OTC 5L 7s: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>FREEZE No edit summary |
m Text replacement - "Category:Tempered_scales↵Category:Pages with mostly numerical content" to "Category:Tempered scales Category:Pages with mostly numerical content" Tag: Manual revert |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 83: | Line 83: | ||
===References=== | ===References=== | ||
<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:Tempered scales]] | |||
[[Category:Pages with mostly numerical content]] | |||
[[Category:MODMOS]] | |||
[[Category:Omnitetrachordal]] | |||
[[Category:Helmholtz]] | |||
[[Category:Garibaldi]] | |||
[[Category:Schismatic]] | |||
[[Category:Superpyth]] | |||
[[Category:Pythagorean]] | |||
Latest revision as of 03:13, 24 June 2025
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 |
