OTC 5L 5s: Difference between revisions

Latest revision as of 03:08, 24 June 2025

Omnitetrachordal MOS scale

10 tones (4+2+4)

temperament: blackwood

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 7L+7s (whitewood) and OTC 12L+12s (catler/compton), which have similar properties.

P = undefined (or -1?)

Q = 5.6500418817 (4/3 = 2L+2.5s)

L = 120.00 to 240.00 cents (203.91 cents @ Q)

s = 0.00 to 120.00 cents (36.09 cents @ Q)

9/8 = L+s (240.00 cents for any L/s)

4/3 = 2L+2s (480.00 cents for any L/s)

generator = s (0.00 to 120.00 cents)

period = 1/5 octave (240.00 cents)

notable EDOs: 15, 20, 25

all modes:

`Ls LsLs LsLs`	`LsLs Ls LsLs`	`LsLs LsLs Ls`
`sL sLsL sLsL`	`sLsL sL sLsL`	`sLsL sLsL sL`

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 <ul><li>[[Omnitetrachordality|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales|Gallery of omnitetrachordal scales]]</li></ul>
 [[Category:10-tone scales]]
-[[Category:Tempered_scales]]
+[[Category:Tempered scales]]
 [[Category:Pages with mostly numerical content]]
 [[Category:MODMOS]]
 [[Category:Omnitetrachordal]]
 [[Category:Blackwood]]