL LssLsLLssL LssLsLLssL LssL

all modes, form 3:

ssLL sLssLLssLL sLssLLssLL ssLLsLssLL ssLLsLssLL ssLL
sLLs LssLLssLLs LssLLssLLs sLLsLssLLs sLLsLssLLs sLLs
LLsLssLLss LLsLssLLss LLss
LsLssLLssL LsLssLLssL LssL
sLssLLssLL sLssLLssLL ssLL
LssLLssLLs LssL LssLLssLLs LssLLssLLs LssLLssLLs sLLs
ssLLssLLsL ssLL ssLLssLLsL
sLLssLLsLs sLLs sLLssLLsLs
LLssLLsLss LLss LLssLLsLss
LssLLsLssL LssL LssLLsLssL
ssLLsLssLL ssLL ssLLsLssLL
sLLsLssLLs sLLs sLLsLssLLs
LLsLssLLss LLss LLsLssLLss
LsLssLLssL LssL LsLssLLssL
sLssLLssLL ssLL sLssLLssLL
LssL LssLLssLLs LssLLssLLs LssLLssLLs sLLs LssLLssLLs
ssLL ssLLssLLsL ssLLssLLsL
sLLs sLLssLLsLs sLLssLLsLs
LLss LLssLLsLss LLssLLsLss
LssL LssLLsLssL LssLLsLssL LssLLssLLs LssLLssLLs LssL
ssLL ssLLsLssLL ssLLsLssLL ssLLssLLsL ssLLssLLsL ssLL
sLLs sLLsLssLLs sLLsLssLLs sLLssLLsLs sLLssLLsLs sLLs
LLss LLsLssLLss LLsLssLLss LLssLLsLss LLssLLsLss LLss
LssL LsLssLLssL LsLssLLssL LssLLsLssL LssLLsLssL LssL



See also