Gallery of omnitetrachordal scales
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[[toc]]
=Scales with two step sizes=
(not necessarily [[MOS]] or [[Distributional Evenness|DE]])
These are mostly tempered (irrational) scales. In some cases (usually where the generator is close to a perfect 4/3 or 3/2), a Pythagorean (3-limit [[Just intonation|JI]]) version is possible.
==5 tones (2+1+2)==
===[[2L 3s|2L+3s]]===
The familiar classic pentatonic scale. Can include [[superpyth]], [[https://en.wikipedia.org/wiki/Pythagorean_tuning|Pythagorean]], [[meantone]], and [[Mavila Temperament Modal Harmony|mavila]] tunings. Is [[MOS]]. [[{$page}#ref1|(1)]]
Pythagorean (3-limit JI): L=[[32_27|32/27]], s=9/8
generator = L+s
[[{$page}#perfect|P]] = 1.4424745962
notable [[EDO]]s: 7, 9, 12, 16, 17, 19, 22, 26, 29, 31
modes:
|| || {{ sL s sL }} || ||
|| || {{ Ls s Ls }} || ||
|| {{ s sL sL }} || || ||
|| {{ s Ls Ls }} || || {{ sL sL s }} ||
|| || || {{ Ls Ls s }} ||
===[[3L 2s|3L+2s]]===
Father? MOS; [[{$page}#perfect|imperfect]]; [[{$page}#ref1|(1)]]
generator = L+s
notable EDOs: 8, 11b, 13, 18, 23b
modes:
|| || {{ Ls L Ls }} || ||
|| || {{ sL L sL }} || ||
|| {{ L Ls Ls }} || || ||
|| {{ L sL sL }} || || {{ Ls Ls L }} ||
|| || || {{ sL sL L }} ||
==7 tones (3+1+3)==
===[[2L 5s|2L+5s]]===
[[Mavila Temperament Modal Harmony|Mavila]] diatonic MOS. [[{$page}#perfect|Imperfect]]. [[{$page}#ref1|(1)]]
generator = L+2s
notable EDOs: 9, 11, 16, 23
modes:
|| || {{ sLs s sLs }} || ||
|| || {{ Lss s Lss }} || ||
|| {{ s ssL ssL }} || || ||
|| {{ s sLs sLs }} || || {{ ssL ssL s }} ||
|| {{ s Lss Lss }} || || {{ sLs sLs s }} ||
|| || || {{ Lss Lss s }} ||
|| || {{ ssL s ssL }} || ||
===[[5L 2s|5L+2s]]===
Classic diatonic scale ([[meantone]], Pythagorean, [[superpyth]]); MOS. [[{$page}#ref1|(1)]]
Pythagorean (3-limit JI): L=9/8, s=[[256_243|256/243]]
P = 2.2600167527
generator = 2L+s
notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc.
modes:
|| || {{ LLs L LLs }} || || Ionian ||
|| || {{ LsL L LsL }} || || Dorian ||
|| || {{ sLL L sLL }} || || Phrygian ||
|| {{ L LLs LLs }} || || || Lydian ||
|| {{ L LsL LsL }} || || {{ LLs LLs L }} || Mixolydian ||
|| {{ L sLL sLL }} || || {{ LsL LsL L }} || Aeolian ||
|| || || {{ sLL sLL L }} || Locrian ||
==10 tones (4+2+4)==
===[[5L 5s|5L+5s]]===
Blackwood MOS. This omnitetrachordal scale has some unusual properties:
* it has only two modes
* either mode may be split in any of the three possible omnitetrachordal ways (9/8-4/3-4/3, 4/3-9/8-4/3, 4/3-4/3-9/8)
* it is its own dual (changing all L to s, and vice versa, gives the same scale)
* the (imperfect) tuning of 3/2 is independent of L/s ratio (fixed at exactly 720 cents)
generator = s
[[periods and generators|period]] = 1/5 octave
notable EDOs: 15, 20, 25
modes:
|| {{ Ls LsLs LsLs }} || {{ LsLs Ls LsLs }} || {{ LsLs LsLs Ls }} ||
|| {{ sL sLsL sLsL }} || {{ sLsL sL sLsL }} || {{ sLsL sLsL sL }} ||
===[[7L 3s|7L+3s]]===
[[Mohajira]] / [[Neutral third scales|neutral-thirds]] [[MODMOS]]
P = 2.5872804832
generator = 2L+s
notable EDOs: 17, 24, 27, 31, 41
{{ sLLsLLsLLL }} (MOS)
{{ || }}
{{ sLLLsLsLLL }} (OTC MODMOS)
modes:
|| || {{ LsLL Ls LsLL }} || ||
|| || {{ sLLL sL sLLL }} || ||
|| || {{ LLLs Ls LLLs }} || ||
|| || {{ LLsL sL LLsL }} || ||
|| {{ Ls LsLL LsLL }} || || ||
|| {{ sL sLLL sLLL }} || || ||
|| {{ Ls LLLs LLLs }} || || {{ LsLL LsLL Ls }} ||
|| {{ sL LLsL LLsL }} || || {{ sLLL sLLL sL }} ||
|| || || {{ LLLs LLLs Ls }} ||
|| || || {{ LLsL LLsL sL }} ||
===[[3L 7s|3L+7s]]===
The [[{$page}#dual|dual]] of 7L+3s, this scale pattern barely qualifies as omnitetrachordal.
notable EDOs: 13, 16b
modes: LsssLsLsss, etc.
===[[2L 8s|2L+8s]]===
[[Pajara]] MODMOS. Best at lower ratios of L/s. [[{$page}#ref1|(1)]]
P = 1.8849491924
generator = s
[[periods and generators|period]] = 1/2 octave
notable EDOs: 12, 14, 16, 22, 26
{{ LssssLssss }} (MOS)
{{ || }}
{{ LsssssLsss }} (OTC MODMOS)
modes:
|| || {{ sssL ss sssL }} || || Standard Pentachordal Minor ||
|| || {{ ssLs ss ssLs }} || || - ||
|| || {{ sLss ss sLss }} || || Alternate Pentachordal Major ||
|| || {{ Lsss ss Lsss }} || || - ||
|| {{ ss sssL sssL }} || || || - ||
|| {{ ss ssLs ssLs }} || || || Alternate Pentachordal Minor ||
|| {{ ss sLss sLss }} || || {{ sssL sssL ss }} || - ||
|| {{ ss Lsss Lsss }} || || {{ ssLs ssLs ss }} || Standard Pentachordal Major ||
|| || || {{ sLss sLss ss }} || - ||
|| || || {{ Lsss Lsss ss }} || - ||
(The names of the modes are Paul Erlich's - see [[http://lumma.org/tuning/erlich/erlich-decatonic.pdf]].)
===[[8L 2s|8L+2s]]===
The dual of 2L+8s, this scale is imperfect and poorly tuned for 3/2 at any L/s ratio.
notable EDOs: 18, 26b
modes: LsLLLLLsLL, etc.
==12 tones (5-2-5)==
===[[5L 7s|5L+7s]]===
12-tone MOS of the helmholtz / garibaldi / [[Schismatic family|schismatic]] and [[superpyth]] temperaments (slightly sharp 3/2). Very usable at any L/s ratio. Many modes may be pentachordally split in two ways.
Pythagorean (3-limit JI): L=2187/2048, s=256/243
P = 1.2600167527
generator = 2L+3s
notable EDOs: 17, 22, 27, 29, 41, 53, etc.
modes:
|| || {{ sLsLs sL sLsLs }} || {{ sLsLs sLsLs Ls }} ||
|| || {{ LsLss Ls LsLss }} || ||
|| || {{ sLssL sL sLssL }} || ||
|| || {{ LssLs Ls LssLs }} || ||
|| || {{ ssLsL sL ssLsL }} || ||
|| {{ sL sLsLs sLsLs }} || {{ sLsLs Ls sLsLs }} || ||
|| {{ Ls LsLss LsLss }} || || ||
|| {{ sL sLssL sLssL }} || || {{ sLsLs sLsLs sL }} ||
|| {{ Ls LssLs LssLs }} || || {{ LsLss LsLss Ls }} ||
|| {{ sL ssLsL ssLsL }} || {{ sLssL sL ssLsL }} || ||
|| {{ Ls sLsLs sLsLs }} || || {{ LssLs LssLs Ls }} ||
|| || || {{ ssLsL ssLsL sL }} ||
===[[7L 5s|7L+5s]]===
12-tone MOS of the [[meantone]] and [[Meantone family#Flattone|flattone]] temperaments (slightly flat 3/2). [[{$page}#perfect|Imperfect]], but very usable at any L/s ratio. Many modes may be pentachordally split in two ways.
generator = 3L+2s
notable EDOs: 19, 26, 31, 33, 43, 45, 50, etc.
modes:
|| || {{ LsLLs Ls LsLLs }} || ||
|| || {{ sLLsL sL sLLsL }} || ||
|| || {{ LLsLs Ls LLsLs }} || ||
|| {{ Ls LsLsL LsLsL }} || {{ LsLsL sL LsLsL }} || ||
|| {{ sL sLsLL sLsLL }} || || ||
|| {{ Ls LsLLs LsLLs }} || || {{ LsLsL LsLsL Ls }} ||
|| {{ sL sLLsL sLLsL }} || || {{ sLsLL sLsLL sL }} ||
|| {{ Ls LLsLs LLsLs }} || || {{ LsLLs LsLLs Ls }} ||
|| {{ sL LsLsL LsLsL }} || || {{ sLLsL sLLsL sL }} ||
|| || || {{ LLsLs LLsLs Ls }} ||
|| || {{ LsLsL Ls LsLsL }} || {{ LsLsL LsLsL sL }} ||
|| || {{ sLsLL sL sLsLL }} ||
===[[10L 2s|10L+2s]]===
[[Pajara]] MODMOS. Good for most any ratio of L to s.
P = 1.1300083763
generator = L
[[periods and generators|period]] = 1/2 octave
notable EDOs: 22, 32, 34, 46
{{ LLLLLsLLLLLs }} (MOS)
{{ || }}
{{ LLLLLLsLLLLs }} (OTC MODMOS)
modes:
|| {{ LL LLLLs LLLLs }} || || ||
|| {{ LL LLLsL LLLsL }} || || ||
|| {{ LL LLsLL LLsLL }} || || {{ LLLLs LLLLs LL }} ||
|| {{ LL LsLLL LsLLL }} || || {{ LLLsL LLLsL LL }} ||
|| {{ LL sLLLL sLLLL }} || || {{ LLsLL LLsLL LL }} ||
|| || || {{ LsLLL LsLLL LL }} ||
|| || || {{ sLLLL sLLLL LL }} ||
|| || {{ LLLLs LL LLLLs }} || ||
|| || {{ LLLsL LL LLLsL }} || ||
|| || {{ LLsLL LL LLsLL }} || ||
|| || {{ LsLLL LL LsLLL }} || ||
|| || {{ sLLLL LL sLLLL }} || ||
===[[2L 10s|2L+10s]]===
[[{$page}#dual|Dual]] of 10L+2s. Probably only useful for small values of L/s.
notable EDOs: 14, 16
modes: ssLssssssLss, etc.
==13 tones (5+3+5)==
===[[7L 6s|7L+6s]]===
[[Tetracot family|Tetracot]] MODMOS. Best tuned at high values of L/s.
P = 5.1745609664
generator = L+s
notable EDOs: 20, 27, 34, 41
{{ sLsLsLsLsLsLL }} (MOS)
{{ || || || }}
{{ ssLLLssLssLLL }} (OTC MODMOS)
modes:
|| {{ Lss LssLL LssLL }} || || ||
|| {{ ssL ssLLL ssLLL }} || || ||
|| {{ sLs sLLLs sLLLs }} || || ||
|| {{ Lss LLLss LLLss }} || || {{ LssLL LssLL Lss }} ||
|| {{ ssL LLssL LLssL }} || || {{ ssLLL ssLLL ssL }} ||
|| || || {{ sLLLs sLLLs sLs }} ||
|| || || {{ LLLss LLLss Lss }} ||
|| || || {{ LLssL LLssL ssL }} ||
|| || {{ LssLL Lss LssLL }} || ||
|| || {{ ssLLL ssL ssLLL }} || ||
|| || {{ sLLLs sLs sLLLs }} || ||
|| || {{ LLLss Lss LLLss }} || ||
|| || {{ LLssL ssL LLssL }} || ||
==14 tones (6+2+6)==
===[[5L 9s|5L+9s]]===
[[Semaphore and Godzilla|Semaphore / godzilla]] MODMOS. Usable at any L/s ratio.
P = 3.5200335053
generator = L+2s
notable EDOs: 19, 24, 29, 33, 34, 53
{{ ssLssLssLssLsL }} ([[MOS]])
{{ || || }}
{{ sssLsLsssLsLsL }} (OTC [[MODMOS]])
modes:
|| {{ sL sLsLss sLsLss }} || || ||
|| {{ Ls LsLsss LsLsss }} || || ||
|| {{ sL sLsssL sLsssL }} || || {{ sLsLss sLsLss sL }} ||
|| {{ Ls LsssLs LsssLs }} || || {{ LsLsss LsLsss Ls }} ||
|| {{ sL sssLsL sssLsL }} || || {{ sLsssL sLsssL sL }} ||
|| {{ Ls ssLsLs ssLsLs }} || || {{ LsssLs LsssLs Ls }} ||
|| || || {{ sssLsL sssLsL sL }} ||
|| || || {{ ssLsLs ssLsLs Ls }} ||
|| || {{ sLsLss sL sLsLss }} || ||
|| || {{ LsLsss Ls LsLsss }} || ||
|| || {{ sLsssL sL sLsssL }} || ||
|| || {{ LsssLs Ls LsssLs }} || ||
|| || {{ sssLsL sL sssLsL }} || ||
|| || {{ ssLsLs Ls ssLsLs }} || ||
===[[12L 2s|12L+2s]]===
[[Injera]] MODMOS. Imperfect (P<0); best for L/s >= 1.5 [[{$page}#ref1|(1)]]
generator = L
[[periods and generators|period]] = 1/2 octave
notable EDOs: 26, 38, 40, 50
{{ LLLLLLsLLLLLLs }} (MOS)
{{ || }}
{{ LLLLLLLsLLLLLs }} (OTC MODMOS)
modes:
|| {{ LL LLLLLs LLLLLs }} || || ||
|| {{ LL LLLLsL LLLLsL }} || || ||
|| {{ LL LLLsLL LLLsLL }} || || {{ LLLLLs LLLLLs LL }} ||
|| {{ LL LLsLLL LLsLLL }} || || {{ LLLLsL LLLLsL LL }} ||
|| {{ LL LsLLLL LsLLLL }} || || {{ LLLsLL LLLsLL LL }} ||
|| {{ LL sLLLLL sLLLLL }} || || {{ LLsLLL LLsLLL LL }} ||
|| || || {{ LsLLLL LsLLLL LL }} ||
|| || || {{ sLLLLL sLLLLL LL }} ||
|| || {{ LLLLLs LL LLLLLs }} || ||
|| || {{ LLLLsL LL LLLLsL }} || ||
|| || {{ LLLsLL LL LLLsLL }} || ||
|| || {{ LLsLLL LL LLsLLL }} || ||
|| || {{ LsLLLL LL LsLLLL }} || ||
|| || {{ sLLLLL LL sLLLLL }} || ||
==15 tones (6+3+6)==
===[[7L 8s|7L+8s]]===
[[Porcupine]] MODMOS
[[{$page}#perfect|P]] = 3.3809207248
generator = L+s
notable EDOs: 22, 29, 36, 37, 43, 65
{{ LsLsLsLsLsLsLss }} (MOS)
{{ || || }}
{{ LsLLssLsLLssLss }} (OTC MODMOS)
modes:
|| || {{ LssLsL Lss LssLsL }} || ||
|| || {{ ssLsLL ssL ssLsLL }} || ||
|| || {{ sLsLLs sLs sLsLLs }} || ||
|| || {{ LsLLss Lss LsLLss }} || ||
|| || {{ sLLssL ssL sLLssL }} || ||
|| || {{ LLssLs sLs LLssLs }} || ||
|| {{ Lss LssLsL LssLsL }} || || ||
|| {{ ssL ssLsLL ssLsLL }} || || ||
|| {{ sLs sLsLLs sLsLLs }} || || ||
|| {{ Lss LsLLss LsLLss }} || || {{ LssLsL LssLsL Lss }} ||
|| {{ ssL sLLssL sLLssL }} || || {{ ssLsLL ssLsLL ssL }} ||
|| {{ sLs LLssLs LLssLs }} || || {{ sLsLLs sLsLLs sLs }} ||
|| || || {{ LsLLss LsLLss Lss }} ||
|| || || {{ sLLssL sLLssL ssL }} ||
|| || || {{ LLssLs LLssLs sLs }} ||
===[[12L 3s|12L+3s]]===
[[Augmented]] MODMOS. Best at higher L/s ratios.
P = 12.5377181246
generator = L
period = 1/3 octave
notable EDOs: 27, 39, 51
{{ LLLLsLLLLsLLLLs }} (MOS)
{{ || || }}
{{ LLLLLsLLsLLLLLs }} (OTC MODMOS)
modes:
|| || {{ LLsLLL LLs LLsLLL }} || ||
|| || {{ LsLLLL LsL LsLLLL }} || ||
|| || {{ sLLLLL sLL sLLLLL }} || ||
|| || {{ LLLLLs LLs LLLLLs }} || ||
|| || {{ LLLLsL LsL LLLLsL }} || ||
|| || {{ LLLsLL sLL LLLsLL }} || ||
|| {{ LLs LLsLLL LLsLLL }} || || ||
|| {{ LsL LsLLLL LsLLLL }} || || ||
|| {{ sLL sLLLLL sLLLLL }} || || ||
|| {{ LLs LLLLLs LLLLLs }} || || ||
|| {{ LsL LLLLsL LLLLsL }} || || {{ LsLLLL LsLLLL LsL }} ||
|| {{ sLL LLLsLL LLLsLL }} || || {{ sLLLLL sLLLLL sLL }} ||
|| || || {{ LLLLLs LLLLLs LLs }} ||
|| || || {{ LLLLsL LLLLsL LsL }} ||
|| || || {{ LLLsLL LLLsLL sLL }} ||
==17 tones (7+3+7)==
===[[5L 12s|5L+12s]]===
[[Superpyth]] / ultrapyth MOS. Imperfect, best at low L/s. Many modes may be split two ways.
generator = 2L+5s
notable EDOs: 22, 27, 32, 37, 39
modes:
|| {{ Lss LssLsss LssLsss }} || || ||
|| {{ ssL ssLsssL ssLsssL }} || || {{ ssLssLs ssLssLs ssL }} ||
|| {{ sLs sLsssLs sLsssLs }} || || {{ sLssLss sLssLss sLs }} ||
|| {{ Lss LsssLss LsssLss }} || || {{ LssLsss LssLsss Lss }} ||
|| {{ sLs ssLssLs ssLssLs }} || || {{ sLsssLs sLsssLs sLs }} ||
|| {{ Lss sLssLss sLssLss }} || || {{ LsssLss LsssLss Lss }} ||
|| || || {{ sssLssL sssLssL ssL }} ||
|| || {{ ssLssLs ssL ssLssLs }} || {{ ssLssLs ssLssLs sLs }} ||
|| || {{ sLssLss sLs sLssLss }} || {{ sLssLss sLssLss Lss }}||
|| || {{ LssLsss Lss LssLsss }} || ||
|| || {{ ssLsssL ssL ssLsssL }} || ||
|| || {{ sLsssLs sLs sLsssLs }} || ||
|| || {{ LsssLss Lss LsssLss }} || ||
|| || {{ sssLssL ssL sssLssL }} || ||
|| || {{ sssLssL ssL sssLssL }} || ||
|| {{ ssL ssLssLs ssLssLs }} || {{ ssLssLs sLs ssLssLs }} || ||
|| {{ sLs sLssLss sLssLss }} || {{ sLssLss Lss sLssLss }} || ||
===[[12L 5s|12L+5s]]===
Helmholtz / [[Schismatic family|schismatic]] MOS; full L/s range very good [[{$page}#ref1|(1)]]
Pythagorean (3-limit JI): L=256/243, s=531441/524288
P = 3.8459060415
generator = 5L+2s
notable EDOs: 29, 41, 46, 53, 65
modes:
|| {{ LLs LLsLLsL LLsLLsL }} || {{ LLsLLsL LsL LLsLLsL }} || ||
|| {{ LsL LsLLsLL LsLLsLL }} || {{ LsLLsLL sLL LsLLsLL }} || ||
|| {{ sLL sLLsLLL sLLsLLL }} || || ||
|| {{ LLs LLsLLLs LLsLLLs }} || || {{ LLsLLsL LLsLLsL LLs }} ||
|| {{ LsL LsLLLsL LsLLLsL }} || || {{ LsLLsLL LsLLsLL LsL }} ||
|| {{ sLL sLLLsLL sLLLsLL }} || || {{ sLLsLLL sLLsLLL sLL }} ||
|| {{ LLs LLLsLLs LLLsLLs }} || || {{ LLsLLLs LLsLLLs LLs }} ||
|| {{ LsL LLsLLsL LLsLLsL }} || || {{ LsLLLsL LsLLLsL LsL }} ||
|| {{ sLL LsLLsLL LsLLsLL }} || || {{ sLLLsLL sLLLsLL sLL }} ||
|| || || {{ LLLsLLs LLLsLLs LLs }} ||
|| || {{ LLsLLsL LLs LLsLLsL }} || {{ LLsLLsL LLsLLsL LsL }} ||
|| || {{ LsLLsLL LsL LsLLsLL }} || {{ LsLLsLL LsLLsLL sLL }} ||
|| || {{ sLLsLLL sLL sLLsLLL }} || ||
|| || {{ LLsLLLs LLs LLsLLLs }} || ||
|| || {{ LsLLLsL LsL LsLLLsL }} || ||
|| || {{ sLLLsLL sLL sLLLsLL }} || ||
|| || {{ LLLsLLs LLs LLLsLLs }} || ||
===[[7L 10s|7L+10s]]===
[[Mohajira]] / [[Neutral third scales|neutral-thirds]] MODMOS; full L/s range good
P = 1.5872804832
generator = 2L+3s
notable EDOs: 24, 31, 41, 65
{{ ssLsLssLsLssLsLsL }} (MOS)
{{ || || || }}
{{ ssLLssLssLssLLssL }} (OTC MODMOS)
modes:
|| {{ Lss LssLssL LssLssL }} || {{ LssLssL ssL LssLssL }} || ||
|| {{ ssL ssLssLL ssLssLL }} || || ||
|| {{ sLs sLssLLs sLssLLs }} || || ||
|| {{ Lss LssLLss LssLLss }} || || ||
|| {{ ssL ssLLssL ssLLssL }} || || {{ ssLssLL ssLssLL ssL }} ||
|| {{ sLs sLLssLs sLLssLs }} || || {{ sLssLLs sLssLLs sLs }} ||
|| {{ Lss LLssLss LLssLss }} || || {{ LssLLss LssLLss Lss }} ||
|| {{ ssL LssLssL LssLssL }} || || {{ ssLLssL ssLLssL ssL }} ||
|| || || {{ sLLssLs sLLssLs sLs }} ||
|| || || {{ LLssLss LLssLss Lss }} ||
|| || {{ LssLssL Lss LssLssL }} || {{ LssLssL LssLssL ssL }} ||
|| || {{ ssLssLL ssL ssLssLL }} || ||
|| || {{ sLssLLs sLs sLssLLs }} || ||
|| || {{ LssLLss Lss LssLLss }} || ||
|| || {{ ssLLssL ssL ssLLssL }} || ||
|| || {{ sLLssLs sLs sLLssLs }} || ||
|| || {{ LLssLss Lss LLssLss }} || ||
===[[10L 7s|10L+7s]]===
Beatles? / [[Dicot family|dicot]]? MODMOS; imperfect; full L/s range mostly good
generator = 3L+2s
notable EDOs: 27, 37, 44, 61
{{ sLsLsLLsLsLLsLsLL }} (MOS)
{{ || || || }}
{{ ssLLsLLssLLsLLsLL }} (OTC MODMOS)
modes:
|| {{ sLL sLLsLLs sLLsLLs }} || {{ sLLsLLs LLs sLLsLLs }} || ||
|| {{ LLs LLsLLss LLsLLss }} || || ||
|| {{ LsL LsLLssL LsLLssL }} || || ||
|| {{ sLL sLLssLL sLLssLL }} || || {{ sLLsLLs sLLsLLs sLL }} ||
|| {{ LLs LLssLLs LLssLLs }} || || {{ LLsLLss LLsLLss LLs }} ||
|| {{ LsL LssLLsL LssLLsL }} || || {{ LsLLssL LsLLssL LsL }} ||
|| {{ sLL ssLLsLL ssLLsLL }} || || {{ sLLssLL sLLssLL sLL }} ||
|| {{ LLs sLLsLLs sLLsLLs }} || || {{ LLssLLs LLssLLs LLs }} ||
|| || || {{ LssLLsL LssLLsL LsL }} ||
|| || || {{ ssLLsLL ssLLsLL sLL }} ||
|| || {{ sLLsLLs sLL sLLsLLs }} || {{ sLLsLLs sLLsLLs LLs }} ||
|| || {{ LLsLLss LLs LLsLLss }} || ||
|| || {{ LsLLssL LsL LsLLssL }} || ||
|| || {{ sLLssLL sLL sLLssLL }} || ||
|| || {{ LLssLLs LLs LLssLLs }} || ||
|| || {{ LssLLsL LsL LssLLsL }} || ||
|| || {{ ssLLsLL sLL ssLLsLL }} || ||
==18 tones (7+4+7)==
===[[7L 11s|7L+11s]]===
Sixix?; best for L/s>2
P = 5.968201208
generator = 2L+3s
notable EDOs: 25, 32, 39, 46, 53
{{ LsLssLsLssLsLssLss }} (MOS)
{{ || | | || }}
{{ LLsssLsLLsssLsssLs }} (OTC MODMOS?)
modes:
|| || {{ LsssLsL Lsss LsssLsL }} || ||
|| || {{ sssLsLL sssL sssLsLL }} || ||
|| || {{ ssLsLLs ssLs ssLsLLs }} || ||
|| || {{ sLsLLss sLss sLsLLss }} || ||
|| || {{ LsLLsss Lsss LsLLsss }} || ||
|| || {{ sLLsssL sssL sLLsssL }} || ||
|| || {{ LLsssLs ssLs LLsssLs }} || ||
|| {{ Lsss LsssLsL LsssLsL }} || || ||
|| {{ sssL sssLsLL sssLsLL }} || || ||
|| {{ ssLs ssLsLLs ssLsLLs }} || || ||
|| {{ sLss sLsLLss sLsLLss }} || || ||
|| {{ Lsss LsLLsss LsLLsss }} || || {{ LsssLsL LsssLsL Lsss }} ||
|| {{ sssL sLLsssL sLLsssL }} || || {{ sssLsLL sssLsLL sssL }} ||
|| {{ ssLs LLsssLs LLsssLs }} || || {{ ssLsLLs ssLsLLs ssLs }} ||
|| || || {{ sLsLLss sLsLLss sLss }} ||
|| || || {{ LsLLsss LsLLsss Lsss }} ||
|| || || {{ sLLsssL sLLsssL sssL }} ||
|| || || {{ LLsssLs LLsssLs ssLs }} ||
==19 tones (8+3+8)==
===[[7L 12s|7L+12s]]===
[[Meantone family#Flattone|Flattone]] MOS; [[{$page}#perfect|P]]<0; [[{$page}#ref1|(1)]]
generator = 3L+5s
notable EDOs: 26, 33, 40, 45
modes:
|| {{ sLs sLssLssL sLssLssL }} || {{ sLssLssL ssL sLssLssL }} || ||
|| {{ Lss LssLssLs LssLssLs }} || {{ LssLssLs sLs LssLssLs }} || ||
|| {{ ssL ssLssLsL ssLssLsL }} || || ||
|| {{ sLs sLssLsLs sLssLsLs }} || || {{ sLssLssL sLssLssL sLs }} ||
|| {{ Lss LssLsLss LssLsLss }} || || {{ LssLssLs LssLssLs Lss }} ||
|| {{ ssL ssLsLssL ssLsLssL }} || || {{ ssLssLsL ssLssLsL ssL }} ||
|| {{ sLs sLsLssLs sLsLssLs }} || || {{ sLssLsLs sLssLsLs sLs }} ||
|| {{ Lss LsLssLss LsLssLss }} || || {{ LssLsLss LssLsLss Lss }} ||
|| {{ ssL sLssLssL sLssLssL }} || || {{ ssLsLssL ssLsLssL ssL }} ||
|| {{ sLs LssLssLs LssLssLs }} || || {{ sLsLssLs sLsLssLs sLs }} ||
|| || || {{ LsLssLss LsLssLss Lss }} ||
|| || {{ sLssLssL sLs sLssLssL }} || {{ sLssLssL sLssLssL ssL }} ||
|| || {{ LssLssLs Lss LssLssLs }} || {{ LssLssLs LssLssLs sLs }} ||
|| || {{ ssLssLsL ssL ssLssLsL }} || ||
|| || {{ sLssLsLs sLs sLssLsLs }} || ||
|| || {{ LssLsLss Lss LssLsLss }} || ||
|| || {{ ssLsLssL ssL ssLsLssL }} || ||
|| || {{ sLsLssLs sLs sLsLssLs }} || ||
|| || {{ LsLssLss Lss LsLssLss }} || ||
===[[12L 7s|12L+7s]]===
[[Meantone]] MOS; [[{$page}#perfect|P]]<0 (oddly, neither this scale nor its [[{$page}#dual|dual]] can be tuned with a perfect 3/2!) [[{$page}#ref1|(1)]]
generator = 5L+3s
notable EDOs: 31, 43, 50, 55
modes:
|| {{ LsL LsLLsLLs LsLLsLLs }} || {{ LsLLsLLs LLs LsLLsLLs }} || ||
|| {{ sLL sLLsLLsL sLLsLLsL }} || {{ sLLsLLsL LsL sLLsLLsL }} || ||
|| {{ LLs LLsLLsLs LLsLLsLs }} || || ||
|| {{ LsL LsLLsLsL LsLLsLsL }} || || {{ LsLLsLLs LsLLsLLs LsL }} ||
|| {{ sLL sLLsLsLL sLLsLsLL }} || || {{ sLLsLLsL sLLsLLsL sLL }} ||
|| {{ LLs LLsLsLLs LLsLsLLs }} || || {{ LLsLLsLs LLsLLsLs LLs }} ||
|| {{ LsL LsLsLLsL LsLsLLsL }} || || {{ LsLLsLsL LsLLsLsL LsL }} ||
|| {{ sLL sLsLLsLL sLsLLsLL }} || || {{ sLLsLsLL sLLsLsLL sLL }} ||
|| {{ LLs LsLLsLLs LsLLsLLs }} || || {{ LLsLsLLs LLsLsLLs LLs }} ||
|| {{ LsL sLLsLLsL sLLsLLsL }} || || {{ LsLsLLsL LsLsLLsL LsL }} ||
|| || || {{ sLsLLsLL sLsLLsLL sLL }} ||
|| || {{ LsLLsLLs LsL LsLLsLLs }} || {{ LsLLsLLs LsLLsLLs LLs }} ||
|| || {{ sLLsLLsL sLL sLLsLLsL }} || {{ sLLsLLsL sLLsLLsL LsL }} ||
|| || {{ LLsLLsLs LLs LLsLLsLs }} || ||
|| || {{ LsLLsLsL LsL LsLLsLsL }} || ||
|| || {{ sLLsLsLL sLL sLLsLsLL }} || ||
|| || {{ LLsLsLLs LLs LLsLsLLs }} || ||
|| || {{ LsLsLLsL LsL LsLsLLsL }} || ||
|| || {{ sLsLLsLL sLL sLsLLsLL }} || ||
===[[5L 14s|5L+14s]]===
Godzilla? MODMOS; full L/s range good
P = 2.5200335053
generator = L+3s
notable EDOs: 24, 29, 34, 39, 43, 53
{{ sssLsssLsssLsssLssL }} (MOS)
{{ || || }}
{{ ssLssssLssLssssLssL }} (OTC MODMOS)
modes:
|| {{ ssL ssLssLss ssLssLss }} || {{ ssLssLss Lss ssLssLss }} || ||
|| {{ sLs sLssLsss sLssLsss }} || || ||
|| {{ Lss LssLssss LssLssss }} || || ||
|| {{ ssL ssLssssL ssLssssL }} || || {{ ssLssLss ssLssLss ssL }} ||
|| {{ sLs sLssssLs sLssssLs }} || || {{ sLssLsss sLssLsss sLs }} ||
|| {{ Lss LssssLss LssssLss }} || || {{ LssLssss LssLssss Lss }} ||
|| {{ ssL ssssLssL ssssLssL }} || || {{ ssLssssL ssLssssL ssL }} ||
|| {{ sLs sssLssLs sssLssLs }} || || {{ sLssssLs sLssssLs sLs }} ||
|| {{ Lss ssLssLss ssLssLss }} || || {{ LssssLss LssssLss Lss }} ||
|| || || {{ ssssLssL ssssLssL ssL }} ||
|| || || {{ sssLssLs sssLssLs sLs }} ||
|| || {{ ssLssLss ssL ssLssLss }} || {{ ssLssLss ssLssLss Lss }} ||
|| || {{ sLssLsss sLs sLssLsss }} || ||
|| || {{ LssLssss Lss LssLssss }} || ||
|| || {{ ssLssssL ssL ssLssssL }} || ||
|| || {{ sLssssLs sLs sLssssLs }} || ||
|| || {{ LssssLss Lss LssssLss }} || ||
|| || {{ ssssLssL ssL ssssLssL }} || ||
|| || {{ sssLssLs sLs sssLssLs }} || ||
===[[14L 5s|14L+5s]]===
[[Semaphore and godzilla|Semaphore / godzilla]] MODMOS; imperfect; full L/s range good
generator = 3L+s
notable EDOs: 33, 47, 52
{{ LLLsLLLsLLLsLLLsLLs }} (MOS)
{{ || || }}
{{ LLLLsLLsLLLLsLLsLLs }} (OTC MODMOS)
modes:
|| || {{ LLsLLLLs LLs LLsLLLLs }} || ||
|| || {{ LsLLLLsL LsL LsLLLLsL }} || ||
|| || {{ sLLLLsLL sLL sLLLLsLL }} || ||
|| || {{ LLLLsLLs LLs LLLLsLLs }} || ||
|| || {{ LLLsLLsL LsL LLLsLLsL }} || ||
|| {{ LLs LLsLLsLL LLsLLsLL }} || {{ LLsLLsLL sLL LLsLLsLL }} || ||
|| {{ LsL LsLLsLLL LsLLsLLL }} || || ||
|| {{ sLL sLLsLLLL sLLsLLLL }} || || ||
|| {{ LLs LLsLLLLs LLsLLLLs }} || || {{ LLsLLsLL LLsLLsLL LLs }} ||
|| {{ LsL LsLLLLsL LsLLLLsL }} || || {{ LsLLsLLL LsLLsLLL LsL }} ||
|| {{ sLL sLLLLsLL sLLLLsLL }} || || {{ sLLsLLLL sLLsLLLL sLL }} ||
|| {{ LLs LLLLsLLs LLLLsLLs }} || || {{ LLsLLLLs LLsLLLLs LLs }} ||
|| {{ LsL LLLsLLsL LLLsLLsL }} || || {{ LsLLLLsL LsLLLLsL LsL }} ||
|| {{ sLL LLsLLsLL LLsLLsLL }} || || {{ sLLLLsLL sLLLLsLL sLL }} ||
|| || || {{ LLLLsLLs LLLLsLLs LLs }} ||
|| || || {{ LLLsLLsL LLLsLLsL LsL }} ||
|| || {{ LLsLLsLL LLs LLsLLsLL }} || {{ LLsLLsLL LLsLLsLL sLL }} ||
|| || {{ LsLLsLLL LsL LsLLsLLL }} || ||
|| || {{ sLLsLLLL sLL sLLsLLLL }} || ||
==22 tones (9+4+9)==
===[[7L 15s|7L+15s]]===
[[Porcupine]] MODMOS; full L/s range good
P = 2.3809207248
generator = L+2s
notable EDOs: 29, 36, 43, 50, 51
{{ LssLssLssLssLssLssLsss }} (MOS)
{{ |||| |||| }}
{{ LsssLLsssLsssLLsssLsss }} (OTC MODMOS)
modes:
|| || {{ sssLsssLL sssL sssLsssLL }} || ||
|| || {{ ssLsssLLs ssLs ssLsssLLs }} || ||
|| || {{ sLsssLLss sLss sLsssLLss }} || ||
|| || {{ LsssLLsss Lsss LsssLLsss }} || ||
|| || {{ sssLLsssL sssL sssLLsssL }} || ||
|| || {{ ssLLsssLs ssLs ssLLsssLs }} || ||
|| || {{ sLLsssLss sLss sLLsssLss }} || ||
|| || {{ LLsssLsss Lsss LLsssLsss }} || ||
|| {{ Lsss LsssLsssL LsssLsssL }} || {{ LsssLsssL sssL LsssLsssL }} || ||
|| {{ sssL sssLsssLL sssLsssLL }} || || ||
|| {{ ssLs ssLsssLLs ssLsssLLs }} || || ||
|| {{ sLss sLsssLLss sLsssLLss }} || || ||
|| {{ Lsss LsssLLsss LsssLLsss }} || || {{ LsssLsssL LsssLsssL Lsss }} ||
|| {{ sssL sssLLsssL sssLLsssL }} || || {{ sssLsssLL sssLsssLL sssL }} ||
|| {{ ssLs ssLLsssLs ssLLsssLs }} || || {{ ssLsssLLs ssLsssLLs ssLs }} ||
|| {{ sLss sLLsssLss sLLsssLss }} || || {{ sLsssLLss sLsssLLss sLss }} ||
|| {{ Lsss LLsssLsss LLsssLsss }} || || {{ LsssLLsss LsssLLsss Lsss }} ||
|| {{ sssL LsssLsssL LsssLsssL }} || || {{ sssLLsssL sssLLsssL sssL }} ||
|| || || {{ ssLLsssLs ssLLsssLs ssLs }} ||
|| || || {{ sLLsssLss sLLsssLss sLss }} ||
|| || || {{ LLsssLsss LLsssLsss Lsss }} ||
|| || {{ LsssLsssL Lsss LsssLsssL }} || {{ LsssLsssL LsssLsssL sssL }} ||
===[[15L 7s|15L+7s]]===
[[Porcupine]] MODMOS; imperfect; full L/s range mostly good
generator = 2L+s
notable EDOs: 37, 52b, 59
{{ sLLsLLsLLsLLsLLsLLsLLL }} (MOS)
{{ |||| |||| }}
{{ sLLLssLLLsLLLssLLLsLLL }} (OTC MODMOS)
modes:
|| || {{ LLLsLLLss LLLs LLLsLLLss }} || ||
|| || {{ LLsLLLssL LLsL LLsLLLssL }} || ||
|| || {{ LsLLLssLL LsLL LsLLLssLL }} || ||
|| || {{ sLLLssLLL sLLL sLLLssLLL }} || ||
|| || {{ LLLssLLLs LLLs LLLssLLLs }} || ||
|| || {{ LLssLLLsL LLsL LLssLLLsL }} || ||
|| || {{ LssLLLsLL LsLL LssLLLsLL }} || ||
|| || {{ ssLLLsLLL sLLL ssLLLsLLL }} || ||
|| {{ sLLL sLLLsLLLs sLLLsLLLs }} || {{ sLLLsLLLs LLLs sLLLsLLLs }} || ||
|| {{ LLLs LLLsLLLss LLLsLLLss }} || || ||
|| {{ LLsL LLsLLLssL LLsLLLssL }} || || ||
|| {{ LsLL LsLLLssLL LsLLLssLL }} || || ||
|| {{ sLLL sLLLssLLL sLLLssLLL }} || || {{ sLLLsLLLs sLLLsLLLs sLLL }} ||
|| {{ LLLs LLLssLLLs LLLssLLLs }} || || {{ LLLsLLLss LLLsLLLss LLLs }} ||
|| {{ LLsL LLssLLLsL LLssLLLsL }} || || {{ LLsLLLssL LLsLLLssL LLsL }} ||
|| {{ LsLL LssLLLsLL LssLLLsLL }} || || {{ LsLLLssLL LsLLLssLL LsLL }} ||
|| {{ sLLL ssLLLsLLL ssLLLsLLL }} || || {{ sLLLssLLL sLLLssLLL sLLL }} ||
|| {{ LLLs sLLLsLLLs sLLLsLLLs }} || || {{ LLLssLLLs LLLssLLLs LLLs }} ||
|| || || {{ LLssLLLsL LLssLLLsL LLsL }} ||
|| || || {{ LssLLLsLL LssLLLsLL LsLL }} ||
|| || || {{ ssLLLsLLL ssLLLsLLL sLLL }} ||
|| || {{ sLLLsLLLs sLLL sLLLsLLLs }} || {{ sLLLsLLLs sLLLsLLLs LLLs }} ||
===[[12L 10s|12L+10s]]===
[[Pajara]] / [[Diaschismic family|srutal (diaschismic)]] MODMOS [[{$page}#ref1|(1)]]
P = 7.6918120831
generator = L+s
period = 1/2 octave
notable EDOs: 34, 46, 56, 58, 70
{{ sLsLsLsLsLLsLsLsLsLsLL }} (MOS)
{{ || }}
{{ sLsLsLsLsLsLLsLsLsLsLL }} (OTC MODMOS)
modes:
|| {{ LsLs LsLsLsLsL LsLsLsLsL }} || {{ LsLsLsLsL sLsL LsLsLsLsL }} || ||
|| {{ sLsL sLsLsLsLL sLsLsLsLL }} || || ||
|| {{ LsLs LsLsLsLLs LsLsLsLLs }} || || ||
|| {{ sLsL sLsLsLLsL sLsLsLLsL }} || || ||
|| {{ LsLs LsLsLLsLs LsLsLLsLs }} || || {{ LsLsLsLsL LsLsLsLsL LsLs }} ||
|| {{ sLsL sLsLLsLsL sLsLLsLsL }} || || {{ sLsLsLsLL sLsLsLsLL sLsL }} ||
|| {{ LsLs LsLLsLsLs LsLLsLsLs }} || || {{ LsLsLsLLs LsLsLsLLs LsLs }} ||
|| {{ sLsL sLLsLsLsL sLLsLsLsL }} || || {{ sLsLsLLsL sLsLsLLsL sLsL }} ||
|| {{ LsLs LLsLsLsLs LLsLsLsLs }} || || {{ LsLsLLsLs LsLsLLsLs LsLs }} ||
|| {{ sLsL LsLsLsLsL LsLsLsLsL }} || || {{ sLsLLsLsL sLsLLsLsL sLsL }} ||
|| || || {{ LsLLsLsLs LsLLsLsLs LsLs }} ||
|| || || {{ sLLsLsLsL sLLsLsLsL sLsL }} ||
|| || || {{ LLsLsLsLs LLsLsLsLs LsLs }} ||
|| || {{ LsLsLsLsL LsLs LsLsLsLsL }} || {{ LsLsLsLsL LsLsLsLsL sLsL }} ||
|| || {{ sLsLsLsLL sLsL sLsLsLsLL }} || ||
|| || {{ LsLsLsLLs LsLs LsLsLsLLs }} || ||
|| || {{ sLsLsLLsL sLsL sLsLsLLsL }} || ||
|| || {{ LsLsLLsLs LsLs LsLsLLsLs }} || ||
|| || {{ sLsLLsLsL sLsL sLsLLsLsL }} || ||
|| || {{ LsLLsLsLs LsLs LsLLsLsLs }} || ||
|| || {{ sLLsLsLsL sLsL sLLsLsLsL }} || ||
|| || {{ LLsLsLsLs LsLs LLsLsLsLs }} || ||
===[[10L 12s|10L+12s]]===
Pajara? MODMOS; imperfect; full L/s range good
notable EDOs: 32, 42, 54
generator = L+s
period = 1/2 octave
{{ LsLsLsLsLssLsLsLsLsLss }} (MOS)
{{ || }}
{{ LsLsLsLsLsLssLsLsLsLss }} (OTC MODMOS)
modes:
|| {{ sLsL sLsLsLsLs sLsLsLsLs }} || {{ sLsLsLsLs LsLs sLsLsLsLs }} || ||
|| {{ LsLs LsLsLsLss LsLsLsLss }} || || ||
|| {{ sLsL sLsLsLssL sLsLsLssL }} || || ||
|| {{ LsLs LsLsLssLs LsLsLssLs }} || || ||
|| {{ sLsL sLsLssLsL sLsLssLsL }} || || {{ sLsLsLsLs sLsLsLsLs sLsL }} ||
|| {{ LsLs LsLssLsLs LsLssLsLs }} || || {{ LsLsLsLss LsLsLsLss LsLs }} ||
|| {{ sLsL sLssLsLsL sLssLsLsL }} || || {{ sLsLsLssL sLsLsLssL sLsL }} ||
|| {{ LsLs LssLsLsLs LssLsLsLs }} || || {{ LsLsLssLs LsLsLssLs LsLs }} ||
|| {{ sLsL ssLsLsLsL ssLsLsLsL }} || || {{ sLsLssLsL sLsLssLsL sLsL }} ||
|| {{ LsLs sLsLsLsLs sLsLsLsLs }} || || {{ LsLssLsLs LsLssLsLs LsLs }} ||
|| || || {{ sLssLsLsL sLssLsLsL sLsL }} ||
|| || || {{ LssLsLsLs LssLsLsLs LsLs }} ||
|| || || {{ ssLsLsLsL ssLsLsLsL sLsL }} ||
|| || {{ sLsLsLsLs sLsL sLsLsLsLs }} || {{ sLsLsLsLs sLsLsLsLs LsLs }} ||
|| || {{ LsLsLsLss LsLs LsLsLsLss }} || ||
|| || {{ sLsLsLssL sLsL sLsLsLssL }} || ||
|| || {{ LsLsLssLs LsLs LsLsLssLs }} || ||
|| || {{ sLsLssLsL sLsL sLsLssLsL }} || ||
|| || {{ LsLssLsLs LsLs LsLssLsLs }} || ||
|| || {{ sLssLsLsL sLsL sLssLsLsL }} || ||
|| || {{ LssLsLsLs LsLs LssLsLsLs }} || ||
|| || {{ ssLsLsLsL sLsL ssLsLsLsL }} || ||
----
=Scales with 3 step sizes=
===22-tone Indian 'sruti' scale===
Pythagorean (3-limit JI)
||= **scale step** ||= **ratio** ||> **cents** ||
||= 0 ||= 1/1 ||> 0.000 ||
||= 1 ||= 256/243 ||> 90.225 ||
||= 2 ||= 16/15 ||> 111.731 ||
||= 3 ||= 10/9 ||> 182.404 ||
||= 4 ||= 9/8 ||> 203.910 ||
||= 5 ||= 32/27 ||> 294.135 ||
||= 6 ||= 6/5 ||> 315.641 ||
||= 7 ||= 5/4 ||> 386.314 ||
||= 8 ||= 81/64 ||> 407.820 ||
||= 9 ||= 4/3 ||> 498.045 ||
||= 10 ||= 27/20 ||> 519.551 ||
||= 11 ||= 45/32 ||> 590.224 ||
||= 12 ||= 729/512 ||> 611.730 ||
||= 13 ||= 3/2 ||> 701.955 ||
||= 14 ||= 128/81 ||> 792.180 ||
||= 15 ||= 8/5 ||> 813.686 ||
||= 16 ||= 5/3 ||> 884.359 ||
||= 17 ||= 27/16 ||> 905.865 ||
||= 18 ||= 16/9 ||> 996.090 ||
||= 19 ||= 9/5 ||> 1017.596 ||
||= 20 ||= 15/8 ||> 1088.269 ||
||= 21 ||= 243/128 ||> 1109.775 ||
||= 22 ||= 2/1 ||> 1200.000 ||
A = 256/243
b = 81/80
c = 25/24
A+2b+c = 9/8
3A+4b+2c = 4/3
7A+10b+5c = 2/1
modes:
|| {{ Abcb AbcbAbcbA AbcbAbcbA }} || {{ AbcbAbcbA bcbA AbcbAbcbA }} || ||
|| {{ bcbA bcbAbcbAA bcbAbcbAA }} || || ||
|| {{ cbAb cbAbcbAAb cbAbcbAAb }} || || ||
|| {{ bAbc bAbcbAAbc bAbcbAAbc }} || || ||
|| {{ Abcb AbcbAAbcb AbcbAAbcb }} || || {{ AbcbAbcbA AbcbAbcbA Abcb }} ||
|| {{ bcbA bcbAAbcbA bcbAAbcbA }} || || {{ bcbAbcbAA bcbAbcbAA bcbA }} ||
|| {{ cbAb cbAAbcbAb cbAAbcbAb }} || || {{ cbAbcbAAb cbAbcbAAb cbAb }} ||
|| {{ bAbc bAAbcbAbc bAAbcbAbc }} || || {{ bAbcbAAbc bAbcbAAbc bAbc }} ||
|| {{ Abcb AAbcbAbcb AAbcbAbcb }} || || {{ AbcbAAbcb AbcbAAbcb Abcb }} ||
|| {{ bcbA AbcbAbcbA AbcbAbcbA }} || || {{ bcbAAbcbA bcbAAbcbA bcbA }} ||
|| || || {{ cbAAbcbAb cbAAbcbAb cbAb }} ||
|| || || {{ bAAbcbAbc bAAbcbAbc bAbc }} ||
|| || || {{ AAbcbAbcb AAbcbAbcb Abcb }} ||
|| || {{ AbcbAbcbA Abcb AbcbAbcbA }} || {{ AbcbAbcbA AbcbAbcbA bcbA }} ||
|| || {{ bcbAbcbAA bcbA bcbAbcbAA }} || ||
|| || {{ cbAbcbAAb cbAb cbAbcbAAb }} || ||
|| || {{ bAbcbAAbc bAbc bAbcbAAbc }} || ||
|| || {{ AbcbAAbcb Abcb AbcbAAbcb }} || ||
|| || {{ bcbAAbcbA bcbA bcbAAbcbA }} || ||
|| || {{ cbAAbcbAb cbAb cbAAbcbAb }} || ||
|| || {{ bAAbcbAbc bAbc bAAbcbAbc }} || ||
|| || {{ AAbcbAbcb Abcb AAbcbAbcb }} || ||
----
=Definitions and formulas=
**"Omnitetrachordal"** (OTC for short): see [[Omnitetrachordality]].
[[#dual]]**"Dual"** refers to the "inverse" of a L+s scale pattern, where every L is replaced by s, and vice versa. For example, {{ sLssL }} and {{ LsLLs }} are duals.
[[#perfect]]**"Perfect"** means that values for L and s exist such that L > s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both). (See also [[Eigenmonzo subgroup]].) In this case the value **"P"** is given, where P = L/s. For a perfect scale, P > 1. Note that if a scale "a" is perfect (P<span style="vertical-align: sub;">a</span> ``=`` L/s), its dual "b" will have the value P<span style="vertical-align: sub;">b</span> ``=`` s/L = 1/P<span style="vertical-align: sub;">a</span>, and therefore must be imperfect (if P<span style="vertical-align: sub;">a</span> > 1, then P<span style="vertical-align: sub;">b</span> < 1 ).
In some cases, P may be less than zero. I'm not yet sure what this means :)
The value of P is calculated as follows:
a = the number of L steps per 2/1
b = the number of s steps per 2/1
c = the number of L steps per 3/2
d = the number of s steps per 3/2
x = log<span style="vertical-align: sub;">2</span>(3/2) = ~0.58496 octaves = ~701.955 cents
aL+bs = log<span style="vertical-align: sub;">2</span>(2/1) = 1
cL+ds = x
s = (c-ax)/(bc-ad)
L = (x-ds)/c
P = L/s
**"L/s range"**: For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended.
----
=References=
* [[#ref1]](1) Several of these scales were noted as omnitetrachordal by Paul Erlich in 2002 (if not before). 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]].
Original HTML content:
<html><head><title>Gallery of omnitetrachordal scales</title></head><body><!-- ws:start:WikiTextTocRule:136:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 1em;"><a href="#Scales with two step sizes">Scales with two step sizes</a></div>
<!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-5 tones (2+1+2)">5 tones (2+1+2)</a></div>
<!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-5 tones (2+1+2)-2L+3s">2L+3s</a></div>
<!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-5 tones (2+1+2)-3L+2s">3L+2s</a></div>
<!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-7 tones (3+1+3)">7 tones (3+1+3)</a></div>
<!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-7 tones (3+1+3)-2L+5s">2L+5s</a></div>
<!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-7 tones (3+1+3)-5L+2s">5L+2s</a></div>
<!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-10 tones (4+2+4)">10 tones (4+2+4)</a></div>
<!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-10 tones (4+2+4)-5L+5s">5L+5s</a></div>
<!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-10 tones (4+2+4)-7L+3s">7L+3s</a></div>
<!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-10 tones (4+2+4)-3L+7s">3L+7s</a></div>
<!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-10 tones (4+2+4)-2L+8s">2L+8s</a></div>
<!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-10 tones (4+2+4)-8L+2s">8L+2s</a></div>
<!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-12 tones (5-2-5)">12 tones (5-2-5)</a></div>
<!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-12 tones (5-2-5)-5L+7s">5L+7s</a></div>
<!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-12 tones (5-2-5)-7L+5s">7L+5s</a></div>
<!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-12 tones (5-2-5)-10L+2s">10L+2s</a></div>
<!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-12 tones (5-2-5)-2L+10s">2L+10s</a></div>
<!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-13 tones (5+3+5)">13 tones (5+3+5)</a></div>
<!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-13 tones (5+3+5)-7L+6s">7L+6s</a></div>
<!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-14 tones (6+2+6)">14 tones (6+2+6)</a></div>
<!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-14 tones (6+2+6)-5L+9s">5L+9s</a></div>
<!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-14 tones (6+2+6)-12L+2s">12L+2s</a></div>
<!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-15 tones (6+3+6)">15 tones (6+3+6)</a></div>
<!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-15 tones (6+3+6)-7L+8s">7L+8s</a></div>
<!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-15 tones (6+3+6)-12L+3s">12L+3s</a></div>
<!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-17 tones (7+3+7)">17 tones (7+3+7)</a></div>
<!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-17 tones (7+3+7)-5L+12s">5L+12s</a></div>
<!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-17 tones (7+3+7)-12L+5s">12L+5s</a></div>
<!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-17 tones (7+3+7)-7L+10s">7L+10s</a></div>
<!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-17 tones (7+3+7)-10L+7s">10L+7s</a></div>
<!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-18 tones (7+4+7)">18 tones (7+4+7)</a></div>
<!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-18 tones (7+4+7)-7L+11s">7L+11s</a></div>
<!-- ws:end:WikiTextTocRule:169 --><!-- ws:start:WikiTextTocRule:170: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-19 tones (8+3+8)">19 tones (8+3+8)</a></div>
<!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-19 tones (8+3+8)-7L+12s">7L+12s</a></div>
<!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-19 tones (8+3+8)-12L+7s">12L+7s</a></div>
<!-- ws:end:WikiTextTocRule:172 --><!-- ws:start:WikiTextTocRule:173: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-19 tones (8+3+8)-5L+14s">5L+14s</a></div>
<!-- ws:end:WikiTextTocRule:173 --><!-- ws:start:WikiTextTocRule:174: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-19 tones (8+3+8)-14L+5s">14L+5s</a></div>
<!-- ws:end:WikiTextTocRule:174 --><!-- ws:start:WikiTextTocRule:175: --><div style="margin-left: 2em;"><a href="#Scales with two step sizes-22 tones (9+4+9)">22 tones (9+4+9)</a></div>
<!-- ws:end:WikiTextTocRule:175 --><!-- ws:start:WikiTextTocRule:176: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-22 tones (9+4+9)-7L+15s">7L+15s</a></div>
<!-- ws:end:WikiTextTocRule:176 --><!-- ws:start:WikiTextTocRule:177: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-22 tones (9+4+9)-15L+7s">15L+7s</a></div>
<!-- ws:end:WikiTextTocRule:177 --><!-- ws:start:WikiTextTocRule:178: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-22 tones (9+4+9)-12L+10s">12L+10s</a></div>
<!-- ws:end:WikiTextTocRule:178 --><!-- ws:start:WikiTextTocRule:179: --><div style="margin-left: 3em;"><a href="#Scales with two step sizes-22 tones (9+4+9)-10L+12s">10L+12s</a></div>
<!-- ws:end:WikiTextTocRule:179 --><!-- ws:start:WikiTextTocRule:180: --><div style="margin-left: 1em;"><a href="#Scales with 3 step sizes">Scales with 3 step sizes</a></div>
<!-- ws:end:WikiTextTocRule:180 --><!-- ws:start:WikiTextTocRule:181: --><div style="margin-left: 3em;"><a href="#Scales with 3 step sizes--22-tone Indian 'sruti' scale">22-tone Indian 'sruti' scale</a></div>
<!-- ws:end:WikiTextTocRule:181 --><!-- ws:start:WikiTextTocRule:182: --><div style="margin-left: 1em;"><a href="#Definitions and formulas">Definitions and formulas</a></div>
<!-- ws:end:WikiTextTocRule:182 --><!-- ws:start:WikiTextTocRule:183: --><div style="margin-left: 1em;"><a href="#References">References</a></div>
<!-- ws:end:WikiTextTocRule:183 --><!-- ws:start:WikiTextTocRule:184: --></div>
<!-- ws:end:WikiTextTocRule:184 --><br />
<!-- ws:start:WikiTextHeadingRule:42:<h1> --><h1 id="toc0"><a name="Scales with two step sizes"></a><!-- ws:end:WikiTextHeadingRule:42 -->Scales with two step sizes</h1>
(not necessarily <a class="wiki_link" href="/MOS">MOS</a> or <a class="wiki_link" href="/Distributional%20Evenness">DE</a>)<br />
These are mostly tempered (irrational) scales. In some cases (usually where the generator is close to a perfect 4/3 or 3/2), a Pythagorean (3-limit <a class="wiki_link" href="/Just%20intonation">JI</a>) version is possible.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:44:<h2> --><h2 id="toc1"><a name="Scales with two step sizes-5 tones (2+1+2)"></a><!-- ws:end:WikiTextHeadingRule:44 -->5 tones (2+1+2)</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:46:<h3> --><h3 id="toc2"><a name="Scales with two step sizes-5 tones (2+1+2)-2L+3s"></a><!-- ws:end:WikiTextHeadingRule:46 --><a class="wiki_link" href="/2L%203s">2L+3s</a></h3>
The familiar classic pentatonic scale. Can include <a class="wiki_link" href="/superpyth">superpyth</a>, <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Pythagorean_tuning" rel="nofollow">Pythagorean</a>, <a class="wiki_link" href="/meantone">meantone</a>, and <a class="wiki_link" href="/Mavila%20Temperament%20Modal%20Harmony">mavila</a> tunings. Is <a class="wiki_link" href="/MOS">MOS</a>. <!-- ws:start:WikiTextVariableComponentRule:03:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:03 --><br />
<br />
Pythagorean (3-limit JI): L=<a class="wiki_link" href="/32_27">32/27</a>, s=9/8<br />
generator = L+s<br />
<!-- ws:start:WikiTextVariableComponentRule:05:[[{$page}#perfect|P]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a><!-- ws:end:WikiTextVariableComponentRule:05 --> = 1.4424745962<br />
notable <a class="wiki_link" href="/EDO">EDO</a>s: 7, 9, 12, 16, 17, 19, 22, 26, 29, 31<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> sL s sL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> Ls s Ls </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> s sL sL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> s Ls Ls </tt><br />
</td>
<td><br />
</td>
<td><tt> sL sL s </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> Ls Ls s </tt><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:48:<h3> --><h3 id="toc3"><a name="Scales with two step sizes-5 tones (2+1+2)-3L+2s"></a><!-- ws:end:WikiTextHeadingRule:48 --><a class="wiki_link" href="/3L%202s">3L+2s</a></h3>
Father? MOS; <!-- ws:start:WikiTextVariableComponentRule:07:[[{$page}#perfect|imperfect]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">imperfect</a><!-- ws:end:WikiTextVariableComponentRule:07 -->; <!-- ws:start:WikiTextVariableComponentRule:09:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:09 --><br />
<br />
generator = L+s<br />
notable EDOs: 8, 11b, 13, 18, 23b<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> Ls L Ls </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sL L sL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> L Ls Ls </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> L sL sL </tt><br />
</td>
<td><br />
</td>
<td><tt> Ls Ls L </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sL sL L </tt><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:50:<h2> --><h2 id="toc4"><a name="Scales with two step sizes-7 tones (3+1+3)"></a><!-- ws:end:WikiTextHeadingRule:50 -->7 tones (3+1+3)</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:52:<h3> --><h3 id="toc5"><a name="Scales with two step sizes-7 tones (3+1+3)-2L+5s"></a><!-- ws:end:WikiTextHeadingRule:52 --><a class="wiki_link" href="/2L%205s">2L+5s</a></h3>
<a class="wiki_link" href="/Mavila%20Temperament%20Modal%20Harmony">Mavila</a> diatonic MOS. <!-- ws:start:WikiTextVariableComponentRule:011:[[{$page}#perfect|Imperfect]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">Imperfect</a><!-- ws:end:WikiTextVariableComponentRule:011 -->. <!-- ws:start:WikiTextVariableComponentRule:013:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:013 --><br />
<br />
generator = L+2s<br />
notable EDOs: 9, 11, 16, 23<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> sLs s sLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> Lss s Lss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> s ssL ssL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> s sLs sLs </tt><br />
</td>
<td><br />
</td>
<td><tt> ssL ssL s </tt><br />
</td>
</tr>
<tr>
<td><tt> s Lss Lss </tt><br />
</td>
<td><br />
</td>
<td><tt> sLs sLs s </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> Lss Lss s </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssL s ssL </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:54:<h3> --><h3 id="toc6"><a name="Scales with two step sizes-7 tones (3+1+3)-5L+2s"></a><!-- ws:end:WikiTextHeadingRule:54 --><a class="wiki_link" href="/5L%202s">5L+2s</a></h3>
Classic diatonic scale (<a class="wiki_link" href="/meantone">meantone</a>, Pythagorean, <a class="wiki_link" href="/superpyth">superpyth</a>); MOS. <!-- ws:start:WikiTextVariableComponentRule:015:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:015 --><br />
<br />
Pythagorean (3-limit JI): L=9/8, s=<a class="wiki_link" href="/256_243">256/243</a><br />
P = 2.2600167527<br />
generator = 2L+s<br />
notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc.<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> LLs L LLs </tt><br />
</td>
<td><br />
</td>
<td>Ionian<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsL L LsL </tt><br />
</td>
<td><br />
</td>
<td>Dorian<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLL L sLL </tt><br />
</td>
<td><br />
</td>
<td>Phrygian<br />
</td>
</tr>
<tr>
<td><tt> L LLs LLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>Lydian<br />
</td>
</tr>
<tr>
<td><tt> L LsL LsL </tt><br />
</td>
<td><br />
</td>
<td><tt> LLs LLs L </tt><br />
</td>
<td>Mixolydian<br />
</td>
</tr>
<tr>
<td><tt> L sLL sLL </tt><br />
</td>
<td><br />
</td>
<td><tt> LsL LsL L </tt><br />
</td>
<td>Aeolian<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLL sLL L </tt><br />
</td>
<td>Locrian<br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:56:<h2> --><h2 id="toc7"><a name="Scales with two step sizes-10 tones (4+2+4)"></a><!-- ws:end:WikiTextHeadingRule:56 -->10 tones (4+2+4)</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:58:<h3> --><h3 id="toc8"><a name="Scales with two step sizes-10 tones (4+2+4)-5L+5s"></a><!-- ws:end:WikiTextHeadingRule:58 --><a class="wiki_link" href="/5L%205s">5L+5s</a></h3>
Blackwood MOS. This omnitetrachordal scale has some unusual properties:<br />
<ul><li>it has only two modes</li><li>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)</li><li>it is its own dual (changing all L to s, and vice versa, gives the same scale)</li><li>the (imperfect) tuning of 3/2 is independent of L/s ratio (fixed at exactly 720 cents)</li></ul><br />
generator = s<br />
<a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/5 octave<br />
notable EDOs: 15, 20, 25<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> Ls LsLs LsLs </tt><br />
</td>
<td><tt> LsLs Ls LsLs </tt><br />
</td>
<td><tt> LsLs LsLs Ls </tt><br />
</td>
</tr>
<tr>
<td><tt> sL sLsL sLsL </tt><br />
</td>
<td><tt> sLsL sL sLsL </tt><br />
</td>
<td><tt> sLsL sLsL sL </tt><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:60:<h3> --><h3 id="toc9"><a name="Scales with two step sizes-10 tones (4+2+4)-7L+3s"></a><!-- ws:end:WikiTextHeadingRule:60 --><a class="wiki_link" href="/7L%203s">7L+3s</a></h3>
<a class="wiki_link" href="/Mohajira">Mohajira</a> / <a class="wiki_link" href="/Neutral%20third%20scales">neutral-thirds</a> <a class="wiki_link" href="/MODMOS">MODMOS</a><br />
<br />
P = 2.5872804832<br />
generator = 2L+s<br />
notable EDOs: 17, 24, 27, 31, 41<br />
<br />
<tt> sLLsLLsLLL </tt> (MOS)<br />
<tt> || </tt> <br />
<tt> sLLLsLsLLL </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> LsLL Ls LsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLL sL sLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLs Ls LLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsL sL LLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Ls LsLL LsLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sL sLLL sLLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Ls LLLs LLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLL LsLL Ls </tt><br />
</td>
</tr>
<tr>
<td><tt> sL LLsL LLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLL sLLL sL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLLs LLLs Ls </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLsL LLsL sL </tt><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:62:<h3> --><h3 id="toc10"><a name="Scales with two step sizes-10 tones (4+2+4)-3L+7s"></a><!-- ws:end:WikiTextHeadingRule:62 --><a class="wiki_link" href="/3L%207s">3L+7s</a></h3>
The <!-- ws:start:WikiTextVariableComponentRule:017:[[{$page}#dual|dual]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual">dual</a><!-- ws:end:WikiTextVariableComponentRule:017 --> of 7L+3s, this scale pattern barely qualifies as omnitetrachordal.<br />
<br />
notable EDOs: 13, 16b<br />
<br />
modes: LsssLsLsss, etc.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:64:<h3> --><h3 id="toc11"><a name="Scales with two step sizes-10 tones (4+2+4)-2L+8s"></a><!-- ws:end:WikiTextHeadingRule:64 --><a class="wiki_link" href="/2L%208s">2L+8s</a></h3>
<a class="wiki_link" href="/Pajara">Pajara</a> MODMOS. Best at lower ratios of L/s. <!-- ws:start:WikiTextVariableComponentRule:019:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:019 --><br />
<br />
P = 1.8849491924<br />
generator = s<br />
<a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/2 octave<br />
notable EDOs: 12, 14, 16, 22, 26<br />
<br />
<tt> LssssLssss </tt> (MOS)<br />
<tt> || </tt> <br />
<tt> LsssssLsss </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> sssL ss sssL </tt><br />
</td>
<td><br />
</td>
<td>Standard Pentachordal Minor<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLs ss ssLs </tt><br />
</td>
<td><br />
</td>
<td>-<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLss ss sLss </tt><br />
</td>
<td><br />
</td>
<td>Alternate Pentachordal Major<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> Lsss ss Lsss </tt><br />
</td>
<td><br />
</td>
<td>-<br />
</td>
</tr>
<tr>
<td><tt> ss sssL sssL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>-<br />
</td>
</tr>
<tr>
<td><tt> ss ssLs ssLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>Alternate Pentachordal Minor<br />
</td>
</tr>
<tr>
<td><tt> ss sLss sLss </tt><br />
</td>
<td><br />
</td>
<td><tt> sssL sssL ss </tt><br />
</td>
<td>-<br />
</td>
</tr>
<tr>
<td><tt> ss Lsss Lsss </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLs ssLs ss </tt><br />
</td>
<td>Standard Pentachordal Major<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLss sLss ss </tt><br />
</td>
<td>-<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> Lsss Lsss ss </tt><br />
</td>
<td>-<br />
</td>
</tr>
</table>
(The names of the modes are Paul Erlich's - see <a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow">http://lumma.org/tuning/erlich/erlich-decatonic.pdf</a>.)<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:66:<h3> --><h3 id="toc12"><a name="Scales with two step sizes-10 tones (4+2+4)-8L+2s"></a><!-- ws:end:WikiTextHeadingRule:66 --><a class="wiki_link" href="/8L%202s">8L+2s</a></h3>
The dual of 2L+8s, this scale is imperfect and poorly tuned for 3/2 at any L/s ratio.<br />
<br />
notable EDOs: 18, 26b<br />
<br />
modes: LsLLLLLsLL, etc.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:68:<h2> --><h2 id="toc13"><a name="Scales with two step sizes-12 tones (5-2-5)"></a><!-- ws:end:WikiTextHeadingRule:68 -->12 tones (5-2-5)</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:70:<h3> --><h3 id="toc14"><a name="Scales with two step sizes-12 tones (5-2-5)-5L+7s"></a><!-- ws:end:WikiTextHeadingRule:70 --><a class="wiki_link" href="/5L%207s">5L+7s</a></h3>
12-tone MOS of the helmholtz / garibaldi / <a class="wiki_link" href="/Schismatic%20family">schismatic</a> and <a class="wiki_link" href="/superpyth">superpyth</a> temperaments (slightly sharp 3/2). Very usable at any L/s ratio. Many modes may be pentachordally split in two ways.<br />
<br />
Pythagorean (3-limit JI): L=2187/2048, s=256/243<br />
P = 1.2600167527<br />
generator = 2L+3s<br />
notable EDOs: 17, 22, 27, 29, 41, 53, etc.<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> sLsLs sL sLsLs </tt><br />
</td>
<td><tt> sLsLs sLsLs Ls </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLss Ls LsLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLssL sL sLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLs Ls LssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLsL sL ssLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sL sLsLs sLsLs </tt><br />
</td>
<td><tt> sLsLs Ls sLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Ls LsLss LsLss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sL sLssL sLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLs sLsLs sL </tt><br />
</td>
</tr>
<tr>
<td><tt> Ls LssLs LssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLss LsLss Ls </tt><br />
</td>
</tr>
<tr>
<td><tt> sL ssLsL ssLsL </tt><br />
</td>
<td><tt> sLssL sL ssLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Ls sLsLs sLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLs LssLs Ls </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> ssLsL ssLsL sL </tt><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:72:<h3> --><h3 id="toc15"><a name="Scales with two step sizes-12 tones (5-2-5)-7L+5s"></a><!-- ws:end:WikiTextHeadingRule:72 --><a class="wiki_link" href="/7L%205s">7L+5s</a></h3>
12-tone MOS of the <a class="wiki_link" href="/meantone">meantone</a> and <a class="wiki_link" href="/Meantone%20family#Flattone">flattone</a> temperaments (slightly flat 3/2). <!-- ws:start:WikiTextVariableComponentRule:021:[[{$page}#perfect|Imperfect]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">Imperfect</a><!-- ws:end:WikiTextVariableComponentRule:021 -->, but very usable at any L/s ratio. Many modes may be pentachordally split in two ways.<br />
<br />
generator = 3L+2s<br />
notable EDOs: 19, 26, 31, 33, 43, 45, 50, etc.<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> LsLLs Ls LsLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLsL sL sLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLs Ls LLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Ls LsLsL LsLsL </tt><br />
</td>
<td><tt> LsLsL sL LsLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sL sLsLL sLsLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Ls LsLLs LsLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLsL LsLsL Ls </tt><br />
</td>
</tr>
<tr>
<td><tt> sL sLLsL sLLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLL sLsLL sL </tt><br />
</td>
</tr>
<tr>
<td><tt> Ls LLsLs LLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLLs LsLLs Ls </tt><br />
</td>
</tr>
<tr>
<td><tt> sL LsLsL LsLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLsL sLLsL sL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLsLs LLsLs Ls </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLsL Ls LsLsL </tt><br />
</td>
<td><tt> LsLsL LsLsL sL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLL sL sLsLL </tt><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:74:<h3> --><h3 id="toc16"><a name="Scales with two step sizes-12 tones (5-2-5)-10L+2s"></a><!-- ws:end:WikiTextHeadingRule:74 --><a class="wiki_link" href="/10L%202s">10L+2s</a></h3>
<a class="wiki_link" href="/Pajara">Pajara</a> MODMOS. Good for most any ratio of L to s.<br />
<br />
P = 1.1300083763<br />
generator = L<br />
<a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/2 octave<br />
notable EDOs: 22, 32, 34, 46<br />
<br />
<tt> LLLLLsLLLLLs </tt> (MOS)<br />
<tt> || </tt> <br />
<tt> LLLLLLsLLLLs </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> LL LLLLs LLLLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LL LLLsL LLLsL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LL LLsLL LLsLL </tt><br />
</td>
<td><br />
</td>
<td><tt> LLLLs LLLLs LL </tt><br />
</td>
</tr>
<tr>
<td><tt> LL LsLLL LsLLL </tt><br />
</td>
<td><br />
</td>
<td><tt> LLLsL LLLsL LL </tt><br />
</td>
</tr>
<tr>
<td><tt> LL sLLLL sLLLL </tt><br />
</td>
<td><br />
</td>
<td><tt> LLsLL LLsLL LL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LsLLL LsLLL LL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLLLL sLLLL LL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLLs LL LLLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLsL LL LLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLL LL LLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLL LL LsLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLLL LL sLLLL </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:76:<h3> --><h3 id="toc17"><a name="Scales with two step sizes-12 tones (5-2-5)-2L+10s"></a><!-- ws:end:WikiTextHeadingRule:76 --><a class="wiki_link" href="/2L%2010s">2L+10s</a></h3>
<!-- ws:start:WikiTextVariableComponentRule:023:[[{$page}#dual|Dual]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual">Dual</a><!-- ws:end:WikiTextVariableComponentRule:023 --> of 10L+2s. Probably only useful for small values of L/s.<br />
<br />
notable EDOs: 14, 16<br />
<br />
modes: ssLssssssLss, etc.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:78:<h2> --><h2 id="toc18"><a name="Scales with two step sizes-13 tones (5+3+5)"></a><!-- ws:end:WikiTextHeadingRule:78 -->13 tones (5+3+5)</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:80:<h3> --><h3 id="toc19"><a name="Scales with two step sizes-13 tones (5+3+5)-7L+6s"></a><!-- ws:end:WikiTextHeadingRule:80 --><a class="wiki_link" href="/7L%206s">7L+6s</a></h3>
<a class="wiki_link" href="/Tetracot%20family">Tetracot</a> MODMOS. Best tuned at high values of L/s.<br />
<br />
P = 5.1745609664<br />
generator = L+s<br />
notable EDOs: 20, 27, 34, 41<br />
<br />
<tt> sLsLsLsLsLsLL </tt> (MOS) <br />
<tt> || || || </tt> <br />
<tt> ssLLLssLssLLL </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> Lss LssLL LssLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssL ssLLL ssLLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLs sLLLs sLLLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Lss LLLss LLLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLL LssLL Lss </tt><br />
</td>
</tr>
<tr>
<td><tt> ssL LLssL LLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLLL ssLLL ssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLLLs sLLLs sLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLLss LLLss Lss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLssL LLssL ssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLL Lss LssLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLLL ssL ssLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLLs sLs sLLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLss Lss LLLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLssL ssL LLssL </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:82:<h2> --><h2 id="toc20"><a name="Scales with two step sizes-14 tones (6+2+6)"></a><!-- ws:end:WikiTextHeadingRule:82 -->14 tones (6+2+6)</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:84:<h3> --><h3 id="toc21"><a name="Scales with two step sizes-14 tones (6+2+6)-5L+9s"></a><!-- ws:end:WikiTextHeadingRule:84 --><a class="wiki_link" href="/5L%209s">5L+9s</a></h3>
<a class="wiki_link" href="/Semaphore%20and%20Godzilla">Semaphore / godzilla</a> MODMOS. Usable at any L/s ratio.<br />
<br />
P = 3.5200335053<br />
generator = L+2s<br />
notable EDOs: 19, 24, 29, 33, 34, 53<br />
<br />
<tt> ssLssLssLssLsL </tt> (<a class="wiki_link" href="/MOS">MOS</a>)<br />
<tt> || || </tt><br />
<tt> sssLsLsssLsLsL </tt> (OTC <a class="wiki_link" href="/MODMOS">MODMOS</a>)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> sL sLsLss sLsLss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Ls LsLsss LsLsss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sL sLsssL sLsssL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLss sLsLss sL </tt><br />
</td>
</tr>
<tr>
<td><tt> Ls LsssLs LsssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLsss LsLsss Ls </tt><br />
</td>
</tr>
<tr>
<td><tt> sL sssLsL sssLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsssL sLsssL sL </tt><br />
</td>
</tr>
<tr>
<td><tt> Ls ssLsLs ssLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsssLs LsssLs Ls </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sssLsL sssLsL sL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> ssLsLs ssLsLs Ls </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLss sL sLsLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLsss Ls LsLsss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsssL sL sLsssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsssLs Ls LsssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sssLsL sL sssLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLsLs Ls ssLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:86:<h3> --><h3 id="toc22"><a name="Scales with two step sizes-14 tones (6+2+6)-12L+2s"></a><!-- ws:end:WikiTextHeadingRule:86 --><a class="wiki_link" href="/12L%202s">12L+2s</a></h3>
<a class="wiki_link" href="/Injera">Injera</a> MODMOS. Imperfect (P<0); best for L/s >= 1.5 <!-- ws:start:WikiTextVariableComponentRule:025:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:025 --><br />
<br />
generator = L<br />
<a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/2 octave<br />
notable EDOs: 26, 38, 40, 50<br />
<br />
<tt> LLLLLLsLLLLLLs </tt> (MOS)<br />
<tt> || </tt><br />
<tt> LLLLLLLsLLLLLs </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> LL LLLLLs LLLLLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LL LLLLsL LLLLsL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LL LLLsLL LLLsLL </tt><br />
</td>
<td><br />
</td>
<td><tt> LLLLLs LLLLLs LL </tt><br />
</td>
</tr>
<tr>
<td><tt> LL LLsLLL LLsLLL </tt><br />
</td>
<td><br />
</td>
<td><tt> LLLLsL LLLLsL LL </tt><br />
</td>
</tr>
<tr>
<td><tt> LL LsLLLL LsLLLL </tt><br />
</td>
<td><br />
</td>
<td><tt> LLLsLL LLLsLL LL </tt><br />
</td>
</tr>
<tr>
<td><tt> LL sLLLLL sLLLLL </tt><br />
</td>
<td><br />
</td>
<td><tt> LLsLLL LLsLLL LL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LsLLLL LsLLLL LL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLLLLL sLLLLL LL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLLLs LL LLLLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLLsL LL LLLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLsLL LL LLLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLLL LL LLsLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLLL LL LsLLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLLLL LL sLLLLL </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:88:<h2> --><h2 id="toc23"><a name="Scales with two step sizes-15 tones (6+3+6)"></a><!-- ws:end:WikiTextHeadingRule:88 -->15 tones (6+3+6)</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:90:<h3> --><h3 id="toc24"><a name="Scales with two step sizes-15 tones (6+3+6)-7L+8s"></a><!-- ws:end:WikiTextHeadingRule:90 --><a class="wiki_link" href="/7L%208s">7L+8s</a></h3>
<a class="wiki_link" href="/Porcupine">Porcupine</a> MODMOS<br />
<br />
<!-- ws:start:WikiTextVariableComponentRule:027:[[{$page}#perfect|P]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a><!-- ws:end:WikiTextVariableComponentRule:027 --> = 3.3809207248<br />
generator = L+s<br />
notable EDOs: 22, 29, 36, 37, 43, 65<br />
<br />
<tt> LsLsLsLsLsLsLss </tt> (MOS)<br />
<tt> || || </tt><br />
<tt> LsLLssLsLLssLss </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> LssLsL Lss LssLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLsLL ssL ssLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLLs sLs sLsLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLss Lss LsLLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLssL ssL sLLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLssLs sLs LLssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Lss LssLsL LssLsL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssL ssLsLL ssLsLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLs sLsLLs sLsLLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Lss LsLLss LsLLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLsL LssLsL Lss </tt><br />
</td>
</tr>
<tr>
<td><tt> ssL sLLssL sLLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLsLL ssLsLL ssL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLs LLssLs LLssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLLs sLsLLs sLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LsLLss LsLLss Lss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLLssL sLLssL ssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLssLs LLssLs sLs </tt><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:92:<h3> --><h3 id="toc25"><a name="Scales with two step sizes-15 tones (6+3+6)-12L+3s"></a><!-- ws:end:WikiTextHeadingRule:92 --><a class="wiki_link" href="/12L%203s">12L+3s</a></h3>
<a class="wiki_link" href="/Augmented">Augmented</a> MODMOS. Best at higher L/s ratios.<br />
<br />
P = 12.5377181246<br />
generator = L<br />
period = 1/3 octave<br />
notable EDOs: 27, 39, 51<br />
<br />
<tt> LLLLsLLLLsLLLLs </tt> (MOS)<br />
<tt> || || </tt><br />
<tt> LLLLLsLLsLLLLLs </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> LLsLLL LLs LLsLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLLL LsL LsLLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLLLL sLL sLLLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLLLs LLs LLLLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLLsL LsL LLLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLsLL sLL LLLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LLs LLsLLL LLsLLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LsL LsLLLL LsLLLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLL sLLLLL sLLLLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LLs LLLLLs LLLLLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LsL LLLLsL LLLLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLLLL LsLLLL LsL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLL LLLsLL LLLsLL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLLLL sLLLLL sLL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLLLLs LLLLLs LLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLLLsL LLLLsL LsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLLsLL LLLsLL sLL </tt><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:94:<h2> --><h2 id="toc26"><a name="Scales with two step sizes-17 tones (7+3+7)"></a><!-- ws:end:WikiTextHeadingRule:94 -->17 tones (7+3+7)</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:96:<h3> --><h3 id="toc27"><a name="Scales with two step sizes-17 tones (7+3+7)-5L+12s"></a><!-- ws:end:WikiTextHeadingRule:96 --><a class="wiki_link" href="/5L%2012s">5L+12s</a></h3>
<a class="wiki_link" href="/Superpyth">Superpyth</a> / ultrapyth MOS. Imperfect, best at low L/s. Many modes may be split two ways.<br />
<br />
generator = 2L+5s<br />
notable EDOs: 22, 27, 32, 37, 39<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> Lss LssLsss LssLsss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssL ssLsssL ssLsssL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLssLs ssLssLs ssL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLs sLsssLs sLsssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLssLss sLssLss sLs </tt><br />
</td>
</tr>
<tr>
<td><tt> Lss LsssLss LsssLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLsss LssLsss Lss </tt><br />
</td>
</tr>
<tr>
<td><tt> sLs ssLssLs ssLssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsssLs sLsssLs sLs </tt><br />
</td>
</tr>
<tr>
<td><tt> Lss sLssLss sLssLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LsssLss LsssLss Lss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sssLssL sssLssL ssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLssLs ssL ssLssLs </tt><br />
</td>
<td><tt> ssLssLs ssLssLs sLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLssLss sLs sLssLss </tt><br />
</td>
<td><tt> sLssLss sLssLss Lss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLsss Lss LssLsss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLsssL ssL ssLsssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsssLs sLs sLsssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsssLss Lss LsssLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sssLssL ssL sssLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sssLssL ssL sssLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssL ssLssLs ssLssLs </tt><br />
</td>
<td><tt> ssLssLs sLs ssLssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLs sLssLss sLssLss </tt><br />
</td>
<td><tt> sLssLss Lss sLssLss </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:98:<h3> --><h3 id="toc28"><a name="Scales with two step sizes-17 tones (7+3+7)-12L+5s"></a><!-- ws:end:WikiTextHeadingRule:98 --><a class="wiki_link" href="/12L%205s">12L+5s</a></h3>
Helmholtz / <a class="wiki_link" href="/Schismatic%20family">schismatic</a> MOS; full L/s range very good <!-- ws:start:WikiTextVariableComponentRule:029:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:029 --><br />
<br />
Pythagorean (3-limit JI): L=256/243, s=531441/524288<br />
P = 3.8459060415<br />
generator = 5L+2s<br />
notable EDOs: 29, 41, 46, 53, 65<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> LLs LLsLLsL LLsLLsL </tt><br />
</td>
<td><tt> LLsLLsL LsL LLsLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LsL LsLLsLL LsLLsLL </tt><br />
</td>
<td><tt> LsLLsLL sLL LsLLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLL sLLsLLL sLLsLLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LLs LLsLLLs LLsLLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LLsLLsL LLsLLsL LLs </tt><br />
</td>
</tr>
<tr>
<td><tt> LsL LsLLLsL LsLLLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLLsLL LsLLsLL LsL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLL sLLLsLL sLLLsLL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLsLLL sLLsLLL sLL </tt><br />
</td>
</tr>
<tr>
<td><tt> LLs LLLsLLs LLLsLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LLsLLLs LLsLLLs LLs </tt><br />
</td>
</tr>
<tr>
<td><tt> LsL LLsLLsL LLsLLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLLLsL LsLLLsL LsL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLL LsLLsLL LsLLsLL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLLsLL sLLLsLL sLL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLLsLLs LLLsLLs LLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLLsL LLs LLsLLsL </tt><br />
</td>
<td><tt> LLsLLsL LLsLLsL LsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLsLL LsL LsLLsLL </tt><br />
</td>
<td><tt> LsLLsLL LsLLsLL sLL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLsLLL sLL sLLsLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLLLs LLs LLsLLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLLsL LsL LsLLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLLsLL sLL sLLLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLsLLs LLs LLLsLLs </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:100:<h3> --><h3 id="toc29"><a name="Scales with two step sizes-17 tones (7+3+7)-7L+10s"></a><!-- ws:end:WikiTextHeadingRule:100 --><a class="wiki_link" href="/7L%2010s">7L+10s</a></h3>
<a class="wiki_link" href="/Mohajira">Mohajira</a> / <a class="wiki_link" href="/Neutral%20third%20scales">neutral-thirds</a> MODMOS; full L/s range good<br />
<br />
P = 1.5872804832<br />
generator = 2L+3s<br />
notable EDOs: 24, 31, 41, 65<br />
<br />
<tt> ssLsLssLsLssLsLsL </tt> (MOS)<br />
<tt> || || || </tt><br />
<tt> ssLLssLssLssLLssL </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> Lss LssLssL LssLssL </tt><br />
</td>
<td><tt> LssLssL ssL LssLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssL ssLssLL ssLssLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLs sLssLLs sLssLLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Lss LssLLss LssLLss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssL ssLLssL ssLLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLssLL ssLssLL ssL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLs sLLssLs sLLssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLssLLs sLssLLs sLs </tt><br />
</td>
</tr>
<tr>
<td><tt> Lss LLssLss LLssLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLLss LssLLss Lss </tt><br />
</td>
</tr>
<tr>
<td><tt> ssL LssLssL LssLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLLssL ssLLssL ssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLLssLs sLLssLs sLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLssLss LLssLss Lss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLssL Lss LssLssL </tt><br />
</td>
<td><tt> LssLssL LssLssL ssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLssLL ssL ssLssLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLssLLs sLs sLssLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLLss Lss LssLLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLLssL ssL ssLLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLssLs sLs sLLssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLssLss Lss LLssLss </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:102:<h3> --><h3 id="toc30"><a name="Scales with two step sizes-17 tones (7+3+7)-10L+7s"></a><!-- ws:end:WikiTextHeadingRule:102 --><a class="wiki_link" href="/10L%207s">10L+7s</a></h3>
Beatles? / <a class="wiki_link" href="/Dicot%20family">dicot</a>? MODMOS; imperfect; full L/s range mostly good<br />
<br />
generator = 3L+2s<br />
notable EDOs: 27, 37, 44, 61<br />
<br />
<tt> sLsLsLLsLsLLsLsLL </tt> (MOS)<br />
<tt> || || || </tt><br />
<tt> ssLLsLLssLLsLLsLL </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> sLL sLLsLLs sLLsLLs </tt><br />
</td>
<td><tt> sLLsLLs LLs sLLsLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LLs LLsLLss LLsLLss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LsL LsLLssL LsLLssL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLL sLLssLL sLLssLL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLsLLs sLLsLLs sLL </tt><br />
</td>
</tr>
<tr>
<td><tt> LLs LLssLLs LLssLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LLsLLss LLsLLss LLs </tt><br />
</td>
</tr>
<tr>
<td><tt> LsL LssLLsL LssLLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLLssL LsLLssL LsL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLL ssLLsLL ssLLsLL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLssLL sLLssLL sLL </tt><br />
</td>
</tr>
<tr>
<td><tt> LLs sLLsLLs sLLsLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LLssLLs LLssLLs LLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LssLLsL LssLLsL LsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> ssLLsLL ssLLsLL sLL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLsLLs sLL sLLsLLs </tt><br />
</td>
<td><tt> sLLsLLs sLLsLLs LLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLLss LLs LLsLLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLssL LsL LsLLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLssLL sLL sLLssLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLssLLs LLs LLssLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLLsL LsL LssLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLLsLL sLL ssLLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:104:<h2> --><h2 id="toc31"><a name="Scales with two step sizes-18 tones (7+4+7)"></a><!-- ws:end:WikiTextHeadingRule:104 -->18 tones (7+4+7)</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:106:<h3> --><h3 id="toc32"><a name="Scales with two step sizes-18 tones (7+4+7)-7L+11s"></a><!-- ws:end:WikiTextHeadingRule:106 --><a class="wiki_link" href="/7L%2011s">7L+11s</a></h3>
Sixix?; best for L/s>2<br />
<br />
P = 5.968201208<br />
generator = 2L+3s<br />
notable EDOs: 25, 32, 39, 46, 53<br />
<br />
<tt> LsLssLsLssLsLssLss </tt> (MOS)<br />
<tt> || | | || </tt><br />
<tt> LLsssLsLLsssLsssLs </tt> (OTC MODMOS?)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> LsssLsL Lsss LsssLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sssLsLL sssL sssLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLsLLs ssLs ssLsLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLLss sLss sLsLLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLsss Lsss LsLLsss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLsssL sssL sLLsssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsssLs ssLs LLsssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Lsss LsssLsL LsssLsL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sssL sssLsLL sssLsLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssLs ssLsLLs ssLsLLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLss sLsLLss sLsLLss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Lsss LsLLsss LsLLsss </tt><br />
</td>
<td><br />
</td>
<td><tt> LsssLsL LsssLsL Lsss </tt><br />
</td>
</tr>
<tr>
<td><tt> sssL sLLsssL sLLsssL </tt><br />
</td>
<td><br />
</td>
<td><tt> sssLsLL sssLsLL sssL </tt><br />
</td>
</tr>
<tr>
<td><tt> ssLs LLsssLs LLsssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLsLLs ssLsLLs ssLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLsLLss sLsLLss sLss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LsLLsss LsLLsss Lsss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLLsssL sLLsssL sssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLsssLs LLsssLs ssLs </tt><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:108:<h2> --><h2 id="toc33"><a name="Scales with two step sizes-19 tones (8+3+8)"></a><!-- ws:end:WikiTextHeadingRule:108 -->19 tones (8+3+8)</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:110:<h3> --><h3 id="toc34"><a name="Scales with two step sizes-19 tones (8+3+8)-7L+12s"></a><!-- ws:end:WikiTextHeadingRule:110 --><a class="wiki_link" href="/7L%2012s">7L+12s</a></h3>
<a class="wiki_link" href="/Meantone%20family#Flattone">Flattone</a> MOS; <!-- ws:start:WikiTextVariableComponentRule:031:[[{$page}#perfect|P]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a><!-- ws:end:WikiTextVariableComponentRule:031 --><0; <!-- ws:start:WikiTextVariableComponentRule:033:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:033 --><br />
<br />
generator = 3L+5s<br />
notable EDOs: 26, 33, 40, 45<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> sLs sLssLssL sLssLssL </tt><br />
</td>
<td><tt> sLssLssL ssL sLssLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Lss LssLssLs LssLssLs </tt><br />
</td>
<td><tt> LssLssLs sLs LssLssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssL ssLssLsL ssLssLsL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLs sLssLsLs sLssLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLssLssL sLssLssL sLs </tt><br />
</td>
</tr>
<tr>
<td><tt> Lss LssLsLss LssLsLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLssLs LssLssLs Lss </tt><br />
</td>
</tr>
<tr>
<td><tt> ssL ssLsLssL ssLsLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLssLsL ssLssLsL ssL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLs sLsLssLs sLsLssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLssLsLs sLssLsLs sLs </tt><br />
</td>
</tr>
<tr>
<td><tt> Lss LsLssLss LsLssLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLsLss LssLsLss Lss </tt><br />
</td>
</tr>
<tr>
<td><tt> ssL sLssLssL sLssLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLsLssL ssLsLssL ssL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLs LssLssLs LssLssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLssLs sLsLssLs sLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LsLssLss LsLssLss Lss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLssLssL sLs sLssLssL </tt><br />
</td>
<td><tt> sLssLssL sLssLssL ssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLssLs Lss LssLssLs </tt><br />
</td>
<td><tt> LssLssLs LssLssLs sLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLssLsL ssL ssLssLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLssLsLs sLs sLssLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLsLss Lss LssLsLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLsLssL ssL ssLsLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLssLs sLs sLsLssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLssLss Lss LsLssLss </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:112:<h3> --><h3 id="toc35"><a name="Scales with two step sizes-19 tones (8+3+8)-12L+7s"></a><!-- ws:end:WikiTextHeadingRule:112 --><a class="wiki_link" href="/12L%207s">12L+7s</a></h3>
<a class="wiki_link" href="/Meantone">Meantone</a> MOS; <!-- ws:start:WikiTextVariableComponentRule:035:[[{$page}#perfect|P]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a><!-- ws:end:WikiTextVariableComponentRule:035 --><0 (oddly, neither this scale nor its <!-- ws:start:WikiTextVariableComponentRule:037:[[{$page}#dual|dual]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual">dual</a><!-- ws:end:WikiTextVariableComponentRule:037 --> can be tuned with a perfect 3/2!) <!-- ws:start:WikiTextVariableComponentRule:039:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:039 --><br />
<br />
generator = 5L+3s<br />
notable EDOs: 31, 43, 50, 55<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> LsL LsLLsLLs LsLLsLLs </tt><br />
</td>
<td><tt> LsLLsLLs LLs LsLLsLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLL sLLsLLsL sLLsLLsL </tt><br />
</td>
<td><tt> sLLsLLsL LsL sLLsLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LLs LLsLLsLs LLsLLsLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LsL LsLLsLsL LsLLsLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLLsLLs LsLLsLLs LsL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLL sLLsLsLL sLLsLsLL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLsLLsL sLLsLLsL sLL </tt><br />
</td>
</tr>
<tr>
<td><tt> LLs LLsLsLLs LLsLsLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LLsLLsLs LLsLLsLs LLs </tt><br />
</td>
</tr>
<tr>
<td><tt> LsL LsLsLLsL LsLsLLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLLsLsL LsLLsLsL LsL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLL sLsLLsLL sLsLLsLL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLsLsLL sLLsLsLL sLL </tt><br />
</td>
</tr>
<tr>
<td><tt> LLs LsLLsLLs LsLLsLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LLsLsLLs LLsLsLLs LLs </tt><br />
</td>
</tr>
<tr>
<td><tt> LsL sLLsLLsL sLLsLLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLsLLsL LsLsLLsL LsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLsLLsLL sLsLLsLL sLL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLsLLs LsL LsLLsLLs </tt><br />
</td>
<td><tt> LsLLsLLs LsLLsLLs LLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLsLLsL sLL sLLsLLsL </tt><br />
</td>
<td><tt> sLLsLLsL sLLsLLsL LsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLLsLs LLs LLsLLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLsLsL LsL LsLLsLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLsLsLL sLL sLLsLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLsLLs LLs LLsLsLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLsLLsL LsL LsLsLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLLsLL sLL sLsLLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:114:<h3> --><h3 id="toc36"><a name="Scales with two step sizes-19 tones (8+3+8)-5L+14s"></a><!-- ws:end:WikiTextHeadingRule:114 --><a class="wiki_link" href="/5L%2014s">5L+14s</a></h3>
Godzilla? MODMOS; full L/s range good<br />
<br />
P = 2.5200335053<br />
generator = L+3s<br />
notable EDOs: 24, 29, 34, 39, 43, 53<br />
<br />
<tt> sssLsssLsssLsssLssL </tt> (MOS)<br />
<tt> || || </tt><br />
<tt> ssLssssLssLssssLssL </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> ssL ssLssLss ssLssLss </tt><br />
</td>
<td><tt> ssLssLss Lss ssLssLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLs sLssLsss sLssLsss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Lss LssLssss LssLssss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssL ssLssssL ssLssssL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLssLss ssLssLss ssL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLs sLssssLs sLssssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLssLsss sLssLsss sLs </tt><br />
</td>
</tr>
<tr>
<td><tt> Lss LssssLss LssssLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLssss LssLssss Lss </tt><br />
</td>
</tr>
<tr>
<td><tt> ssL ssssLssL ssssLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLssssL ssLssssL ssL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLs sssLssLs sssLssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLssssLs sLssssLs sLs </tt><br />
</td>
</tr>
<tr>
<td><tt> Lss ssLssLss ssLssLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LssssLss LssssLss Lss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> ssssLssL ssssLssL ssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sssLssLs sssLssLs sLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLssLss ssL ssLssLss </tt><br />
</td>
<td><tt> ssLssLss ssLssLss Lss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLssLsss sLs sLssLsss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLssss Lss LssLssss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLssssL ssL ssLssssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLssssLs sLs sLssssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssssLss Lss LssssLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssssLssL ssL ssssLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sssLssLs sLs sssLssLs </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:116:<h3> --><h3 id="toc37"><a name="Scales with two step sizes-19 tones (8+3+8)-14L+5s"></a><!-- ws:end:WikiTextHeadingRule:116 --><a class="wiki_link" href="/14L%205s">14L+5s</a></h3>
<a class="wiki_link" href="/Semaphore%20and%20godzilla">Semaphore / godzilla</a> MODMOS; imperfect; full L/s range good<br />
<br />
generator = 3L+s<br />
notable EDOs: 33, 47, 52<br />
<br />
<tt> LLLsLLLsLLLsLLLsLLs </tt> (MOS)<br />
<tt> || || </tt><br />
<tt> LLLLsLLsLLLLsLLsLLs </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> LLsLLLLs LLs LLsLLLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLLLsL LsL LsLLLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLLLsLL sLL sLLLLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLLsLLs LLs LLLLsLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLsLLsL LsL LLLsLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LLs LLsLLsLL LLsLLsLL </tt><br />
</td>
<td><tt> LLsLLsLL sLL LLsLLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LsL LsLLsLLL LsLLsLLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLL sLLsLLLL sLLsLLLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LLs LLsLLLLs LLsLLLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LLsLLsLL LLsLLsLL LLs </tt><br />
</td>
</tr>
<tr>
<td><tt> LsL LsLLLLsL LsLLLLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLLsLLL LsLLsLLL LsL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLL sLLLLsLL sLLLLsLL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLsLLLL sLLsLLLL sLL </tt><br />
</td>
</tr>
<tr>
<td><tt> LLs LLLLsLLs LLLLsLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LLsLLLLs LLsLLLLs LLs </tt><br />
</td>
</tr>
<tr>
<td><tt> LsL LLLsLLsL LLLsLLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLLLLsL LsLLLLsL LsL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLL LLsLLsLL LLsLLsLL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLLLsLL sLLLLsLL sLL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLLLsLLs LLLLsLLs LLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLLsLLsL LLLsLLsL LsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLLsLL LLs LLsLLsLL </tt><br />
</td>
<td><tt> LLsLLsLL LLsLLsLL sLL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLsLLL LsL LsLLsLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLsLLLL sLL sLLsLLLL </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:118:<h2> --><h2 id="toc38"><a name="Scales with two step sizes-22 tones (9+4+9)"></a><!-- ws:end:WikiTextHeadingRule:118 -->22 tones (9+4+9)</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:120:<h3> --><h3 id="toc39"><a name="Scales with two step sizes-22 tones (9+4+9)-7L+15s"></a><!-- ws:end:WikiTextHeadingRule:120 --><a class="wiki_link" href="/7L%2015s">7L+15s</a></h3>
<a class="wiki_link" href="/Porcupine">Porcupine</a> MODMOS; full L/s range good<br />
<br />
P = 2.3809207248<br />
generator = L+2s<br />
notable EDOs: 29, 36, 43, 50, 51<br />
<br />
<tt> LssLssLssLssLssLssLsss </tt> (MOS)<br />
<tt> |||| |||| </tt><br />
<tt> LsssLLsssLsssLLsssLsss </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> sssLsssLL sssL sssLsssLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLsssLLs ssLs ssLsssLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsssLLss sLss sLsssLLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsssLLsss Lsss LsssLLsss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sssLLsssL sssL sssLLsssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLLsssLs ssLs ssLLsssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLsssLss sLss sLLsssLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsssLsss Lsss LLsssLsss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Lsss LsssLsssL LsssLsssL </tt><br />
</td>
<td><tt> LsssLsssL sssL LsssLsssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sssL sssLsssLL sssLsssLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssLs ssLsssLLs ssLsssLLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLss sLsssLLss sLsssLLss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Lsss LsssLLsss LsssLLsss </tt><br />
</td>
<td><br />
</td>
<td><tt> LsssLsssL LsssLsssL Lsss </tt><br />
</td>
</tr>
<tr>
<td><tt> sssL sssLLsssL sssLLsssL </tt><br />
</td>
<td><br />
</td>
<td><tt> sssLsssLL sssLsssLL sssL </tt><br />
</td>
</tr>
<tr>
<td><tt> ssLs ssLLsssLs ssLLsssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLsssLLs ssLsssLLs ssLs </tt><br />
</td>
</tr>
<tr>
<td><tt> sLss sLLsssLss sLLsssLss </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsssLLss sLsssLLss sLss </tt><br />
</td>
</tr>
<tr>
<td><tt> Lsss LLsssLsss LLsssLsss </tt><br />
</td>
<td><br />
</td>
<td><tt> LsssLLsss LsssLLsss Lsss </tt><br />
</td>
</tr>
<tr>
<td><tt> sssL LsssLsssL LsssLsssL </tt><br />
</td>
<td><br />
</td>
<td><tt> sssLLsssL sssLLsssL sssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> ssLLsssLs ssLLsssLs ssLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLLsssLss sLLsssLss sLss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLsssLsss LLsssLsss Lsss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsssLsssL Lsss LsssLsssL </tt><br />
</td>
<td><tt> LsssLsssL LsssLsssL sssL </tt><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:122:<h3> --><h3 id="toc40"><a name="Scales with two step sizes-22 tones (9+4+9)-15L+7s"></a><!-- ws:end:WikiTextHeadingRule:122 --><a class="wiki_link" href="/15L%207s">15L+7s</a></h3>
<a class="wiki_link" href="/Porcupine">Porcupine</a> MODMOS; imperfect; full L/s range mostly good<br />
<br />
generator = 2L+s<br />
notable EDOs: 37, 52b, 59<br />
<br />
<tt> sLLsLLsLLsLLsLLsLLsLLL </tt> (MOS)<br />
<tt> |||| |||| </tt><br />
<tt> sLLLssLLLsLLLssLLLsLLL </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> LLLsLLLss LLLs LLLsLLLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLLLssL LLsL LLsLLLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLLssLL LsLL LsLLLssLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLLssLLL sLLL sLLLssLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLLssLLLs LLLs LLLssLLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLssLLLsL LLsL LLssLLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLLLsLL LsLL LssLLLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLLLsLLL sLLL ssLLLsLLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLLL sLLLsLLLs sLLLsLLLs </tt><br />
</td>
<td><tt> sLLLsLLLs LLLs sLLLsLLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LLLs LLLsLLLss LLLsLLLss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LLsL LLsLLLssL LLsLLLssL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LsLL LsLLLssLL LsLLLssLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLLL sLLLssLLL sLLLssLLL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLLsLLLs sLLLsLLLs sLLL </tt><br />
</td>
</tr>
<tr>
<td><tt> LLLs LLLssLLLs LLLssLLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LLLsLLLss LLLsLLLss LLLs </tt><br />
</td>
</tr>
<tr>
<td><tt> LLsL LLssLLLsL LLssLLLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> LLsLLLssL LLsLLLssL LLsL </tt><br />
</td>
</tr>
<tr>
<td><tt> LsLL LssLLLsLL LssLLLsLL </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLLLssLL LsLLLssLL LsLL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLLL ssLLLsLLL ssLLLsLLL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLLssLLL sLLLssLLL sLLL </tt><br />
</td>
</tr>
<tr>
<td><tt> LLLs sLLLsLLLs sLLLsLLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LLLssLLLs LLLssLLLs LLLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLssLLLsL LLssLLLsL LLsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LssLLLsLL LssLLLsLL LsLL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> ssLLLsLLL ssLLLsLLL sLLL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLLsLLLs sLLL sLLLsLLLs </tt><br />
</td>
<td><tt> sLLLsLLLs sLLLsLLLs LLLs </tt><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:124:<h3> --><h3 id="toc41"><a name="Scales with two step sizes-22 tones (9+4+9)-12L+10s"></a><!-- ws:end:WikiTextHeadingRule:124 --><a class="wiki_link" href="/12L%2010s">12L+10s</a></h3>
<a class="wiki_link" href="/Pajara">Pajara</a> / <a class="wiki_link" href="/Diaschismic%20family">srutal (diaschismic)</a> MODMOS <!-- ws:start:WikiTextVariableComponentRule:041:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:041 --> <br />
<br />
P = 7.6918120831<br />
generator = L+s<br />
period = 1/2 octave<br />
notable EDOs: 34, 46, 56, 58, 70<br />
<br />
<tt> sLsLsLsLsLLsLsLsLsLsLL </tt> (MOS)<br />
<tt> || </tt><br />
<tt> sLsLsLsLsLsLLsLsLsLsLL </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> LsLs LsLsLsLsL LsLsLsLsL </tt><br />
</td>
<td><tt> LsLsLsLsL sLsL LsLsLsLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLsL sLsLsLsLL sLsLsLsLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LsLs LsLsLsLLs LsLsLsLLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLsL sLsLsLLsL sLsLsLLsL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LsLs LsLsLLsLs LsLsLLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLsLsLsL LsLsLsLsL LsLs </tt><br />
</td>
</tr>
<tr>
<td><tt> sLsL sLsLLsLsL sLsLLsLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLsLsLL sLsLsLsLL sLsL </tt><br />
</td>
</tr>
<tr>
<td><tt> LsLs LsLLsLsLs LsLLsLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLsLsLLs LsLsLsLLs LsLs </tt><br />
</td>
</tr>
<tr>
<td><tt> sLsL sLLsLsLsL sLLsLsLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLsLLsL sLsLsLLsL sLsL </tt><br />
</td>
</tr>
<tr>
<td><tt> LsLs LLsLsLsLs LLsLsLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLsLLsLs LsLsLLsLs LsLs </tt><br />
</td>
</tr>
<tr>
<td><tt> sLsL LsLsLsLsL LsLsLsLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLLsLsL sLsLLsLsL sLsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LsLLsLsLs LsLLsLsLs LsLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLLsLsLsL sLLsLsLsL sLsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLsLsLsLs LLsLsLsLs LsLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLsLsLsL LsLs LsLsLsLsL </tt><br />
</td>
<td><tt> LsLsLsLsL LsLsLsLsL sLsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLsLsLL sLsL sLsLsLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLsLsLLs LsLs LsLsLsLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLsLLsL sLsL sLsLsLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLsLLsLs LsLs LsLsLLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLLsLsL sLsL sLsLLsLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLsLsLs LsLs LsLLsLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLsLsLsL sLsL sLLsLsLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLsLsLs LsLs LLsLsLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:126:<h3> --><h3 id="toc42"><a name="Scales with two step sizes-22 tones (9+4+9)-10L+12s"></a><!-- ws:end:WikiTextHeadingRule:126 --><a class="wiki_link" href="/10L%2012s">10L+12s</a></h3>
Pajara? MODMOS; imperfect; full L/s range good<br />
<br />
notable EDOs: 32, 42, 54<br />
generator = L+s<br />
period = 1/2 octave<br />
<br />
<tt> LsLsLsLsLssLsLsLsLsLss </tt> (MOS)<br />
<tt> || </tt><br />
<tt> LsLsLsLsLsLssLsLsLsLss </tt> (OTC MODMOS)<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> sLsL sLsLsLsLs sLsLsLsLs </tt><br />
</td>
<td><tt> sLsLsLsLs LsLs sLsLsLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LsLs LsLsLsLss LsLsLsLss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLsL sLsLsLssL sLsLsLssL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LsLs LsLsLssLs LsLsLssLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLsL sLsLssLsL sLsLssLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLsLsLs sLsLsLsLs sLsL </tt><br />
</td>
</tr>
<tr>
<td><tt> LsLs LsLssLsLs LsLssLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLsLsLss LsLsLsLss LsLs </tt><br />
</td>
</tr>
<tr>
<td><tt> sLsL sLssLsLsL sLssLsLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLsLssL sLsLsLssL sLsL </tt><br />
</td>
</tr>
<tr>
<td><tt> LsLs LssLsLsLs LssLsLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLsLssLs LsLsLssLs LsLs </tt><br />
</td>
</tr>
<tr>
<td><tt> sLsL ssLsLsLsL ssLsLsLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLssLsL sLsLssLsL sLsL </tt><br />
</td>
</tr>
<tr>
<td><tt> LsLs sLsLsLsLs sLsLsLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLssLsLs LsLssLsLs LsLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLssLsLsL sLssLsLsL sLsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LssLsLsLs LssLsLsLs LsLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> ssLsLsLsL ssLsLsLsL sLsL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLsLsLs sLsL sLsLsLsLs </tt><br />
</td>
<td><tt> sLsLsLsLs sLsLsLsLs LsLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLsLsLss LsLs LsLsLsLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLsLssL sLsL sLsLsLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLsLssLs LsLs LsLsLssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLssLsL sLsL sLsLssLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLssLsLs LsLs LsLssLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLssLsLsL sLsL sLssLsLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLsLsLs LsLs LssLsLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLsLsLsL sLsL ssLsLsLsL </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<hr />
<br />
<!-- ws:start:WikiTextHeadingRule:128:<h1> --><h1 id="toc43"><a name="Scales with 3 step sizes"></a><!-- ws:end:WikiTextHeadingRule:128 -->Scales with 3 step sizes</h1>
<br />
<!-- ws:start:WikiTextHeadingRule:130:<h3> --><h3 id="toc44"><a name="Scales with 3 step sizes--22-tone Indian 'sruti' scale"></a><!-- ws:end:WikiTextHeadingRule:130 -->22-tone Indian 'sruti' scale</h3>
Pythagorean (3-limit JI)<br />
<br />
<table class="wiki_table">
<tr>
<td style="text-align: center;"><strong>scale step</strong><br />
</td>
<td style="text-align: center;"><strong>ratio</strong><br />
</td>
<td style="text-align: right;"><strong>cents</strong><br />
</td>
</tr>
<tr>
<td style="text-align: center;">0<br />
</td>
<td style="text-align: center;">1/1<br />
</td>
<td style="text-align: right;">0.000<br />
</td>
</tr>
<tr>
<td style="text-align: center;">1<br />
</td>
<td style="text-align: center;">256/243<br />
</td>
<td style="text-align: right;">90.225<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2<br />
</td>
<td style="text-align: center;">16/15<br />
</td>
<td style="text-align: right;">111.731<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3<br />
</td>
<td style="text-align: center;">10/9<br />
</td>
<td style="text-align: right;">182.404<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4<br />
</td>
<td style="text-align: center;">9/8<br />
</td>
<td style="text-align: right;">203.910<br />
</td>
</tr>
<tr>
<td style="text-align: center;">5<br />
</td>
<td style="text-align: center;">32/27<br />
</td>
<td style="text-align: right;">294.135<br />
</td>
</tr>
<tr>
<td style="text-align: center;">6<br />
</td>
<td style="text-align: center;">6/5<br />
</td>
<td style="text-align: right;">315.641<br />
</td>
</tr>
<tr>
<td style="text-align: center;">7<br />
</td>
<td style="text-align: center;">5/4<br />
</td>
<td style="text-align: right;">386.314<br />
</td>
</tr>
<tr>
<td style="text-align: center;">8<br />
</td>
<td style="text-align: center;">81/64<br />
</td>
<td style="text-align: right;">407.820<br />
</td>
</tr>
<tr>
<td style="text-align: center;">9<br />
</td>
<td style="text-align: center;">4/3<br />
</td>
<td style="text-align: right;">498.045<br />
</td>
</tr>
<tr>
<td style="text-align: center;">10<br />
</td>
<td style="text-align: center;">27/20<br />
</td>
<td style="text-align: right;">519.551<br />
</td>
</tr>
<tr>
<td style="text-align: center;">11<br />
</td>
<td style="text-align: center;">45/32<br />
</td>
<td style="text-align: right;">590.224<br />
</td>
</tr>
<tr>
<td style="text-align: center;">12<br />
</td>
<td style="text-align: center;">729/512<br />
</td>
<td style="text-align: right;">611.730<br />
</td>
</tr>
<tr>
<td style="text-align: center;">13<br />
</td>
<td style="text-align: center;">3/2<br />
</td>
<td style="text-align: right;">701.955<br />
</td>
</tr>
<tr>
<td style="text-align: center;">14<br />
</td>
<td style="text-align: center;">128/81<br />
</td>
<td style="text-align: right;">792.180<br />
</td>
</tr>
<tr>
<td style="text-align: center;">15<br />
</td>
<td style="text-align: center;">8/5<br />
</td>
<td style="text-align: right;">813.686<br />
</td>
</tr>
<tr>
<td style="text-align: center;">16<br />
</td>
<td style="text-align: center;">5/3<br />
</td>
<td style="text-align: right;">884.359<br />
</td>
</tr>
<tr>
<td style="text-align: center;">17<br />
</td>
<td style="text-align: center;">27/16<br />
</td>
<td style="text-align: right;">905.865<br />
</td>
</tr>
<tr>
<td style="text-align: center;">18<br />
</td>
<td style="text-align: center;">16/9<br />
</td>
<td style="text-align: right;">996.090<br />
</td>
</tr>
<tr>
<td style="text-align: center;">19<br />
</td>
<td style="text-align: center;">9/5<br />
</td>
<td style="text-align: right;">1017.596<br />
</td>
</tr>
<tr>
<td style="text-align: center;">20<br />
</td>
<td style="text-align: center;">15/8<br />
</td>
<td style="text-align: right;">1088.269<br />
</td>
</tr>
<tr>
<td style="text-align: center;">21<br />
</td>
<td style="text-align: center;">243/128<br />
</td>
<td style="text-align: right;">1109.775<br />
</td>
</tr>
<tr>
<td style="text-align: center;">22<br />
</td>
<td style="text-align: center;">2/1<br />
</td>
<td style="text-align: right;">1200.000<br />
</td>
</tr>
</table>
<br />
A = 256/243<br />
b = 81/80<br />
c = 25/24<br />
A+2b+c = 9/8<br />
3A+4b+2c = 4/3<br />
7A+10b+5c = 2/1<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><tt> Abcb AbcbAbcbA AbcbAbcbA </tt><br />
</td>
<td><tt> AbcbAbcbA bcbA AbcbAbcbA </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> bcbA bcbAbcbAA bcbAbcbAA </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> cbAb cbAbcbAAb cbAbcbAAb </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> bAbc bAbcbAAbc bAbcbAAbc </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Abcb AbcbAAbcb AbcbAAbcb </tt><br />
</td>
<td><br />
</td>
<td><tt> AbcbAbcbA AbcbAbcbA Abcb </tt><br />
</td>
</tr>
<tr>
<td><tt> bcbA bcbAAbcbA bcbAAbcbA </tt><br />
</td>
<td><br />
</td>
<td><tt> bcbAbcbAA bcbAbcbAA bcbA </tt><br />
</td>
</tr>
<tr>
<td><tt> cbAb cbAAbcbAb cbAAbcbAb </tt><br />
</td>
<td><br />
</td>
<td><tt> cbAbcbAAb cbAbcbAAb cbAb </tt><br />
</td>
</tr>
<tr>
<td><tt> bAbc bAAbcbAbc bAAbcbAbc </tt><br />
</td>
<td><br />
</td>
<td><tt> bAbcbAAbc bAbcbAAbc bAbc </tt><br />
</td>
</tr>
<tr>
<td><tt> Abcb AAbcbAbcb AAbcbAbcb </tt><br />
</td>
<td><br />
</td>
<td><tt> AbcbAAbcb AbcbAAbcb Abcb </tt><br />
</td>
</tr>
<tr>
<td><tt> bcbA AbcbAbcbA AbcbAbcbA </tt><br />
</td>
<td><br />
</td>
<td><tt> bcbAAbcbA bcbAAbcbA bcbA </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> cbAAbcbAb cbAAbcbAb cbAb </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> bAAbcbAbc bAAbcbAbc bAbc </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> AAbcbAbcb AAbcbAbcb Abcb </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> AbcbAbcbA Abcb AbcbAbcbA </tt><br />
</td>
<td><tt> AbcbAbcbA AbcbAbcbA bcbA </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> bcbAbcbAA bcbA bcbAbcbAA </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> cbAbcbAAb cbAb cbAbcbAAb </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> bAbcbAAbc bAbc bAbcbAAbc </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> AbcbAAbcb Abcb AbcbAAbcb </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> bcbAAbcbA bcbA bcbAAbcbA </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> cbAAbcbAb cbAb cbAAbcbAb </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> bAAbcbAbc bAbc bAAbcbAbc </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> AAbcbAbcb Abcb AAbcbAbcb </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<hr />
<br />
<!-- ws:start:WikiTextHeadingRule:132:<h1> --><h1 id="toc45"><a name="Definitions and formulas"></a><!-- ws:end:WikiTextHeadingRule:132 -->Definitions and formulas</h1>
<br />
<strong>"Omnitetrachordal"</strong> (OTC for short): see <a class="wiki_link" href="/Omnitetrachordality">Omnitetrachordality</a>.<br />
<br />
<!-- ws:start:WikiTextAnchorRule:185:<img src="/i/anchor.gif" class="WikiAnchor" alt="Anchor" id="wikitext@@anchor@@dual" title="Anchor: dual"/> --><a name="dual"></a><!-- ws:end:WikiTextAnchorRule:185 --><strong>"Dual"</strong> refers to the "inverse" of a L+s scale pattern, where every L is replaced by s, and vice versa. For example, <tt> sLssL </tt> and <tt> LsLLs </tt> are duals.<br />
<br />
<!-- ws:start:WikiTextAnchorRule:186:<img src="/i/anchor.gif" class="WikiAnchor" alt="Anchor" id="wikitext@@anchor@@perfect" title="Anchor: perfect"/> --><a name="perfect"></a><!-- ws:end:WikiTextAnchorRule:186 --><strong>"Perfect"</strong> means that values for L and s exist such that L > s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both). (See also <a class="wiki_link" href="/Eigenmonzo%20subgroup">Eigenmonzo subgroup</a>.) In this case the value <strong>"P"</strong> is given, where P = L/s. For a perfect scale, P > 1. Note that if a scale "a" is perfect (P<span style="vertical-align: sub;">a</span> <!-- ws:start:WikiTextRawRule:00:``=`` -->=<!-- ws:end:WikiTextRawRule:00 --> L/s), its dual "b" will have the value P<span style="vertical-align: sub;">b</span> <!-- ws:start:WikiTextRawRule:01:``=`` -->=<!-- ws:end:WikiTextRawRule:01 --> s/L = 1/P<span style="vertical-align: sub;">a</span>, and therefore must be imperfect (if P<span style="vertical-align: sub;">a</span> > 1, then P<span style="vertical-align: sub;">b</span> < 1 ).<br />
<br />
In some cases, P may be less than zero. I'm not yet sure what this means :)<br />
<br />
The value of P is calculated as follows:<br />
<br />
a = the number of L steps per 2/1<br />
b = the number of s steps per 2/1<br />
c = the number of L steps per 3/2<br />
d = the number of s steps per 3/2<br />
x = log<span style="vertical-align: sub;">2</span>(3/2) = ~0.58496 octaves = ~701.955 cents<br />
<br />
aL+bs = log<span style="vertical-align: sub;">2</span>(2/1) = 1<br />
cL+ds = x<br />
<br />
s = (c-ax)/(bc-ad)<br />
L = (x-ds)/c<br />
P = L/s<br />
<br />
<strong>"L/s range"</strong>: For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended.<br />
<br />
<br />
<hr />
<br />
<!-- ws:start:WikiTextHeadingRule:134:<h1> --><h1 id="toc46"><a name="References"></a><!-- ws:end:WikiTextHeadingRule:134 -->References</h1>
<br />
<ul><li><!-- ws:start:WikiTextAnchorRule:187:<img src="/i/anchor.gif" class="WikiAnchor" alt="Anchor" id="wikitext@@anchor@@ref1" title="Anchor: ref1"/> --><a name="ref1"></a><!-- ws:end:WikiTextAnchorRule:187 -->(1) Several of these scales were noted as omnitetrachordal by Paul Erlich in 2002 (if not before). See tuning-math list messages <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685" rel="nofollow">3685</a> and <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987" rel="nofollow">10987</a>.</li></ul></body></html>