OTC 5L 7s

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Omnitetrachordal MOS scale

5L+7s

12 tones (5+2+5)

MOS of the helmholtz / garibaldi / schismatic and superpyth temperaments, as well as Pythagorean. Very good 3/2 at almost any L/s ratio. Many modes may be pentachordally split in two ways. See also OTC 7L+5s.

P = 1.2600167527 (L=2187/2048, s=256/243)

Q = 7.9100586343 (2L+3.5s)

L = 100.00 to 240.00 cents (113.68 cents @ P, 203.91 cents @ Q)

s = 0.00 to 100.00 cents (90.23 cents @ P, 25.78 cents @ Q)

9/8 = L+s (200.00 to 240.00 cents)

4/3 = 2L+3s (480.00 to 500.00 cents)

generator = 4/3

notable EDOs: 17, 22, 27, 29, 41, 53, etc.

all modes:

Ls LsLss LsLss
sL sLssL sLssL sLsLs sLsLs sL
Ls LssLs LssLs LsLss LsLss Ls
sL ssLsL ssLsL sLssL sLssL sL
Ls sLsLs sLsLs LssLs LssLs Ls
ssLsL ssLsL sL
sLsLs sL sLsLs sLsLs sLsLs Ls
LsLss Ls LsLss
sLssL sL sLssL
LssLs Ls LssLs
ssLsL sL ssLsL
sL sLsLs sLsLs sLsLs Ls sLsLs

12_05_07_sLssL_sL_sLssL.png

See also

References

  • Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages 3685 and 10987.