OTC 12L 12s
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 |
