OTC 5L 7s: Difference between revisions
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m Text replacement - "Category:Tempered scales↵Category:Pages with mostly numerical content" to "Category:Tempered_scales Category:Pages with mostly numerical content" Tags: Reverted Mobile edit Mobile web edit |
m Text replacement - "Category:Schismatic" to "Category:Schismic" Tags: Mobile edit Mobile web edit |
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<ul><li>Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul> | <ul><li>Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul> | ||
[[Category:12-tone scales]] | [[Category:12-tone scales]] | ||
[[Category: | [[Category:Tempered scales]] | ||
[[Category:Pages with mostly numerical content]] | [[Category:Pages with mostly numerical content]] | ||
[[Category:MODMOS]] | [[Category:MODMOS]] | ||
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[[Category:Helmholtz]] | [[Category:Helmholtz]] | ||
[[Category:Garibaldi]] | [[Category:Garibaldi]] | ||
[[Category: | [[Category:Schismic]] | ||
[[Category:Superpyth]] | [[Category:Superpyth]] | ||
[[Category:Pythagorean]] | [[Category:Pythagorean]] | ||
Latest revision as of 09:11, 7 January 2026
Omnitetrachordal MOS scale
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 |
