OTC 7L 7s: Difference between revisions

Latest revision as of 03:13, 24 June 2025

Omnitetrachordal MOS scale

14 tones (6+2+6)

temperament: whitewood

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

See also OTC 5L+5s (blackwood) and OTC 12L+12s (catler/compton).

P = undefined (-1?)

Q = 4.2777408456 (4/3 = 3L+2.5s)

L = 85.71 to 171.43 cents (138.95 cents @ Q)

s = 0.00 to 85.71 cents (32.48 cents @ Q)

9/8 = L+s (171.43 cents for any L/s)

4/3 = 3L+3s (514.29 cents for any L/s)

generator = s (0.00 to 85.71 cents)

period = 1/7 octave (171.43 cents)

notable EDOs: 21, 28, 35 (for 35edo, use L/s=3/2)

all modes:

`Ls LsLsLs LsLsLs`	`LsLsLs Ls LsLsLs`	`LsLsLs LsLsLs Ls`
`sL sLsLsL sLsLsL`	`sLsLsL sL sLsLsL`	`sLsLsL sLsLsL sL`

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 <ul><li>[[Omnitetrachordality|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales|Gallery of omnitetrachordal scales]]</li></ul>
 [[Category:14-tone scales]]
-[[Category:Tempered_scales]]
+[[Category:Tempered scales]]
 [[Category:Pages with mostly numerical content]]
 [[Category:MODMOS]]
 [[Category:Omnitetrachordal]]
 [[Category:Whitewood]]