Gallery of omnitetrachordal scales: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-08-13 11:17:52 UTC</tt>.<br>
: The original revision id was <tt>589280430</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc]]


An (incomplete) list of [[Omnitetrachordality|omnitetrachordal]] (OTC) scale patterns.
An (incomplete) list of [[Omnitetrachordality|omnitetrachordal]] (OTC) scales.


-----


=Scales with two step sizes=
=Scales with two step sizes=
(not necessarily [[MOS]] or [[Distributional Evenness|DE]])
(not necessarily [[MOS|MOS]] or [[Distributional_Evenness|DE]])
[[Omnitetrachordal scale|Omnitetrachordal scales]] 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)==
These are mostly tempered (irrational) scales.  For a few patterns (usually where the generator is close to a perfect 4/3 or 3/2), a Pythagorean (3-limit [[Just_intonation|JI]]) version with only two step sizes is possible.


===[[2L 3s|2L+3s]]===
In some cases, multiple OTC patterns with the same number of large and small steps exist.  
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)]]


[[image:TN_05_02_03_sL_s_sL.png link="file:05_02_03_sL_s_sL.png"]]
Follow the links for more detailed info on each scale!


Pythagorean (3-limit JI): L=[[32_27|32/27]], s=9/8
==3 tones==
generator = L+s (480.0 to 600.0 cents)
[[OTC_2L_ns|2L+s]] (the simplest possible OTC scale; s=9/8, L=4/3)
[[{$page}#perfect|P]] = 1.4424745962
notable [[EDO]]s: 7, 9, 12, 16, 17, 19, 22, 26, 29, 31


modes:
==4 tones==
|| || {{ sL s sL }} || ||
(no OTC scales possible)
|| || {{ Ls s Ls }} || ||
|| {{ s sL sL }} || || ||
|| {{ s Ls Ls }} || || {{ sL sL s }} ||
|| || || {{ Ls Ls s }} ||


==5 tones==
[[OTC_2L_3s|2L+3s]] - sLsLs (MOS)


===[[3L 2s|3L+2s]]===
[[OTC_3L_2s|3L+2s]] - LsLsL (MOS)
Father? MOS; [[{$page}#perfect|imperfect]]; [[{$page}#ref1|(1)]]


[[image:TN_05_03_02_Ls_L_Ls.png link="file:05_03_02_Ls_L_Ls.png"]]
==6 tones==
[[OTC_2L_ns|2L+4s]] - LsssLs


generator = L+s (400.0 to 480.0 cents)
==7 tones==
notable EDOs: 8, 11b, 13, 18, 23b
[[OTC_2L_5s|2L+5s]] - sLsssLs (MOS)


modes:
[[OTC_5L_2s|5L+2s]] - LsLLLsL (MOS)
|| || {{ Ls L Ls }} || ||
|| || {{ sL L sL }} || ||
|| {{ L Ls Ls }} || || ||
|| {{ L sL sL }} || || {{ Ls Ls L }} ||
|| || || {{ sL sL L }} ||


==8 tones==
[[OTC_2L_ns|2L+6s]] - LssssLss


==7 tones (3+1+3)==
==9 tones==
[[OTC_2L_ns|2L+7s]] - LsssssLss


===[[2L 5s|2L+5s]]===
==10 tones==
[[Mavila Temperament Modal Harmony|Mavila]] diatonic MOS.  [[{$page}#perfect|Imperfect]].  [[{$page}#ref1|(1)]]
[[OTC_2L_8s|2L+8s]] - LsssssLsss


[[image:TN_07_02_05_sLs_s_sLs.png link="file:07_02_05_sLs_s_sLs.png"]]
[[OTC_3L_7s|3L+7s]] - LsssLsLsss


generator = L+2s (514.3 to 600.0 cents)
[[OTC_5L_5s|5L+5s]] - LsLsLsLsLs (MOS)
notable EDOs: 9, 11, 16, 23


modes:
[[OTC_7L_3s|7L+3s]] - sLLLsLLLsL
|| || {{ 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 }} || ||


[[OTC_8L_2s|8L+2s]] - LLsLLLsLLL


===[[5L 2s|5L+2s]]===
==11 tones==
Classic diatonic scale ([[meantone]], Pythagorean, [[superpyth]]); MOS. [[{$page}#ref1|(1)]]
[[OTC_2L_ns|2L+9s]] - LssssssLsss


[[image:TN_07_05_02_LsL_L_Ls.png link="file:07_05_02_LsL_L_Ls.png"]]
==12 tones==
[[OTC_2L_10s|2L+10s]] - LsssLsssssss (4+4+4), sssLssssLsss (5+2+5)


Pythagorean (3-limit JI): L=9/8, s=[[256_243|256/243]]
[[OTC_5L_7s|5L+7s]] - ssLsLssLsLsL (MOS)
P = 2.2600167527
generator = 2L+s (480.0 to 514.3 cents)
notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc.


modes:
[[OTC_7L_5s|7L+5s]] - LLsLsLLsLsLs (MOS)
|| || {{ 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 ||


[[OTC_10L_2s|10L+2s]] - LLLsLLLLsLLL


==10 tones (4+2+4)==
==13 tones==
[[OTC_2L_ns|2L+11s]] - LsssssssLssss


===[[5L 5s|5L+5s]]===
[[OTC_7L_6s|7L+6s]] - sLLLssLssLLLs
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)


[[image:TN_10_05_05_LsLs_Ls_LsLs.png link="file:10_05_05_LsLs_Ls_LsLs.png"]]
==14 tones==
[[OTC_2L_ns|2L+12s]] - LssssssssLssss


generator = s (0 to 120 cents)
[[OTC_5L_9s|5L+9s]] - sssLsLsssLsLsL
[[periods and generators|period]] = 1/5 octave
notable EDOs: 15, 20, 25


modes:
[[OTC_7L_7s|7L+7s]] - LsLsLsLsLsLsLs (MOS)
|| {{ Ls LsLs LsLs }} || {{ LsLs Ls LsLs }} || {{ LsLs LsLs Ls }} ||
|| {{ sL sLsL sLsL }} || {{ sLsL sL sLsL }} || {{ sLsL sLsL sL }} ||


[[OTC_12L_2s|12L+2s]] - LLLLLLLsLLLLLs


===[[7L 3s|7L+3s]]===
==15 tones==
[[Mohajira]] / [[Neutral third scales|neutral-thirds]] [[MODMOS]]
[[OTC_2L_ns|2L+13s]] - LssssssssLsssss


[[image:TN_10_07_03_sLLL_sL_sLLL.png link="file:10_07_03_sLLL_sL_sLLL.png"]]
[[OTC_7L_8s|7L+8s]] - LsLLssLsLLssLss, LssLLsLssLLsLss


P = 2.5872804832
[[OTC_12L_3s|12L+3s]] - LsLLLLLsLLLLLsL
generator = 2L+s (342.9 to 360.0 cents)
notable EDOs: 17, 24, 27, 31, 41


{{ sLLsLLsLLL }} (MOS)
==16 tones==
{{    ||      }}
[[OTC_2L_ns|2L+14s]] - LsssssssssLsssss
{{ sLLLsLsLLL }} (OTC MODMOS)


modes:
==17 tones==
|| || {{ LsLL Ls LsLL }} || ||
[[OTC_2L_ns|2L+15s]] - LsssssssssLssssss (7+3+7), LssssssssssLsssss (6+5+6)
|| || {{ 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 }} ||


[[OTC_5L_12s|5L+12s]] - sLsssLssLssLsssLs (MOS)


===[[3L 7s|3L+7s]]===
[[OTC_7L_10s|7L+10s]] - sLsLsLssLssLsLsLs, sLssLLssLssLLssLs
The [[{$page}#dual|dual]] of 7L+3s, this scale pattern barely qualifies as omnitetrachordal.


[[image:TN_10_03_07_Lsss_Ls_Lsss.png link="file:10_03_07_Lsss_Ls_Lsss.png"]]
[[OTC_10L_7s|10L+7s]] - LsLsLsLLsLLsLsLsL, LsLLssLLsLLssLLsL


notable EDOs: 13, 16b
[[OTC_12L_5s|12L+5s]] - LsLLLsLLsLLsLLLsL (MOS)


modes: LsssLsLsss, etc.
==18 tones==
[[OTC_2L_ns|2L+16s]] - LssssssssssLssssss


[[OTC_7L_11s|7L+11s]] - LLsssLsLLsssLsssLs, LsssLLsLsssLLsLsss


===[[2L 8s|2L+8s]]===
==19 tones==
[[Pajara]] MODMOS.  Best at lower ratios of L/s.  [[{$page}#ref1|(1)]]
[[OTC_2L_ns|2L+17s]] - LsssssssssssLssssss


[[image:TN_10_02_08_sLss_ss_sLss.png link="file:10_02_08_sLss_ss_sLss.png"]]
[[OTC_5L_14s|5L+14s]] - sLssssLssLssLssssLs


P = 1.8849491924
[[OTC_7L_12s|7L+12s]] - sLssLsLssLssLsLssLs (MOS)
generator = s (0 to 120 cents)
[[periods and generators|period]] = 1/2 octave
notable EDOs: 12, 14, 16, 22, 26


{{ LssssLssss }} (MOS)
[[OTC_10L_9s|10L+9s]] - LsLLsssLLsLLsssLLsL
{{      ||    }}
{{ LsssssLsss }} (OTC MODMOS)


modes:
[[OTC_12L_7s|12L+7s]] - LsLLsLsLLsLLsLsLLsL (MOS)
|| || {{ 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]].)


[[OTC_14L_5s|14L+5s]] - LLLLsLLsLLLLsLLsLLs


===[[8L 2s|8L+2s]]===
[[OTC_17L_2s|17L+2s]] - LLLLLsLLLLLLLsLLLLL
The dual of 2L+8s, this scale is imperfect and poorly tuned for 3/2 at any L/s ratio.


[[image:TN_10_08_02_LsLL_LL_LsLL.png link="file:10_08_02_LsLL_LL_LsLL.png"]]
==20 tones==
[[OTC_2L_ns|2L+18s]] - LsssssssssssLsssssss


notable EDOs: 18, 26b
[[OTC_7L_13s|7L+13s]] - sssLsssLssLLsssLssLL, sssLsssLsLsLsssLsLsL, sssLsssLLssLsssLLssL


modes: LsLLLLLsLL, etc.
[[OTC_12L_8s|12L+8s]] - sLLssLLsLLLssLLsLLLs, sLLssLLLsLLssLLLsLLs, sLsLsLLLsLsLsLLLsLsL


==21 tones==
[[OTC_2L_ns|2L+19s]] - LssssssssssssLsssssss


==12 tones (5-2-5)==
[[OTC_5L_16s|5L+16s]] - sLsssssLssLssLsssssLs


===[[5L 7s|5L+7s]]===
[[OTC_7L_14s|7L+14s]] - ssssLssssLsLLssssLsLL, ssssLssssLLsLssssLLsL
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.


[[image:TN_12_05_07_sLssL_sL_sLssL.png link="file:12_05_07_sLssL_sL_sLssL.png"]]
==22 tones==
[[OTC_2L_ns|2L+20s]] - LssssssssssssLssssssss (9+4+9), LsssssssssssssLsssssss (8+6+8)


Pythagorean (3-limit JI): L=2187/2048, s=256/243
[[OTC_5L_17s|5L+17s]] - ssssLsssLssssLsssLsssL (MOS)
P = 1.2600167527
generator = 2L+3s (480.0 to 500.0 cents)
notable EDOs: 17, 22, 27, 29, 41, 53, etc.


modes:
[[OTC_7L_15s|7L+15s]] - LssLsLsssLssLsLsssLsss, LsssLsLssLsssLsLssLsss, LsssLLsssLsssLLsssLsss
|| || {{ 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 }} ||


[[OTC_10L_12s|10L+12s]] - LsLsLsLsLsLssLsLsLsLss


===[[7L 5s|7L+5s]]===
[[OTC_12L_10s|12L+10s]] - sLsLsLsLsLsLLsLsLsLsLL, sLLsLsLLssLLssLLsLsLLs, sLLssLLLssLLssLLLssLLs
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.


[[image:TN_12_07_05_LsLLs_Ls_LsLLs.png link="file:12_07_05_LsLLs_Ls_LsLLs.png"]]
[[OTC_15L_7s|15L+7s]] - sLLLssLLLsLLLssLLLsLLL


generator = 3L+2s (500.0 to 514.3 cents)
[[OTC_17L_5s|17L+5s]] - sLLLsLLLsLLLLsLLLsLLLL (MOS)
notable EDOs: 19, 26, 31, 33, 43, 45, 50, etc.


modes:
==23 tones==
|| || {{ LsLLs Ls LsLLs }} || ||
[[OTC_2L_ns|2L+21s]] - LsssssssssssssLssssssss
|| || {{ 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 }} ||


[[OTC_7L_16s|7L+16s]] - ssssLssssLssLLssssLssLL, ssLsLsLssssLssssLsLsLss, ssssLssssLLssLssssLLssL


===[[10L 2s|10L+2s]]===
==24 tones==
[[Pajara]] MODMOS.  Good for most any ratio of L to s.
[[OTC_2L_ns|2L+22s]] - LssssssssssssssLssssssss


[[image:TN_12_10_02_LLsLL_LL_LLsLL.png link="file:12_10_02_LLsLL_LL_LLsLL.png"]]
[[OTC_5L_19s|5L+19s]] - sssssLsssLsssssLsssLsssL


P = 1.1300083763
[[OTC_7L_17s|7L+17s]] - sssLsssLssLssLsssLssLssL, sssLsssLsssLsLsssLsssLsL
generator = L (100.0 to 120.0 cents)
[[periods and generators|period]] = 1/2 octave
notable EDOs: 22, 32, 34, 46


{{ LLLLLsLLLLLs }} (MOS)
[[OTC_10L_14s|10L+14s]] - LssLLssssLLssLLssssLLssL, sssLsLsLsLsssLsLsLsLsLsL
{{      ||      }}
{{ LLLLLLsLLLLs }} (OTC MODMOS)


modes:
[[OTC_12L_12s|12L+12s]] - LsLsLsLsLsLsLsLsLsLsLsLs (MOS), ssLsLLssLLssLsLLssLLssLL, ssLLsLssLLssLLsLssLLssLL
|| {{ 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 }} || ||


[[OTC_14L_10s|14L+10s]] - LssLLLLssLLssLLssLLLLssL, LLsLsLsLsLsLsLLLsLsLsLsL


===[[2L 10s|2L+10s]]===
[[OTC_15L_9s|15L+9s]] - LLsssLLLsLLLsLLLsssLLLsL
[[{$page}#dual|Dual]] of 10L+2s.  Probably only useful for small values of L/s.


[[image:TN_12_02_10_ssLss_ss_ssLss.png link="file:12_02_10_ssLss_ss_ssLss.png"]]
[[OTC_17L_7s|17L+7s]] - LLLsLLsLLsLLLsLLsLLsLLLs, LLLsLsLLLsLLLsLLLsLsLLLs


notable EDOs: 14, 16
[[OTC_19L_5s|19L+5s]] - LLLsLLLLLsLLLsLLLLLsLLLs


modes: ssLssssssLss, etc.
==&gt;24 tones==
Many larger OTC L+s scales are believed to exist, but due to exponentially increasing computation time, these have not yet been studied in detail.  Scales of the form [[OTC_2L_ns|2L+ns]] are known to exist up to size 53, and assumed to exist for any larger size.


==L/s matrix==


==13 tones (5+3+5)==
{| class="wikitable"
|-
| style="text-align:center;" |
| style="text-align:center;" | '''1'''
| style="text-align:center;" | '''2'''
| style="text-align:center;" | '''3'''
| style="text-align:center;" | '''4'''
| style="text-align:center;" | '''5'''
| style="text-align:center;" | '''6'''
| style="text-align:center;" | '''7'''
| style="text-align:center;" | '''8'''
| style="text-align:center;" | '''9'''
| style="text-align:center;" | '''10'''
| style="text-align:center;" | '''11'''
| style="text-align:center;" | '''12'''
| style="text-align:center;" | '''13'''
| style="text-align:center;" | '''14'''
| style="text-align:center;" | '''15'''
| style="text-align:center;" | '''16'''
| style="text-align:center;" | '''17'''
| style="text-align:center;" | '''18'''
| style="text-align:center;" | '''19'''
| style="text-align:center;" | '''20'''
| style="text-align:center;" | '''21'''
| style="text-align:center;" | '''22'''
| style="text-align:center;" | '''23'''
| style="text-align:center;" | '''24'''
| style="text-align:center;" | '''L'''
|-
| style="text-align:center;" | '''1'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''2'''
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_3L_2s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_5L_2s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_8L_2s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_10L_2s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_12L_2s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_17L_2s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_22L_2s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''3'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_3s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_3s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_12L_3s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''4'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''5'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_5s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_5L_5s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_5s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_12L_5s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_14L_5s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_17L_5s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_19L_5s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''6'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_6s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''7'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" | [[OTC_3L_7s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_5L_7s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_7s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_10L_7s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_12L_7s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_15L_7s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_17L_7s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''8'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_8s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_8s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_12L_8s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''9'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_5L_9s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_10L_9s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_15L_9s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''10'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_10s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_10s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_12L_10s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_14L_10s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''11'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_11s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''12'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_5L_12s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_12s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_10L_12s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_12L_12s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''13'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_13s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''14'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_5L_14s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_14s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_10L_14s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''15'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_15s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''16'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_5L_16s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_16s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''17'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_5L_17s|x]]
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_7L_17s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''18'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''19'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_5L_19s|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''20'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''21'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''22'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''23'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
|-
| style="text-align:center;" | '''24'''
| style="text-align:center;" |
| style="text-align:center;" | [[OTC_2L_ns|x]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
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| style="text-align:center;" | '''s'''
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
| style="text-align:center;" | <tt>   </tt>
|}


===[[7L 6s|7L+6s]]===
-----
[[Tetracot family|Tetracot]] MODMOS.  Best tuned at high values of L/s.


[[image:TN_13_07_06_ssLLL_ssL_ssLLL.png link="file:13_07_06_ssLLL_ssL_ssLLL.png"]]
=Scales with 3 step sizes=


P = 5.1745609664
== 8 notes ==
generator = L+s (171.4 to 184.6 cents)
ABCABCAB ([[Fokker block]])
notable EDOs: 20, 27, 34, 41


{{ sLsLsLsLsLsLL }} (MOS)
2L+3M+3s - LMsMsLMs, sMLsMsML
{{  || || ||     }}
{{ ssLLLssLssLLL }} (OTC MODMOS)


modes:
== 10 tones ==
|| {{ Lss LssLL LssLL }} || || ||
ABACABACAB (3-[[SN scale|SN]])
|| {{ 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 }} || ||


2L+3M+5s - sMsLsMsMsL


2L+5M+3s - MsMLMsMsML


==14 tones (6+2+6)==
5L+2M+3s - LsLMLsLsLm


===[[5L 9s|5L+9s]]===
== 11 tones ==
[[Semaphore and Godzilla|Semaphore / godzilla]] MODMOS.  Usable at any L/s ratio.
ABACABACABA (3-[[SN scale|SN]])


[[image:TN_14_05_09_LsssLs_Ls_LsssLs.png link="file:14_05_09_LsssLs_Ls_LsssLs.png"]]
2L+3M+6s - sMsLsMssMsL


P = 3.5200335053
2L+6M+3s - MsMLMsMMsML
generator = L+2s (240.0 to 257.1 cents)
notable EDOs: 19, 24, 29, 33, 34, 53


{{ ssLssLssLssLsL }} ([[MOS]])
ABCAABCAABA
{{   ||    ||     }}
{{ sssLsLsssLsLsL }} (OTC [[MODMOS]])


modes:
2L+3M+6s - sMLssMssMLs, sLMssMssLMs
|| {{ 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 }} || ||


2L+6M+3s - MsLMMsMMsLM, MLsMMsMMLsM


== 12 tones ==
ABABCABABCAB ([[Fokker block]])


===[[12L 2s|12L+2s]]===
5L+2M+5s - LsLsMLsLsLsM, MsLsLsLMsLsL
[[Injera]] MODMOS.  Imperfect (P&lt;0); best for L/s &gt;= 1.5 [[{$page}#ref1|(1)]]


[[image:TN_14_12_02_sLLLLL_LL_sLLLLL.png link="file:14_12_02_sLLLLL_LL_sLLLLL.png"]]
5L+5M+2s - LMLMsLMLMLMs, sMLMLMLsMLML


generator = L (85.7 to 100.0 cents)
== 13 tones ==
[[periods and generators|period]] = 1/2 octave
ABACAABACAABA
notable EDOs: 26, 38, 40, 50


{{ LLLLLLsLLLLLLs }} (MOS)
2L+3M+8s - sMsLssMssMsLs, sLsMssMssLsMs
{{       ||       }}
{{ LLLLLLLsLLLLLs }} (OTC MODMOS)


modes:
2L+8M+3s - MsMLMMsMMsMLM, MLMsMMsMMLMsM
|| {{ 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 }} || ||


== 14 tones ==
ABABACABABACAB (3-[[SN scale|SN]])


==15 tones (6+3+6)==
5L+2M+7s - sLsMsLsLsLsMsL


===[[7L 8s|7L+8s]]===
5L+7M+2s - MLMsMLMLMLMsML
[[Porcupine]] MODMOS


[[image:TN_15_07_08_ssLsLL_ssL_ssLsLL.png link="file:15_07_08_ssLsLL_ssL_ssLsLL.png"]]
== 15 tones ==
ABAACAABAACAABA (3-[[SN scale|SN]])


[[{$page}#perfect|P]] = 3.3809207248
2L+3M+10s - sMssLssMssMssLs
generator = L+s (160.0 to 171.4 cents)
notable EDOs: 22, 29, 36, 37, 43, 65


{{ LsLsLsLsLsLsLss }} (MOS)
2L+5M+3s - MsMMLMMsMMsMMLM
{{    ||    ||     }}
{{ LsLLssLsLLssLss }} (OTC MODMOS)


modes:
10L+2M+3s - LsLLMLLsLLsLLML
|| || {{ 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 }} ||


== 17 tones ==
ABAABACABAABACABA (3-[[SN scale|SN]])


===[[12L 3s|12L+3s]]===
2L+5M+10s - sMsLsMssMssMsLsMs
[[Augmented]] MODMOS.  Best at higher L/s ratios.


[[image:TN_15_12_03_LLLLLs_LLs_LLLLLs.png link="file:15_12_03_LLLLLs_LLs_LLLLLs.png"]]
2L+10M+5s - MsMLMsMMsMMsMLMsM


P = 12.5377181246
5L+2M+10s - sLsMsLssLssLsMsLs
generator = L (80.0 to 100.0 cents)
period = 1/3 octave
notable EDOs: 27, 39, 51


{{ LLLLsLLLLsLLLLs }} (MOS)
10L+2M+5s - LsLMLsLLsLLsLMLsL
{{     ||  ||      }}
{{ LLLLLsLLsLLLLLs }} (OTC MODMOS)


modes:
ABAABCAABAABCAABA
|| || {{ 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 }} ||


2L+5M+10s - sMssMLssMssMLssMs


==17 tones (7+3+7)==
2L+10M+5s - MsMMsLMMsMMsLMMsM


===[[5L 12s|5L+12s]]===
5L+2M+10s - sLssLMssLssLMssLs
[[Superpyth]] / ultrapyth MOS.  Imperfect, best at low L/s.  Many modes may be split two ways.


[[image:TN_17_05_12_sssLssL_ssL_sssLssL.png link="file:17_05_12_sssLssL_ssL_sssLssL.png"]]
10L+2M+5s - LsLLsMLLsLLsMLLsL


generator = 2L+5s (480.0 to 494.1 cents)
ABACABCABACABCABC ([[Fokker block]])
notable EDOs: 22, 27, 32, 37, 39


modes:
5L+7M+5s - MLMsMLsMLsMLMsMLs, sLMsMLMsLMsLMsMLM
|| {{ 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 }} || ||


7L+5M+5s - LMLsLMsLMsLMLsLMs, sMLsLMLsMLsMLsLML


===[[12L 5s|12L+5s]]===
ABCABCAABCABCAABC ([[Fokker block]])
Helmholtz / [[Schismatic family|schismatic]] MOS; full L/s range very good [[{$page}#ref1|(1)]]


[[image:TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png link="file:17_12_05_LLLsLLs_LLs_LLLsLLs.png"]]
5L+7M+5s - MLsMLsMMLsMLsMMLs, sLMMsLMsLMMsLMsLM


Pythagorean (3-limit JI): L=256/243, s=531441/524288
7L+5M+5s - LMsLMsLLMsLMsLLMs, sMLLsMLsMLLsMLsML
P = 3.8459060415
generator = 5L+2s (494.1 to 500.0 cents)
notable EDOs: 29, 41, 46, 53, 65


modes:
== 19 tones ==
|| {{ LLs LLsLLsL LLsLLsL }} || {{ LLsLLsL LsL LLsLLsL }} || ||
ABCBAABAABCBAABAABA (3-[[SN scale|SN]])
|| {{ 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 }} || ||


ABA=9/8


===[[7L 10s|7L+10s]]===
ABCBA=32/27, BC=256/243
[[Mohajira]] / [[Neutral third scales|neutral-thirds]] MODMOS; full L/s range good


[[image:TN_17_07_10_LssLssL_ssL_LssLssL.png link="file:17_07_10_LssLssL_ssL_LssLssL.png"]]
10L+2M+7s: LsMsLLsLLsMsLLsLLsL


P = 1.5872804832
ABCABCABABCABCABCAB ([[Fokker block]])  
generator = 2L+3s (342.9 to 352.9 cents)
notable EDOs: 24, 31, 41, 65


{{ ssLsLssLsLssLsLsL }} (MOS)
== 20 tones ==
{{    || ||     ||   }}
ABACABABABABABACABAB
{{ ssLLssLssLssLLssL }} (OTC MODMOS)


modes:
== 22 tones ==
|| {{ Lss LssLssL LssLssL }} || {{ LssLssL ssL LssLssL }} || ||
ABABCABABABABABABCABAB
|| {{ 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 }} || ||


ACABBACABACABBACABACAB


===[[10L 7s|10L+7s]]===
AbcbAbcbAAbcbAbcbAbcbA<ul><li>[[OTC_JI_22_sruti_scale|22-tone Indian 'sruti' scale]]</li></ul>
Beatles? / [[Dicot family|dicot]]? MODMOS; imperfect; full L/s range mostly good


[[image:TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png link="file:17_10_07_sLLsLLs_LLs_sLLsLLs.png"]]
-----


generator = 3L+2s (352.9 to 360.0 cents)
== 24 tones ==
notable EDOs: 27, 37, 44, 61
ACABABACABACABABACABACAB (3-[[SN scale|SN]])


{{ sLsLsLLsLsLLsLsLL }} (MOS)
MET-24 has this structure as 5L+12M+7s: MLMsMsMLMsMLMsMsMLMsMLMs
{{  ||     || ||     }}
{{ ssLLsLLssLLsLLsLL }} (OTC MODMOS)


modes:
AABAAABAACAABAAABAACAABA (3-[[SN scale|SN]])
|| {{ 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 }} || ||


== 29 tones ==
BABBABABBABCBABBABABBABCBABBA (3-[[SN scale|SN]])


==18 tones (7+4+7)==
2L+10m+17s: smsmssmsLsmssmsmssmsLsmssmsms


===[[7L 11s|7L+11s]]===
== 31 tones ==
Sixix?; best for L/s&gt;2
BABBCBBABABBABABBCBBABABBABABBA (3-[[SN scale|SN]])


[[image:TN_18_07_11_sssLsLL_sssL_sssLsLL.png link="file:18_07_11_sssLsLL_sssL_sssLsLL.png"]]
10L+19m+2s: mLmmLmsmLmmLmmLmLmmLmmLmsmLmmLm


P = 5.968201208
10L+2m+19s: sLssLsmsLssLssLsLssLssLsmsLssLs
generator = 2L+3s (333.3 to 342.9 cents)
notable EDOs: 25, 32, 39, 46, 53


{{ LsLssLsLssLsLssLss }} (MOS)
== 41 tones ==
{{  ||     | |    ||  }}
BABCBABBABBABCBABBABCBABBABBABCBABBABCBAB (3-[[SN scale|SN]])
{{ LLsssLsLLsssLsssLs }} (OTC MODMOS?)


modes:
5L+12M+24s: sMsLsMssMssMsLsMssMsLsMssMssMsLsMssMsLsMs
|| || {{ 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 }} ||


BBABBBABBABBBABBCBBABBBABBABBBABBCBBABBBA  (3-[[SN scale|SN]])


==19 tones (8+3+8)==
29L+2M+10s: LsLLLsLLMLLsLLLsLLsLLLsLLsLLLsLLMLLsLLLsL


===[[7L 12s|7L+12s]]===
2L+29M+10s: MsMMMsMMLMMsMMMsMMsMMMsMMsMMMsMMLMMsMMMsM
[[Meantone family#Flattone|Flattone]] MOS; [[{$page}#perfect|P]]&lt;0; [[{$page}#ref1|(1)]]


[[image:TN_19_07_12_LssLsLss_Lss_LssLsLss.png link="file:19_07_12_LssLsLss_Lss_LssLsLss.png"]]
== 46 tones ==
CACACBCACACACBCACACCACACBCACACACBCACACCACACBCA (3-[[SN scale|SN]])


generator = 3L+5s (505.3 to 514.3 cents)
== 72 tones ==
notable EDOs: 26, 33, 40, 45
ABAABABABAABABACABABAABABABAABABAABABABAABABAABABABAABABACABABAABABABAAB (3-[[SN scale|SN]])


modes:
29L+2M+41s: sLssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssL
|| {{ 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 }} || ||


2L+29M+41s: sMssMsMsMssMsMsLsMsMssMsMsMssMsMssMsMsMssMsMssMsMsMssMsMsLsMssMsMsMssM


===[[12L 7s|12L+7s]]===
=Definitions and formulas=
[[Meantone]] MOS; [[{$page}#perfect|P]]&lt;0 (oddly, neither this scale nor its [[{$page}#dual|dual]] can be tuned with a perfect 3/2!)  [[{$page}#ref1|(1)]]
 
[[image:TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png link="file:19_12_07_sLLsLsLL_sLL_sLLsLsLL.png"]]
 
generator = 5L+3s (500.0 to 505.3 cents)
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
 
[[image:TN_19_05_14_ssLssssL_ssL_ssLssssL.png link="file:19_05_14_ssLssssL_ssL_ssLssssL.png"]]
 
P = 2.5200335053
generator = L+3s (240.0 to 252.6 cents)
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
 
[[image:TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png link="file:19_14_05_LLsLLLLs_LLs_LLsLLLLs.png"]]
 
generator = 3L+s (252.6 to 257.1 cents)
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
 
[[image:TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png link="file:22_07_15_sssLsssLL_sssL_sssLsssLL.png"]]
 
P = 2.3809207248
generator = L+2s (163.6 to 171.4 cents)
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
 
[[image:TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png link="file:22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png"]]
 
generator = 2L+s (160.0 to 163.6 cents)
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)]]
 
[[image:TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png link="file:22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png"]]
 
P = 7.6918120831
generator = L+s (100.0 to 109.1 cents)
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
 
[[image:TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png link="file:22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png"]]
 
notable EDOs: 32, 42, 54
generator = L+s (10.91 to 120.0 cents)
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===
'''"Dual"''' 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.  If a scale is OTC, its dual is often OTC as well, but not always!
(5-limit [[Just intonation|JI]])


||= **scale step** ||= **ratio** ||&gt; **cents** ||
'''"Perfect"''' means that values for L and s exist such that L &gt; s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both).  (See also [[Eigenmonzo_subgroup|Eigenmonzo subgroup]], or [[unchanged-interval basis]].)
||=  0 ||= 1/1    ||&gt;    0.000 ||
||=  1 ||= 256/243 ||&gt;  90.225 ||
||=  2 ||= 16/15  ||&gt;  111.731 ||
||=  3 ||= 10/9    ||&gt;  182.404 ||
||=  4 ||= 9/8    ||&gt;  203.910 ||
||=  5 ||= 32/27  ||&gt;  294.135 ||
||=  6 ||= 6/5    ||&gt;  315.641 ||
||=  7 ||= 5/4    ||&gt;  386.314 ||
||=  8 ||= 81/64  ||&gt;  407.820 ||
||=  9 ||= 4/3     ||&gt;  498.045 ||
||= 10 ||= 27/20  ||&gt; 519.551 ||
||= 11 ||= 45/32  ||&gt;  590.224 ||
||= 12 ||= 729/512 ||&gt;  611.730 ||
||= 13 ||= 3/2    ||&gt;  701.955 ||
||= 14 ||= 128/81  ||&gt;  792.180 ||
||= 15 ||= 8/5    ||&gt;  813.686 ||
||= 16 ||= 5/3    ||&gt;  884.359 ||
||= 17 ||= 27/16  ||&gt;  905.865 ||
||= 18 ||= 16/9    ||&gt;  996.090 ||
||= 19 ||= 9/5    ||&gt; 1017.596 ||
||= 20 ||= 15/8    ||&gt; 1088.269 ||
||= 21 ||= 243/128 ||&gt; 1109.775 ||
||= 22 ||= 2/1    ||&gt; 1200.000 ||


A = 256/243
In this case the value '''P''' is given, where P = L/s.  For a perfect scale, P &gt; 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> &gt; 1, then P<span style="vertical-align: sub;">b</span> &lt; 1 ).
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=
 
[[#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 &gt; 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 &gt; 1.  Note that if a scale "a" is perfect (P&lt;span style="vertical-align: sub;"&gt;a&lt;/span&gt; ``=`` L/s), its dual "b" will have the value P&lt;span style="vertical-align: sub;"&gt;b&lt;/span&gt; ``=`` s/L = 1/P&lt;span style="vertical-align: sub;"&gt;a&lt;/span&gt;, and therefore must be imperfect (if P&lt;span style="vertical-align: sub;"&gt;a&lt;/span&gt; &gt; 1, then P&lt;span style="vertical-align: sub;"&gt;b&lt;/span&gt; &lt; 1 ).


In some cases, P may be less than zero.  I'm not yet sure what this means :)
In some cases, P may be less than zero.  I'm not yet sure what this means :)
Line 957: Line 1,050:


a = the number of L steps per 2/1
a = the number of L steps per 2/1
b = the number of s 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&lt;span style="vertical-align: sub;"&gt;2&lt;/span&gt;(3/2) = ~0.58496 octaves = ~701.955 cents


aL+bs = log&lt;span style="vertical-align: sub;"&gt;2&lt;/span&gt;(2/1) = 1
c = the number of L steps per 4/3
cL+ds = x


s = (c-ax)/(bc-ad)
d = the number of s steps per 4/3
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.
x = log<span style="vertical-align: sub;">2</span>(4/3) = ~0.41504 octaves = ~498.045 cents


aL+bs = log<span style="vertical-align: sub;">2</span>(2/1) = 1


----
cL+ds = x


=References=
s = (c-ax)/(bc-ad)


* [[#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]].
L = (x-ds)/c
</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Gallery of omnitetrachordal scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:136:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:136 --&gt;&lt;!-- ws:start:WikiTextTocRule:137: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Scales with two step sizes"&gt;Scales with two step sizes&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:137 --&gt;&lt;!-- ws:start:WikiTextTocRule:138: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Scales with two step sizes-5 tones (2+1+2)"&gt;5 tones (2+1+2)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:138 --&gt;&lt;!-- ws:start:WikiTextTocRule:139: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-5 tones (2+1+2)-2L+3s"&gt;2L+3s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:139 --&gt;&lt;!-- ws:start:WikiTextTocRule:140: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-5 tones (2+1+2)-3L+2s"&gt;3L+2s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:140 --&gt;&lt;!-- ws:start:WikiTextTocRule:141: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Scales with two step sizes-7 tones (3+1+3)"&gt;7 tones (3+1+3)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:141 --&gt;&lt;!-- ws:start:WikiTextTocRule:142: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-7 tones (3+1+3)-2L+5s"&gt;2L+5s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:142 --&gt;&lt;!-- ws:start:WikiTextTocRule:143: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-7 tones (3+1+3)-5L+2s"&gt;5L+2s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:143 --&gt;&lt;!-- ws:start:WikiTextTocRule:144: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Scales with two step sizes-10 tones (4+2+4)"&gt;10 tones (4+2+4)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:144 --&gt;&lt;!-- ws:start:WikiTextTocRule:145: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-10 tones (4+2+4)-5L+5s"&gt;5L+5s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:145 --&gt;&lt;!-- ws:start:WikiTextTocRule:146: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-10 tones (4+2+4)-7L+3s"&gt;7L+3s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:146 --&gt;&lt;!-- ws:start:WikiTextTocRule:147: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-10 tones (4+2+4)-3L+7s"&gt;3L+7s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:147 --&gt;&lt;!-- ws:start:WikiTextTocRule:148: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-10 tones (4+2+4)-2L+8s"&gt;2L+8s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:148 --&gt;&lt;!-- ws:start:WikiTextTocRule:149: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-10 tones (4+2+4)-8L+2s"&gt;8L+2s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:149 --&gt;&lt;!-- ws:start:WikiTextTocRule:150: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Scales with two step sizes-12 tones (5-2-5)"&gt;12 tones (5-2-5)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:150 --&gt;&lt;!-- ws:start:WikiTextTocRule:151: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-12 tones (5-2-5)-5L+7s"&gt;5L+7s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:151 --&gt;&lt;!-- ws:start:WikiTextTocRule:152: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-12 tones (5-2-5)-7L+5s"&gt;7L+5s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:152 --&gt;&lt;!-- ws:start:WikiTextTocRule:153: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-12 tones (5-2-5)-10L+2s"&gt;10L+2s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:153 --&gt;&lt;!-- ws:start:WikiTextTocRule:154: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-12 tones (5-2-5)-2L+10s"&gt;2L+10s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:154 --&gt;&lt;!-- ws:start:WikiTextTocRule:155: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Scales with two step sizes-13 tones (5+3+5)"&gt;13 tones (5+3+5)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:155 --&gt;&lt;!-- ws:start:WikiTextTocRule:156: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-13 tones (5+3+5)-7L+6s"&gt;7L+6s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:156 --&gt;&lt;!-- ws:start:WikiTextTocRule:157: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Scales with two step sizes-14 tones (6+2+6)"&gt;14 tones (6+2+6)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:157 --&gt;&lt;!-- ws:start:WikiTextTocRule:158: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-14 tones (6+2+6)-5L+9s"&gt;5L+9s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:158 --&gt;&lt;!-- ws:start:WikiTextTocRule:159: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-14 tones (6+2+6)-12L+2s"&gt;12L+2s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:159 --&gt;&lt;!-- ws:start:WikiTextTocRule:160: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Scales with two step sizes-15 tones (6+3+6)"&gt;15 tones (6+3+6)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:160 --&gt;&lt;!-- ws:start:WikiTextTocRule:161: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-15 tones (6+3+6)-7L+8s"&gt;7L+8s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:161 --&gt;&lt;!-- ws:start:WikiTextTocRule:162: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-15 tones (6+3+6)-12L+3s"&gt;12L+3s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:162 --&gt;&lt;!-- ws:start:WikiTextTocRule:163: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Scales with two step sizes-17 tones (7+3+7)"&gt;17 tones (7+3+7)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:163 --&gt;&lt;!-- ws:start:WikiTextTocRule:164: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-17 tones (7+3+7)-5L+12s"&gt;5L+12s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:164 --&gt;&lt;!-- ws:start:WikiTextTocRule:165: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-17 tones (7+3+7)-12L+5s"&gt;12L+5s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:165 --&gt;&lt;!-- ws:start:WikiTextTocRule:166: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-17 tones (7+3+7)-7L+10s"&gt;7L+10s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:166 --&gt;&lt;!-- ws:start:WikiTextTocRule:167: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-17 tones (7+3+7)-10L+7s"&gt;10L+7s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:167 --&gt;&lt;!-- ws:start:WikiTextTocRule:168: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Scales with two step sizes-18 tones (7+4+7)"&gt;18 tones (7+4+7)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:168 --&gt;&lt;!-- ws:start:WikiTextTocRule:169: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-18 tones (7+4+7)-7L+11s"&gt;7L+11s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:169 --&gt;&lt;!-- ws:start:WikiTextTocRule:170: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Scales with two step sizes-19 tones (8+3+8)"&gt;19 tones (8+3+8)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:170 --&gt;&lt;!-- ws:start:WikiTextTocRule:171: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-19 tones (8+3+8)-7L+12s"&gt;7L+12s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:171 --&gt;&lt;!-- ws:start:WikiTextTocRule:172: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-19 tones (8+3+8)-12L+7s"&gt;12L+7s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:172 --&gt;&lt;!-- ws:start:WikiTextTocRule:173: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-19 tones (8+3+8)-5L+14s"&gt;5L+14s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:173 --&gt;&lt;!-- ws:start:WikiTextTocRule:174: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-19 tones (8+3+8)-14L+5s"&gt;14L+5s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:174 --&gt;&lt;!-- ws:start:WikiTextTocRule:175: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Scales with two step sizes-22 tones (9+4+9)"&gt;22 tones (9+4+9)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:175 --&gt;&lt;!-- ws:start:WikiTextTocRule:176: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-22 tones (9+4+9)-7L+15s"&gt;7L+15s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:176 --&gt;&lt;!-- ws:start:WikiTextTocRule:177: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-22 tones (9+4+9)-15L+7s"&gt;15L+7s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:177 --&gt;&lt;!-- ws:start:WikiTextTocRule:178: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-22 tones (9+4+9)-12L+10s"&gt;12L+10s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:178 --&gt;&lt;!-- ws:start:WikiTextTocRule:179: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with two step sizes-22 tones (9+4+9)-10L+12s"&gt;10L+12s&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:179 --&gt;&lt;!-- ws:start:WikiTextTocRule:180: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Scales with 3 step sizes"&gt;Scales with 3 step sizes&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:180 --&gt;&lt;!-- ws:start:WikiTextTocRule:181: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Scales with 3 step sizes--22-tone Indian 'sruti' scale"&gt;22-tone Indian 'sruti' scale&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:181 --&gt;&lt;!-- ws:start:WikiTextTocRule:182: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Definitions and formulas"&gt;Definitions and formulas&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:182 --&gt;&lt;!-- ws:start:WikiTextTocRule:183: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#References"&gt;References&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:183 --&gt;&lt;!-- ws:start:WikiTextTocRule:184: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:184 --&gt;&lt;br /&gt;
An (incomplete) list of &lt;a class="wiki_link" href="/Omnitetrachordality"&gt;omnitetrachordal&lt;/a&gt; (OTC) scale patterns.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Scales with two step sizes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Scales with two step sizes&lt;/h1&gt;
(not necessarily &lt;a class="wiki_link" href="/MOS"&gt;MOS&lt;/a&gt; or &lt;a class="wiki_link" href="/Distributional%20Evenness"&gt;DE&lt;/a&gt;)&lt;br /&gt;
&lt;a class="wiki_link" href="/Omnitetrachordal%20scale"&gt;Omnitetrachordal scales&lt;/a&gt; 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 &lt;a class="wiki_link" href="/Just%20intonation"&gt;JI&lt;/a&gt;) version is possible.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Scales with two step sizes-5 tones (2+1+2)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;5 tones (2+1+2)&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="Scales with two step sizes-5 tones (2+1+2)-2L+3s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;&lt;a class="wiki_link" href="/2L%203s"&gt;2L+3s&lt;/a&gt;&lt;/h3&gt;
The familiar classic pentatonic scale. Can include &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt;, &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Pythagorean_tuning" rel="nofollow"&gt;Pythagorean&lt;/a&gt;, &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;, and &lt;a class="wiki_link" href="/Mavila%20Temperament%20Modal%20Harmony"&gt;mavila&lt;/a&gt; tunings.  Is &lt;a class="wiki_link" href="/MOS"&gt;MOS&lt;/a&gt;.  &lt;!-- ws:start:WikiTextVariableComponentRule:03:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:03 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3890:&amp;lt;a href=&amp;quot;/file/view/05_02_03_sL_s_sL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_05_02_03_sL_s_sL.png/589273922/TN_05_02_03_sL_s_sL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/05_02_03_sL_s_sL.png"&gt;&lt;img src="/file/view/TN_05_02_03_sL_s_sL.png/589273922/TN_05_02_03_sL_s_sL.png" alt="TN_05_02_03_sL_s_sL.png" title="TN_05_02_03_sL_s_sL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3890 --&gt;&lt;br /&gt;
&lt;br /&gt;
Pythagorean (3-limit JI): L=&lt;a class="wiki_link" href="/32_27"&gt;32/27&lt;/a&gt;, s=9/8&lt;br /&gt;
generator = L+s (480.0 to 600.0 cents)&lt;br /&gt;
&lt;!-- ws:start:WikiTextVariableComponentRule:05:[[{$page}#perfect|P]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:05 --&gt; = 1.4424745962&lt;br /&gt;
notable &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;s: 7, 9, 12, 16, 17, 19, 22, 26, 29, 31&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;


P = L/s


&lt;table class="wiki_table"&gt;
Note that the same procedure could be used to calculate the L/s ratio necessary to give any other just interval, such as 5/4, 11/8, etc.
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sL s sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; Ls s Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; s sL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; s Ls Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sL sL s &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; Ls Ls s &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Scales with two step sizes-5 tones (2+1+2)-3L+2s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;&lt;a class="wiki_link" href="/3L%202s"&gt;3L+2s&lt;/a&gt;&lt;/h3&gt;
Father? MOS; &lt;!-- ws:start:WikiTextVariableComponentRule:07:[[{$page}#perfect|imperfect]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;imperfect&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:07 --&gt;; &lt;!-- ws:start:WikiTextVariableComponentRule:09:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:09 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3892:&amp;lt;a href=&amp;quot;/file/view/05_03_02_Ls_L_Ls.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_05_03_02_Ls_L_Ls.png/589273924/TN_05_03_02_Ls_L_Ls.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/05_03_02_Ls_L_Ls.png"&gt;&lt;img src="/file/view/TN_05_03_02_Ls_L_Ls.png/589273924/TN_05_03_02_Ls_L_Ls.png" alt="TN_05_03_02_Ls_L_Ls.png" title="TN_05_03_02_Ls_L_Ls.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3892 --&gt;&lt;br /&gt;
&lt;br /&gt;
generator = L+s (400.0 to 480.0 cents)&lt;br /&gt;
notable EDOs: 8, 11b, 13, 18, 23b&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; Ls L Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sL L sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; L Ls Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; L sL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; Ls Ls L &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sL sL L &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Scales with two step sizes-7 tones (3+1+3)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;7 tones (3+1+3)&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Scales with two step sizes-7 tones (3+1+3)-2L+5s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;&lt;a class="wiki_link" href="/2L%205s"&gt;2L+5s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Mavila%20Temperament%20Modal%20Harmony"&gt;Mavila&lt;/a&gt; diatonic MOS.  &lt;!-- ws:start:WikiTextVariableComponentRule:011:[[{$page}#perfect|Imperfect]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;Imperfect&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:011 --&gt;.  &lt;!-- ws:start:WikiTextVariableComponentRule:013:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:013 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3894:&amp;lt;a href=&amp;quot;/file/view/07_02_05_sLs_s_sLs.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_07_02_05_sLs_s_sLs.png/589273926/TN_07_02_05_sLs_s_sLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/07_02_05_sLs_s_sLs.png"&gt;&lt;img src="/file/view/TN_07_02_05_sLs_s_sLs.png/589273926/TN_07_02_05_sLs_s_sLs.png" alt="TN_07_02_05_sLs_s_sLs.png" title="TN_07_02_05_sLs_s_sLs.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3894 --&gt;&lt;br /&gt;
&lt;br /&gt;
generator = L+2s (514.3 to 600.0 cents)&lt;br /&gt;
notable EDOs: 9, 11, 16, 23&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLs s sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; Lss s Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; s ssL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; s sLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssL s &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; s Lss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLs s &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; Lss Lss s &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssL s ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Scales with two step sizes-7 tones (3+1+3)-5L+2s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;&lt;a class="wiki_link" href="/5L%202s"&gt;5L+2s&lt;/a&gt;&lt;/h3&gt;
Classic diatonic scale (&lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;, Pythagorean, &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt;); MOS. &lt;!-- ws:start:WikiTextVariableComponentRule:015:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:015 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3896:&amp;lt;a href=&amp;quot;/file/view/07_05_02_LsL_L_Ls.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_07_05_02_LsL_L_Ls.png/589273928/TN_07_05_02_LsL_L_Ls.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/07_05_02_LsL_L_Ls.png"&gt;&lt;img src="/file/view/TN_07_05_02_LsL_L_Ls.png/589273928/TN_07_05_02_LsL_L_Ls.png" alt="TN_07_05_02_LsL_L_Ls.png" title="TN_07_05_02_LsL_L_Ls.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3896 --&gt;&lt;br /&gt;
&lt;br /&gt;
Pythagorean (3-limit JI): L=9/8, s=&lt;a class="wiki_link" href="/256_243"&gt;256/243&lt;/a&gt;&lt;br /&gt;
P = 2.2600167527&lt;br /&gt;
generator = 2L+s (480.0 to 514.3 cents)&lt;br /&gt;
notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc.&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLs L LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ionian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsL L LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Dorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLL L sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Phrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; L LLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Lydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; L LsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLs L &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Mixolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; L sLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsL L &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Aeolian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLL L &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Locrian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Scales with two step sizes-10 tones (4+2+4)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;10 tones (4+2+4)&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Scales with two step sizes-10 tones (4+2+4)-5L+5s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;&lt;a class="wiki_link" href="/5L%205s"&gt;5L+5s&lt;/a&gt;&lt;/h3&gt;
Blackwood MOS.  This omnitetrachordal scale has some unusual properties:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;it has only two modes&lt;/li&gt;&lt;li&gt;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)&lt;/li&gt;&lt;li&gt;it is its own dual (changing all L to s, and vice versa, gives the same scale)&lt;/li&gt;&lt;li&gt;the (imperfect) tuning of 3/2 is independent of L/s ratio (fixed at exactly 720 cents)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3898:&amp;lt;a href=&amp;quot;/file/view/10_05_05_LsLs_Ls_LsLs.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_10_05_05_LsLs_Ls_LsLs.png/589273946/TN_10_05_05_LsLs_Ls_LsLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/10_05_05_LsLs_Ls_LsLs.png"&gt;&lt;img src="/file/view/TN_10_05_05_LsLs_Ls_LsLs.png/589273946/TN_10_05_05_LsLs_Ls_LsLs.png" alt="TN_10_05_05_LsLs_Ls_LsLs.png" title="TN_10_05_05_LsLs_Ls_LsLs.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3898 --&gt;&lt;br /&gt;
&lt;br /&gt;
generator = s (0 to 120 cents)&lt;br /&gt;
&lt;a class="wiki_link" href="/periods%20and%20generators"&gt;period&lt;/a&gt; = 1/5 octave&lt;br /&gt;
notable EDOs: 15, 20, 25&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LsLs LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLs Ls LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLs LsLs Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLsL sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsL sL sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsL sLsL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Scales with two step sizes-10 tones (4+2+4)-7L+3s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;&lt;a class="wiki_link" href="/7L%203s"&gt;7L+3s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Mohajira"&gt;Mohajira&lt;/a&gt; / &lt;a class="wiki_link" href="/Neutral%20third%20scales"&gt;neutral-thirds&lt;/a&gt; &lt;a class="wiki_link" href="/MODMOS"&gt;MODMOS&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3900:&amp;lt;a href=&amp;quot;/file/view/10_07_03_sLLL_sL_sLLL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_10_07_03_sLLL_sL_sLLL.png/589273948/TN_10_07_03_sLLL_sL_sLLL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/10_07_03_sLLL_sL_sLLL.png"&gt;&lt;img src="/file/view/TN_10_07_03_sLLL_sL_sLLL.png/589273948/TN_10_07_03_sLLL_sL_sLLL.png" alt="TN_10_07_03_sLLL_sL_sLLL.png" title="TN_10_07_03_sLLL_sL_sLLL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3900 --&gt;&lt;br /&gt;
&lt;br /&gt;
P = 2.5872804832&lt;br /&gt;
generator = 2L+s (342.9 to 360.0 cents)&lt;br /&gt;
notable EDOs: 17, 24, 27, 31, 41&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; sLLsLLsLLL &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;    ||      &lt;/tt&gt; &lt;br /&gt;
&lt;tt&gt; sLLLsLsLLL &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLL Ls LsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLL sL sLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLs Ls LLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsL sL LLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LsLL LsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLLL sLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LLLs LLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLL LsLL Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL LLsL LLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLL sLLL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLs LLLs Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsL LLsL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Scales with two step sizes-10 tones (4+2+4)-3L+7s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;&lt;a class="wiki_link" href="/3L%207s"&gt;3L+7s&lt;/a&gt;&lt;/h3&gt;
The &lt;!-- ws:start:WikiTextVariableComponentRule:017:[[{$page}#dual|dual]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual"&gt;dual&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:017 --&gt; of 7L+3s, this scale pattern barely qualifies as omnitetrachordal.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3902:&amp;lt;a href=&amp;quot;/file/view/10_03_07_Lsss_Ls_Lsss.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_10_03_07_Lsss_Ls_Lsss.png/589273940/TN_10_03_07_Lsss_Ls_Lsss.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/10_03_07_Lsss_Ls_Lsss.png"&gt;&lt;img src="/file/view/TN_10_03_07_Lsss_Ls_Lsss.png/589273940/TN_10_03_07_Lsss_Ls_Lsss.png" alt="TN_10_03_07_Lsss_Ls_Lsss.png" title="TN_10_03_07_Lsss_Ls_Lsss.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3902 --&gt;&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 13, 16b&lt;br /&gt;
&lt;br /&gt;
modes: LsssLsLsss, etc.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="Scales with two step sizes-10 tones (4+2+4)-2L+8s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;&lt;a class="wiki_link" href="/2L%208s"&gt;2L+8s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Pajara"&gt;Pajara&lt;/a&gt; MODMOS.  Best at lower ratios of L/s.  &lt;!-- ws:start:WikiTextVariableComponentRule:019:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:019 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3904:&amp;lt;a href=&amp;quot;/file/view/10_02_08_sLss_ss_sLss.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_10_02_08_sLss_ss_sLss.png/589273936/TN_10_02_08_sLss_ss_sLss.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/10_02_08_sLss_ss_sLss.png"&gt;&lt;img src="/file/view/TN_10_02_08_sLss_ss_sLss.png/589273936/TN_10_02_08_sLss_ss_sLss.png" alt="TN_10_02_08_sLss_ss_sLss.png" title="TN_10_02_08_sLss_ss_sLss.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3904 --&gt;&lt;br /&gt;
&lt;br /&gt;
P = 1.8849491924&lt;br /&gt;
generator = s (0 to 120 cents)&lt;br /&gt;
&lt;a class="wiki_link" href="/periods%20and%20generators"&gt;period&lt;/a&gt; = 1/2 octave&lt;br /&gt;
notable EDOs: 12, 14, 16, 22, 26&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; LssssLssss &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;      ||    &lt;/tt&gt; &lt;br /&gt;
&lt;tt&gt; LsssssLsss &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssL ss sssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Standard Pentachordal Minor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLs ss ssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLss ss sLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Alternate Pentachordal Major&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; Lsss ss Lsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ss sssL sssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ss ssLs ssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Alternate Pentachordal Minor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ss sLss sLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssL sssL ss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ss Lsss Lsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLs ssLs ss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Standard Pentachordal Major&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLss sLss ss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; Lsss Lsss ss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
(The names of the modes are Paul Erlich's - see &lt;a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow"&gt;http://lumma.org/tuning/erlich/erlich-decatonic.pdf&lt;/a&gt;.)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Scales with two step sizes-10 tones (4+2+4)-8L+2s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;&lt;a class="wiki_link" href="/8L%202s"&gt;8L+2s&lt;/a&gt;&lt;/h3&gt;
The dual of 2L+8s, this scale is imperfect and poorly tuned for 3/2 at any L/s ratio.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3906:&amp;lt;a href=&amp;quot;/file/view/10_08_02_LsLL_LL_LsLL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_10_08_02_LsLL_LL_LsLL.png/589273954/TN_10_08_02_LsLL_LL_LsLL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/10_08_02_LsLL_LL_LsLL.png"&gt;&lt;img src="/file/view/TN_10_08_02_LsLL_LL_LsLL.png/589273954/TN_10_08_02_LsLL_LL_LsLL.png" alt="TN_10_08_02_LsLL_LL_LsLL.png" title="TN_10_08_02_LsLL_LL_LsLL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3906 --&gt;&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 18, 26b&lt;br /&gt;
&lt;br /&gt;
modes: LsLLLLLsLL, etc.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Scales with two step sizes-12 tones (5-2-5)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;12 tones (5-2-5)&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Scales with two step sizes-12 tones (5-2-5)-5L+7s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;&lt;a class="wiki_link" href="/5L%207s"&gt;5L+7s&lt;/a&gt;&lt;/h3&gt;
12-tone MOS of the helmholtz / garibaldi / &lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic&lt;/a&gt; and &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt; temperaments (slightly sharp 3/2).  Very usable at any L/s ratio.  Many modes may be pentachordally split in two ways.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3908:&amp;lt;a href=&amp;quot;/file/view/12_05_07_sLssL_sL_sLssL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_12_05_07_sLssL_sL_sLssL.png/589273964/TN_12_05_07_sLssL_sL_sLssL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/12_05_07_sLssL_sL_sLssL.png"&gt;&lt;img src="/file/view/TN_12_05_07_sLssL_sL_sLssL.png/589273964/TN_12_05_07_sLssL_sL_sLssL.png" alt="TN_12_05_07_sLssL_sL_sLssL.png" title="TN_12_05_07_sLssL_sL_sLssL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3908 --&gt;&lt;br /&gt;
&lt;br /&gt;
Pythagorean (3-limit JI): L=2187/2048, s=256/243&lt;br /&gt;
P = 1.2600167527&lt;br /&gt;
generator = 2L+3s (480.0 to 500.0 cents)&lt;br /&gt;
notable EDOs: 17, 22, 27, 29, 41, 53, etc.&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLs sL sLsLs  &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLs sLsLs Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLss Ls LsLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssL sL sLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLs Ls LssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsL sL ssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLsLs sLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLs Ls sLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LsLss LsLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLssL sLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLs sLsLs sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LssLs LssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLss LsLss Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL ssLsL ssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssL sL ssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls sLsLs sLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLs LssLs Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsL ssLsL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="Scales with two step sizes-12 tones (5-2-5)-7L+5s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;&lt;a class="wiki_link" href="/7L%205s"&gt;7L+5s&lt;/a&gt;&lt;/h3&gt;
12-tone MOS of the &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; and &lt;a class="wiki_link" href="/Meantone%20family#Flattone"&gt;flattone&lt;/a&gt; temperaments (slightly flat 3/2).  &lt;!-- ws:start:WikiTextVariableComponentRule:021:[[{$page}#perfect|Imperfect]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;Imperfect&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:021 --&gt;, but very usable at any L/s ratio.  Many modes may be pentachordally split in two ways.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3910:&amp;lt;a href=&amp;quot;/file/view/12_07_05_LsLLs_Ls_LsLLs.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_12_07_05_LsLLs_Ls_LsLLs.png/589273968/TN_12_07_05_LsLLs_Ls_LsLLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/12_07_05_LsLLs_Ls_LsLLs.png"&gt;&lt;img src="/file/view/TN_12_07_05_LsLLs_Ls_LsLLs.png/589273968/TN_12_07_05_LsLLs_Ls_LsLLs.png" alt="TN_12_07_05_LsLLs_Ls_LsLLs.png" title="TN_12_07_05_LsLLs_Ls_LsLLs.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3910 --&gt;&lt;br /&gt;
&lt;br /&gt;
generator = 3L+2s (500.0 to 514.3 cents)&lt;br /&gt;
notable EDOs: 19, 26, 31, 33, 43, 45, 50, etc.&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLs Ls LsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsL sL sLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLs Ls LLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LsLsL LsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsL sL LsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLsLL sLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LsLLs LsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsL LsLsL Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLLsL sLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLL sLsLL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LLsLs LLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLs LsLLs Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL LsLsL LsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsL sLLsL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLs LLsLs Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsL Ls LsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsL LsLsL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLL sL sLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Scales with two step sizes-12 tones (5-2-5)-10L+2s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;&lt;a class="wiki_link" href="/10L%202s"&gt;10L+2s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Pajara"&gt;Pajara&lt;/a&gt; MODMOS.  Good for most any ratio of L to s.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3912:&amp;lt;a href=&amp;quot;/file/view/12_10_02_LLsLL_LL_LLsLL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_12_10_02_LLsLL_LL_LLsLL.png/589273970/TN_12_10_02_LLsLL_LL_LLsLL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/12_10_02_LLsLL_LL_LLsLL.png"&gt;&lt;img src="/file/view/TN_12_10_02_LLsLL_LL_LLsLL.png/589273970/TN_12_10_02_LLsLL_LL_LLsLL.png" alt="TN_12_10_02_LLsLL_LL_LLsLL.png" title="TN_12_10_02_LLsLL_LL_LLsLL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3912 --&gt;&lt;br /&gt;
&lt;br /&gt;
P = 1.1300083763&lt;br /&gt;
generator = L (100.0 to 120.0 cents)&lt;br /&gt;
&lt;a class="wiki_link" href="/periods%20and%20generators"&gt;period&lt;/a&gt; = 1/2 octave&lt;br /&gt;
notable EDOs: 22, 32, 34, 46&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; LLLLLsLLLLLs &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;      ||      &lt;/tt&gt; &lt;br /&gt;
&lt;tt&gt; LLLLLLsLLLLs &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LL LLLLs LLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LL LLLsL LLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LL LLsLL LLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLs LLLLs LL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LL LsLLL LsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsL LLLsL LL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LL sLLLL sLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLL LLsLL LL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLL LsLLL LL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLL sLLLL LL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLs LL LLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsL LL LLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLL LL LLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLL LL LsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLL LL sLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc17"&gt;&lt;a name="Scales with two step sizes-12 tones (5-2-5)-2L+10s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;&lt;a class="wiki_link" href="/2L%2010s"&gt;2L+10s&lt;/a&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextVariableComponentRule:023:[[{$page}#dual|Dual]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual"&gt;Dual&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:023 --&gt; of 10L+2s.  Probably only useful for small values of L/s.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3914:&amp;lt;a href=&amp;quot;/file/view/12_02_10_ssLss_ss_ssLss.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_12_02_10_ssLss_ss_ssLss.png/589273958/TN_12_02_10_ssLss_ss_ssLss.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/12_02_10_ssLss_ss_ssLss.png"&gt;&lt;img src="/file/view/TN_12_02_10_ssLss_ss_ssLss.png/589273958/TN_12_02_10_ssLss_ss_ssLss.png" alt="TN_12_02_10_ssLss_ss_ssLss.png" title="TN_12_02_10_ssLss_ss_ssLss.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3914 --&gt;&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 14, 16&lt;br /&gt;
&lt;br /&gt;
modes: ssLssssssLss, etc.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Scales with two step sizes-13 tones (5+3+5)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;13 tones (5+3+5)&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc19"&gt;&lt;a name="Scales with two step sizes-13 tones (5+3+5)-7L+6s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;&lt;a class="wiki_link" href="/7L%206s"&gt;7L+6s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Tetracot%20family"&gt;Tetracot&lt;/a&gt; MODMOS.  Best tuned at high values of L/s.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3916:&amp;lt;a href=&amp;quot;/file/view/13_07_06_ssLLL_ssL_ssLLL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_13_07_06_ssLLL_ssL_ssLLL.png/589273972/TN_13_07_06_ssLLL_ssL_ssLLL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/13_07_06_ssLLL_ssL_ssLLL.png"&gt;&lt;img src="/file/view/TN_13_07_06_ssLLL_ssL_ssLLL.png/589273972/TN_13_07_06_ssLLL_ssL_ssLLL.png" alt="TN_13_07_06_ssLLL_ssL_ssLLL.png" title="TN_13_07_06_ssLLL_ssL_ssLLL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3916 --&gt;&lt;br /&gt;
&lt;br /&gt;
P = 5.1745609664&lt;br /&gt;
generator = L+s (171.4 to 184.6 cents)&lt;br /&gt;
notable EDOs: 20, 27, 34, 41&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; sLsLsLsLsLsLL &lt;/tt&gt; (MOS) &lt;br /&gt;
&lt;tt&gt;  || || ||     &lt;/tt&gt; &lt;br /&gt;
&lt;tt&gt; ssLLLssLssLLL &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LssLL LssLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssLLL ssLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLLLs sLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LLLss LLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLL LssLL Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL LLssL LLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLLL ssLLL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLs sLLLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLss LLLss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLssL LLssL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLL Lss LssLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLLL ssL ssLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLs sLs sLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLss Lss LLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLssL ssL LLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Scales with two step sizes-14 tones (6+2+6)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;14 tones (6+2+6)&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc21"&gt;&lt;a name="Scales with two step sizes-14 tones (6+2+6)-5L+9s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;&lt;a class="wiki_link" href="/5L%209s"&gt;5L+9s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Semaphore%20and%20Godzilla"&gt;Semaphore / godzilla&lt;/a&gt; MODMOS.  Usable at any L/s ratio.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3918:&amp;lt;a href=&amp;quot;/file/view/14_05_09_LsssLs_Ls_LsssLs.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_14_05_09_LsssLs_Ls_LsssLs.png/589273978/TN_14_05_09_LsssLs_Ls_LsssLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/14_05_09_LsssLs_Ls_LsssLs.png"&gt;&lt;img src="/file/view/TN_14_05_09_LsssLs_Ls_LsssLs.png/589273978/TN_14_05_09_LsssLs_Ls_LsssLs.png" alt="TN_14_05_09_LsssLs_Ls_LsssLs.png" title="TN_14_05_09_LsssLs_Ls_LsssLs.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3918 --&gt;&lt;br /&gt;
&lt;br /&gt;
P = 3.5200335053&lt;br /&gt;
generator = L+2s (240.0 to 257.1 cents)&lt;br /&gt;
notable EDOs: 19, 24, 29, 33, 34, 53&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; ssLssLssLssLsL &lt;/tt&gt; (&lt;a class="wiki_link" href="/MOS"&gt;MOS&lt;/a&gt;)&lt;br /&gt;
&lt;tt&gt;   ||    ||     &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; sssLsLsssLsLsL &lt;/tt&gt; (OTC &lt;a class="wiki_link" href="/MODMOS"&gt;MODMOS&lt;/a&gt;)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLsLss sLsLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LsLsss LsLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLsssL sLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLss sLsLss sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LsssLs LsssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsss LsLsss Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sssLsL sssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsssL sLsssL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls ssLsLs ssLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLs LsssLs Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLsL sssLsL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsLs ssLsLs Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLss sL sLsLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsss Ls LsLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsssL sL sLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLs Ls LsssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLsL sL sssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsLs Ls ssLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc22"&gt;&lt;a name="Scales with two step sizes-14 tones (6+2+6)-12L+2s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;&lt;a class="wiki_link" href="/12L%202s"&gt;12L+2s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Injera"&gt;Injera&lt;/a&gt; MODMOS.  Imperfect (P&amp;lt;0); best for L/s &amp;gt;= 1.5 &lt;!-- ws:start:WikiTextVariableComponentRule:025:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:025 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3920:&amp;lt;a href=&amp;quot;/file/view/14_12_02_sLLLLL_LL_sLLLLL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_14_12_02_sLLLLL_LL_sLLLLL.png/589273982/TN_14_12_02_sLLLLL_LL_sLLLLL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/14_12_02_sLLLLL_LL_sLLLLL.png"&gt;&lt;img src="/file/view/TN_14_12_02_sLLLLL_LL_sLLLLL.png/589273982/TN_14_12_02_sLLLLL_LL_sLLLLL.png" alt="TN_14_12_02_sLLLLL_LL_sLLLLL.png" title="TN_14_12_02_sLLLLL_LL_sLLLLL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3920 --&gt;&lt;br /&gt;
&lt;br /&gt;
generator = L (85.7 to 100.0 cents)&lt;br /&gt;
&lt;a class="wiki_link" href="/periods%20and%20generators"&gt;period&lt;/a&gt; = 1/2 octave&lt;br /&gt;
notable EDOs: 26, 38, 40, 50&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; LLLLLLsLLLLLLs &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;       ||       &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; LLLLLLLsLLLLLs &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LL LLLLLs LLLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LL LLLLsL LLLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LL LLLsLL LLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLLs LLLLLs LL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LL LLsLLL LLsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLsL LLLLsL LL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LL LsLLLL LsLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsLL LLLsLL LL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LL sLLLLL sLLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLL LLsLLL LL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLL LsLLLL LL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLLL sLLLLL LL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLLs LL LLLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLsL LL LLLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsLL LL LLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLL LL LLsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLL LL LsLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLLL LL sLLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Scales with two step sizes-15 tones (6+3+6)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;15 tones (6+3+6)&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc24"&gt;&lt;a name="Scales with two step sizes-15 tones (6+3+6)-7L+8s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;&lt;a class="wiki_link" href="/7L%208s"&gt;7L+8s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt; MODMOS&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3922:&amp;lt;a href=&amp;quot;/file/view/15_07_08_ssLsLL_ssL_ssLsLL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_15_07_08_ssLsLL_ssL_ssLsLL.png/589273986/TN_15_07_08_ssLsLL_ssL_ssLsLL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/15_07_08_ssLsLL_ssL_ssLsLL.png"&gt;&lt;img src="/file/view/TN_15_07_08_ssLsLL_ssL_ssLsLL.png/589273986/TN_15_07_08_ssLsLL_ssL_ssLsLL.png" alt="TN_15_07_08_ssLsLL_ssL_ssLsLL.png" title="TN_15_07_08_ssLsLL_ssL_ssLsLL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3922 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextVariableComponentRule:027:[[{$page}#perfect|P]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:027 --&gt; = 3.3809207248&lt;br /&gt;
generator = L+s (160.0 to 171.4 cents)&lt;br /&gt;
notable EDOs: 22, 29, 36, 37, 43, 65&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; LsLsLsLsLsLsLss &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;    ||    ||     &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; LsLLssLsLLssLss &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLsL Lss LssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsLL ssL ssLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLLs sLs sLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLss Lss LsLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLssL ssL sLLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLssLs sLs LLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LssLsL LssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssLsLL ssLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLsLLs sLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LsLLss LsLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt;  LssLsL LssLsL Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL sLLssL sLLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt;  ssLsLL ssLsLL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs LLssLs LLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt;  sLsLLs sLsLLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLss LsLLss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLssL sLLssL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLssLs LLssLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:92:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc25"&gt;&lt;a name="Scales with two step sizes-15 tones (6+3+6)-12L+3s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&gt;&lt;a class="wiki_link" href="/12L%203s"&gt;12L+3s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Augmented"&gt;Augmented&lt;/a&gt; MODMOS.  Best at higher L/s ratios.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3924:&amp;lt;a href=&amp;quot;/file/view/15_12_03_LLLLLs_LLs_LLLLLs.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_15_12_03_LLLLLs_LLs_LLLLLs.png/589273990/TN_15_12_03_LLLLLs_LLs_LLLLLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/15_12_03_LLLLLs_LLs_LLLLLs.png"&gt;&lt;img src="/file/view/TN_15_12_03_LLLLLs_LLs_LLLLLs.png/589273990/TN_15_12_03_LLLLLs_LLs_LLLLLs.png" alt="TN_15_12_03_LLLLLs_LLs_LLLLLs.png" title="TN_15_12_03_LLLLLs_LLs_LLLLLs.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3924 --&gt;&lt;br /&gt;
&lt;br /&gt;
P = 12.5377181246&lt;br /&gt;
generator = L (80.0 to 100.0 cents)&lt;br /&gt;
period = 1/3 octave&lt;br /&gt;
notable EDOs: 27, 39, 51&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; LLLLsLLLLsLLLLs &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;     ||  ||      &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; LLLLLsLLsLLLLLs &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLL LLs LLsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLL LsL LsLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLLL sLL sLLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLLs LLs LLLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLsL LsL LLLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsLL sLL LLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLsLLL LLsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsLLLL LsLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLLLLL sLLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLLLLs LLLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LLLLsL LLLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLL LsLLLL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL LLLsLL LLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLLL sLLLLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLLs LLLLLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLsL LLLLsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsLL LLLsLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Scales with two step sizes-17 tones (7+3+7)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;17 tones (7+3+7)&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc27"&gt;&lt;a name="Scales with two step sizes-17 tones (7+3+7)-5L+12s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;&lt;a class="wiki_link" href="/5L%2012s"&gt;5L+12s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Superpyth"&gt;Superpyth&lt;/a&gt; / ultrapyth MOS.  Imperfect, best at low L/s.  Many modes may be split two ways.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3926:&amp;lt;a href=&amp;quot;/file/view/17_05_12_sssLssL_ssL_sssLssL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_17_05_12_sssLssL_ssL_sssLssL.png/589273994/TN_17_05_12_sssLssL_ssL_sssLssL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/17_05_12_sssLssL_ssL_sssLssL.png"&gt;&lt;img src="/file/view/TN_17_05_12_sssLssL_ssL_sssLssL.png/589273994/TN_17_05_12_sssLssL_ssL_sssLssL.png" alt="TN_17_05_12_sssLssL_ssL_sssLssL.png" title="TN_17_05_12_sssLssL_ssL_sssLssL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3926 --&gt;&lt;br /&gt;
&lt;br /&gt;
generator = 2L+5s (480.0 to 494.1 cents)&lt;br /&gt;
notable EDOs: 22, 27, 32, 37, 39&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LssLsss LssLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssLsssL ssLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLs ssLssLs ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLsssLs sLsssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLss sLssLss sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LsssLss LsssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLsss LssLsss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs ssLssLs ssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsssLs sLsssLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss sLssLss sLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLss LsssLss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLssL sssLssL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLs ssL ssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLs ssLssLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLss sLs sLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLss sLssLss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLsss Lss LssLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsssL ssL ssLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsssLs sLs sLsssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLss Lss LsssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLssL ssL sssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLssL ssL sssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssLssLs ssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLs sLs ssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLssLss sLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLss Lss sLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc28"&gt;&lt;a name="Scales with two step sizes-17 tones (7+3+7)-12L+5s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;&lt;a class="wiki_link" href="/12L%205s"&gt;12L+5s&lt;/a&gt;&lt;/h3&gt;
Helmholtz / &lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic&lt;/a&gt; MOS; full L/s range very good &lt;!-- ws:start:WikiTextVariableComponentRule:029:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:029 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3928:&amp;lt;a href=&amp;quot;/file/view/17_12_05_LLLsLLs_LLs_LLLsLLs.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png/589274008/TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/17_12_05_LLLsLLs_LLs_LLLsLLs.png"&gt;&lt;img src="/file/view/TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png/589274008/TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png" alt="TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png" title="TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3928 --&gt;&lt;br /&gt;
&lt;br /&gt;
Pythagorean (3-limit JI): L=256/243, s=531441/524288&lt;br /&gt;
P = 3.8459060415&lt;br /&gt;
generator = 5L+2s (494.1 to 500.0 cents)&lt;br /&gt;
notable EDOs: 29, 41, 46, 53, 65&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLsLLsL LLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsL LsL LLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsLLsLL LsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLL sLL LsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLLsLLL sLLsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLsLLLs LLsLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsL LLsLLsL LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsLLLsL LsLLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLL LsLLsLL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLLLsLL sLLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLL sLLsLLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLLsLLs LLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLLs LLsLLLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LLsLLsL LLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLsL LsLLLsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL LsLLsLL LsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLsLL sLLLsLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsLLs LLLsLLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsL LLs LLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsL LLsLLsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLL LsL LsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLL LsLLsLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLL sLL sLLsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLLs LLs LLsLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLsL LsL LsLLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLsLL sLL sLLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsLLs LLs LLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc29"&gt;&lt;a name="Scales with two step sizes-17 tones (7+3+7)-7L+10s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;&lt;a class="wiki_link" href="/7L%2010s"&gt;7L+10s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Mohajira"&gt;Mohajira&lt;/a&gt; / &lt;a class="wiki_link" href="/Neutral%20third%20scales"&gt;neutral-thirds&lt;/a&gt; MODMOS; full L/s range good&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3930:&amp;lt;a href=&amp;quot;/file/view/17_07_10_LssLssL_ssL_LssLssL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_17_07_10_LssLssL_ssL_LssLssL.png/589273998/TN_17_07_10_LssLssL_ssL_LssLssL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/17_07_10_LssLssL_ssL_LssLssL.png"&gt;&lt;img src="/file/view/TN_17_07_10_LssLssL_ssL_LssLssL.png/589273998/TN_17_07_10_LssLssL_ssL_LssLssL.png" alt="TN_17_07_10_LssLssL_ssL_LssLssL.png" title="TN_17_07_10_LssLssL_ssL_LssLssL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3930 --&gt;&lt;br /&gt;
&lt;br /&gt;
P = 1.5872804832&lt;br /&gt;
generator = 2L+3s (342.9 to 352.9 cents)&lt;br /&gt;
notable EDOs: 24, 31, 41, 65&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; ssLsLssLsLssLsLsL &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;    || ||     ||   &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; ssLLssLssLssLLssL &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LssLssL LssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssL ssL LssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssLssLL ssLssLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLssLLs sLssLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LssLLss LssLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssLLssL ssLLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLL ssLssLL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLLssLs sLLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLLs sLssLLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LLssLss LLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLLss LssLLss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL LssLssL LssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLLssL ssLLssL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLssLs sLLssLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLssLss LLssLss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssL Lss LssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssL LssLssL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLL ssL ssLssLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLLs sLs sLssLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLLss Lss LssLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLLssL ssL ssLLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLssLs sLs sLLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLssLss Lss LLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc30"&gt;&lt;a name="Scales with two step sizes-17 tones (7+3+7)-10L+7s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;&lt;a class="wiki_link" href="/10L%207s"&gt;10L+7s&lt;/a&gt;&lt;/h3&gt;
Beatles? / &lt;a class="wiki_link" href="/Dicot%20family"&gt;dicot&lt;/a&gt;? MODMOS; imperfect; full L/s range mostly good&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3932:&amp;lt;a href=&amp;quot;/file/view/17_10_07_sLLsLLs_LLs_sLLsLLs.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png/589274004/TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/17_10_07_sLLsLLs_LLs_sLLsLLs.png"&gt;&lt;img src="/file/view/TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png/589274004/TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png" alt="TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png" title="TN_17_10_07_sLLsLLs_LLs_sLLsLLs.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3932 --&gt;&lt;br /&gt;
&lt;br /&gt;
generator = 3L+2s (352.9 to 360.0 cents)&lt;br /&gt;
notable EDOs: 27, 37, 44, 61&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; sLsLsLLsLsLLsLsLL &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;  ||     || ||     &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; ssLLsLLssLLsLLsLL &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLLsLLs sLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLs LLs sLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLsLLss LLsLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsLLssL LsLLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLLssLL sLLssLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLs sLLsLLs sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLssLLs LLssLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLss LLsLLss LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LssLLsL LssLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLssL LsLLssL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL ssLLsLL ssLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLssLL sLLssLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs sLLsLLs sLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLssLLs LLssLLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLLsL LssLLsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLLsLL ssLLsLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLs sLL sLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLs sLLsLLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLss LLs LLsLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLssL LsL LsLLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLssLL sLL sLLssLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLssLLs LLs LLssLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLLsL LsL LssLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLLsLL sLL ssLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Scales with two step sizes-18 tones (7+4+7)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;18 tones (7+4+7)&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc32"&gt;&lt;a name="Scales with two step sizes-18 tones (7+4+7)-7L+11s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;&lt;a class="wiki_link" href="/7L%2011s"&gt;7L+11s&lt;/a&gt;&lt;/h3&gt;
Sixix?; best for L/s&amp;gt;2&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3934:&amp;lt;a href=&amp;quot;/file/view/18_07_11_sssLsLL_sssL_sssLsLL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_18_07_11_sssLsLL_sssL_sssLsLL.png/589274012/TN_18_07_11_sssLsLL_sssL_sssLsLL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/18_07_11_sssLsLL_sssL_sssLsLL.png"&gt;&lt;img src="/file/view/TN_18_07_11_sssLsLL_sssL_sssLsLL.png/589274012/TN_18_07_11_sssLsLL_sssL_sssLsLL.png" alt="TN_18_07_11_sssLsLL_sssL_sssLsLL.png" title="TN_18_07_11_sssLsLL_sssL_sssLsLL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3934 --&gt;&lt;br /&gt;
&lt;br /&gt;
P = 5.968201208&lt;br /&gt;
generator = 2L+3s (333.3 to 342.9 cents)&lt;br /&gt;
notable EDOs: 25, 32, 39, 46, 53&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; LsLssLsLssLsLssLss &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;  ||     | |    ||  &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; LLsssLsLLsssLsssLs &lt;/tt&gt; (OTC MODMOS?)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLsL Lsss LsssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLsLL sssL sssLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsLLs ssLs ssLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLLss sLss sLsLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsss Lsss LsLLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsssL sssL sLLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsssLs ssLs LLsssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lsss LsssLsL LsssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sssL sssLsLL sssLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssLs ssLsLLs ssLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLss sLsLLss sLsLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lsss LsLLsss LsLLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLsL LsssLsL Lsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sssL sLLsssL sLLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLsLL sssLsLL sssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssLs LLsssLs LLsssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsLLs ssLsLLs ssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLLss sLsLLss sLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsss LsLLsss Lsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsssL sLLsssL sssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsssLs LLsssLs ssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Scales with two step sizes-19 tones (8+3+8)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;19 tones (8+3+8)&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc34"&gt;&lt;a name="Scales with two step sizes-19 tones (8+3+8)-7L+12s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;&lt;a class="wiki_link" href="/7L%2012s"&gt;7L+12s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Meantone%20family#Flattone"&gt;Flattone&lt;/a&gt; MOS; &lt;!-- ws:start:WikiTextVariableComponentRule:031:[[{$page}#perfect|P]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:031 --&gt;&amp;lt;0; &lt;!-- ws:start:WikiTextVariableComponentRule:033:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:033 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3936:&amp;lt;a href=&amp;quot;/file/view/19_07_12_LssLsLss_Lss_LssLsLss.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_19_07_12_LssLsLss_Lss_LssLsLss.png/589274018/TN_19_07_12_LssLsLss_Lss_LssLsLss.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/19_07_12_LssLsLss_Lss_LssLsLss.png"&gt;&lt;img src="/file/view/TN_19_07_12_LssLsLss_Lss_LssLsLss.png/589274018/TN_19_07_12_LssLsLss_Lss_LssLsLss.png" alt="TN_19_07_12_LssLsLss_Lss_LssLsLss.png" title="TN_19_07_12_LssLsLss_Lss_LssLsLss.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3936 --&gt;&lt;br /&gt;
&lt;br /&gt;
generator = 3L+5s (505.3 to 514.3 cents)&lt;br /&gt;
notable EDOs: 26, 33, 40, 45&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLssLssL sLssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLssL ssL sLssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LssLssLs LssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssLs sLs LssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssLssLsL ssLssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLssLsLs sLssLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLssL sLssLssL sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LssLsLss LssLsLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssLs LssLssLs Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssLsLssL ssLsLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLsL ssLssLsL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLsLssLs sLsLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLsLs sLssLsLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LsLssLss LsLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLsLss LssLsLss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL sLssLssL sLssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsLssL ssLsLssL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs LssLssLs LssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLssLs sLsLssLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLssLss LsLssLss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLssL sLs sLssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLssL sLssLssL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssLs Lss LssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssLs LssLssLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLsL ssL ssLssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLsLs sLs sLssLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLsLss Lss LssLsLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsLssL ssL ssLsLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLssLs sLs sLsLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLssLss Lss LsLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:112:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc35"&gt;&lt;a name="Scales with two step sizes-19 tones (8+3+8)-12L+7s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:112 --&gt;&lt;a class="wiki_link" href="/12L%207s"&gt;12L+7s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Meantone"&gt;Meantone&lt;/a&gt; MOS; &lt;!-- ws:start:WikiTextVariableComponentRule:035:[[{$page}#perfect|P]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:035 --&gt;&amp;lt;0 (oddly, neither this scale nor its &lt;!-- ws:start:WikiTextVariableComponentRule:037:[[{$page}#dual|dual]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual"&gt;dual&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:037 --&gt; can be tuned with a perfect 3/2!)  &lt;!-- ws:start:WikiTextVariableComponentRule:039:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:039 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3938:&amp;lt;a href=&amp;quot;/file/view/19_12_07_sLLsLsLL_sLL_sLLsLsLL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png/589274022/TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/19_12_07_sLLsLsLL_sLL_sLLsLsLL.png"&gt;&lt;img src="/file/view/TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png/589274022/TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png" alt="TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png" title="TN_19_12_07_sLLsLsLL_sLL_sLLsLsLL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3938 --&gt;&lt;br /&gt;
&lt;br /&gt;
generator = 5L+3s (500.0 to 505.3 cents)&lt;br /&gt;
notable EDOs: 31, 43, 50, 55&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsLLsLLs LsLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLLs LLs LsLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLLsLLsL sLLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLsL LsL sLLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLsLLsLs LLsLLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsLLsLsL LsLLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLLs LsLLsLLs LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLLsLsLL sLLsLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLsL sLLsLLsL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLsLsLLs LLsLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsLs LLsLLsLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsLsLLsL LsLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLsL LsLLsLsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLsLLsLL sLsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLsLL sLLsLsLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LsLLsLLs LsLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLsLLs LLsLsLLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL sLLsLLsL sLLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLLsL LsLsLLsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLLsLL sLsLLsLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLLs LsL LsLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLLs LsLLsLLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLsL sLL sLLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLsL sLLsLLsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsLs LLs LLsLLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLsL LsL LsLLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLsLL sLL sLLsLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLsLLs LLs LLsLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLLsL LsL LsLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLLsLL sLL sLsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:114:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc36"&gt;&lt;a name="Scales with two step sizes-19 tones (8+3+8)-5L+14s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:114 --&gt;&lt;a class="wiki_link" href="/5L%2014s"&gt;5L+14s&lt;/a&gt;&lt;/h3&gt;
Godzilla? MODMOS; full L/s range good&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3940:&amp;lt;a href=&amp;quot;/file/view/19_05_14_ssLssssL_ssL_ssLssssL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_19_05_14_ssLssssL_ssL_ssLssssL.png/589274014/TN_19_05_14_ssLssssL_ssL_ssLssssL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/19_05_14_ssLssssL_ssL_ssLssssL.png"&gt;&lt;img src="/file/view/TN_19_05_14_ssLssssL_ssL_ssLssssL.png/589274014/TN_19_05_14_ssLssssL_ssL_ssLssssL.png" alt="TN_19_05_14_ssLssssL_ssL_ssLssssL.png" title="TN_19_05_14_ssLssssL_ssL_ssLssssL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3940 --&gt;&lt;br /&gt;
&lt;br /&gt;
P = 2.5200335053&lt;br /&gt;
generator = L+3s (240.0 to 252.6 cents)&lt;br /&gt;
notable EDOs: 24, 29, 34, 39, 43, 53&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; sssLsssLsssLsssLssL &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;   ||      ||        &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; ssLssssLssLssssLssL &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssLssLss ssLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLss Lss ssLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLssLsss sLssLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LssLssss LssLssss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssLssssL ssLssssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLss ssLssLss ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLssssLs sLssssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLsss sLssLsss sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LssssLss LssssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssss LssLssss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssssLssL ssssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssssL ssLssssL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sssLssLs sssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssssLs sLssssLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss ssLssLss ssLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssssLss LssssLss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssssLssL ssssLssL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLssLs sssLssLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLss ssL ssLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLss ssLssLss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLsss sLs sLssLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssss Lss LssLssss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssssL ssL ssLssssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssssLs sLs sLssssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssssLss Lss LssssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssssLssL ssL ssssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLssLs sLs sssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:116:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc37"&gt;&lt;a name="Scales with two step sizes-19 tones (8+3+8)-14L+5s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:116 --&gt;&lt;a class="wiki_link" href="/14L%205s"&gt;14L+5s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Semaphore%20and%20godzilla"&gt;Semaphore / godzilla&lt;/a&gt; MODMOS; imperfect; full L/s range good&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3942:&amp;lt;a href=&amp;quot;/file/view/19_14_05_LLsLLLLs_LLs_LLsLLLLs.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png/589274028/TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/19_14_05_LLsLLLLs_LLs_LLsLLLLs.png"&gt;&lt;img src="/file/view/TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png/589274028/TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png" alt="TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png" title="TN_19_14_05_LLsLLLLs_LLs_LLsLLLLs.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3942 --&gt;&lt;br /&gt;
&lt;br /&gt;
generator = 3L+s (252.6 to 257.1 cents)&lt;br /&gt;
notable EDOs: 33, 47, 52&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; LLLsLLLsLLLsLLLsLLs &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;    ||      ||       &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; LLLLsLLsLLLLsLLsLLs &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLLLs LLs LLsLLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLLsL LsL LsLLLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLLsLL sLL sLLLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLsLLs LLs LLLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsLLsL LsL LLLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLsLLsLL LLsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsLL sLL LLsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsLLsLLL LsLLsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLLsLLLL sLLsLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLsLLLLs LLsLLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsLL LLsLLsLL LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsLLLLsL LsLLLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLLL LsLLsLLL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLLLLsLL sLLLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLLL sLLsLLLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLLLsLLs LLLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLLLs LLsLLLLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LLLsLLsL LLLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLLsL LsLLLLsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL LLsLLsLL LLsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLLsLL sLLLLsLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLLsLLs LLLLsLLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsLLsL LLLsLLsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsLL LLs LLsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsLL LLsLLsLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLLL LsL LsLLsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLLL sLL sLLsLLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:118:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="Scales with two step sizes-22 tones (9+4+9)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:118 --&gt;22 tones (9+4+9)&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:120:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc39"&gt;&lt;a name="Scales with two step sizes-22 tones (9+4+9)-7L+15s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:120 --&gt;&lt;a class="wiki_link" href="/7L%2015s"&gt;7L+15s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt; MODMOS; full L/s range good&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3944:&amp;lt;a href=&amp;quot;/file/view/22_07_15_sssLsssLL_sssL_sssLsssLL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png/589274032/TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/22_07_15_sssLsssLL_sssL_sssLsssLL.png"&gt;&lt;img src="/file/view/TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png/589274032/TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png" alt="TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png" title="TN_22_07_15_sssLsssLL_sssL_sssLsssLL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3944 --&gt;&lt;br /&gt;
&lt;br /&gt;
P = 2.3809207248&lt;br /&gt;
generator = L+2s (163.6 to 171.4 cents)&lt;br /&gt;
notable EDOs: 29, 36, 43, 50, 51&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; LssLssLssLssLssLssLsss &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;    ||||     ||||       &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; LsssLLsssLsssLLsssLsss &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLsssLL sssL sssLsssLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsssLLs ssLs ssLsssLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsssLLss sLss sLsssLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLLsss Lsss LsssLLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLLsssL sssL sssLLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLLsssLs ssLs ssLLsssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsssLss sLss sLLsssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsssLsss Lsss LLsssLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lsss LsssLsssL LsssLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLsssL sssL LsssLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sssL sssLsssLL sssLsssLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssLs ssLsssLLs ssLsssLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLss sLsssLLss sLsssLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lsss LsssLLsss LsssLLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLsssL LsssLsssL Lsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sssL sssLLsssL sssLLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLsssLL sssLsssLL sssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssLs ssLLsssLs ssLLsssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsssLLs ssLsssLLs ssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLss sLLsssLss sLLsssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsssLLss sLsssLLss sLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lsss LLsssLsss LLsssLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLLsss LsssLLsss Lsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sssL LsssLsssL LsssLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLLsssL sssLLsssL sssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLLsssLs ssLLsssLs ssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsssLss sLLsssLss sLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsssLsss LLsssLsss Lsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLsssL Lsss LsssLsssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsssLsssL LsssLsssL sssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:122:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc40"&gt;&lt;a name="Scales with two step sizes-22 tones (9+4+9)-15L+7s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:122 --&gt;&lt;a class="wiki_link" href="/15L%207s"&gt;15L+7s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt; MODMOS; imperfect; full L/s range mostly good&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3946:&amp;lt;a href=&amp;quot;/file/view/22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png/589274046/TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png"&gt;&lt;img src="/file/view/TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png/589274046/TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png" alt="TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png" title="TN_22_15_07_LLLsLLLss_LLLs_LLLsLLLss.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3946 --&gt;&lt;br /&gt;
&lt;br /&gt;
generator = 2L+s (160.0 to 163.6 cents)&lt;br /&gt;
notable EDOs: 37, 52b, 59&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; sLLsLLsLLsLLsLLsLLsLLL &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;    ||||     ||||       &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; sLLLssLLLsLLLssLLLsLLL &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsLLLss LLLs LLLsLLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLLssL LLsL LLsLLLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLssLL LsLL LsLLLssLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLssLLL sLLL sLLLssLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLssLLLs LLLs LLLssLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLssLLLsL LLsL LLssLLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLLLsLL LsLL LssLLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLLLsLLL sLLL ssLLLsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLLL sLLLsLLLs sLLLsLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLsLLLs LLLs sLLLsLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLLs LLLsLLLss LLLsLLLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLsL LLsLLLssL LLsLLLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLL LsLLLssLL LsLLLssLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLLL sLLLssLLL sLLLssLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLsLLLs sLLLsLLLs sLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLLs LLLssLLLs LLLssLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLsLLLss LLLsLLLss LLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLsL LLssLLLsL LLssLLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLLssL LLsLLLssL LLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLL LssLLLsLL LssLLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLssLL LsLLLssLL LsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLLL ssLLLsLLL ssLLLsLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLssLLL sLLLssLLL sLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLLs sLLLsLLLs sLLLsLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLLssLLLs LLLssLLLs LLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLssLLLsL LLssLLLsL LLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLLLsLL LssLLLsLL LsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLLLsLLL ssLLLsLLL sLLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLsLLLs sLLL sLLLsLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLsLLLs sLLLsLLLs LLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:124:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc41"&gt;&lt;a name="Scales with two step sizes-22 tones (9+4+9)-12L+10s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:124 --&gt;&lt;a class="wiki_link" href="/12L%2010s"&gt;12L+10s&lt;/a&gt;&lt;/h3&gt;
&lt;a class="wiki_link" href="/Pajara"&gt;Pajara&lt;/a&gt; / &lt;a class="wiki_link" href="/Diaschismic%20family"&gt;srutal (diaschismic)&lt;/a&gt; MODMOS &lt;!-- ws:start:WikiTextVariableComponentRule:041:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:041 --&gt; &lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3948:&amp;lt;a href=&amp;quot;/file/view/22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png/589274040/TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png"&gt;&lt;img src="/file/view/TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png/589274040/TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png" alt="TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png" title="TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3948 --&gt;&lt;br /&gt;
&lt;br /&gt;
P = 7.6918120831&lt;br /&gt;
generator = L+s (100.0 to 109.1 cents)&lt;br /&gt;
period = 1/2 octave&lt;br /&gt;
notable EDOs: 34, 46, 56, 58, 70&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; sLsLsLsLsLLsLsLsLsLsLL &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;           ||           &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; sLsLsLsLsLsLLsLsLsLsLL &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;
 


&lt;table class="wiki_table"&gt;
'''Q'''  is calculated similarly to P, but indicates a limit of sorts -- a point on the L/s continuum beyond which the omnitetrachordality of the scale can be considered to 'break down' in some way.
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLs LsLsLsLsL LsLsLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLsLsL sLsL LsLsLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLsL sLsLsLsLL sLsLsLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLs LsLsLsLLs LsLsLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLsL sLsLsLLsL sLsLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLs LsLsLLsLs LsLsLLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLsLsL LsLsLsLsL LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLsL sLsLLsLsL sLsLLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLsLsLL sLsLsLsLL sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLs LsLLsLsLs LsLLsLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLsLLs LsLsLsLLs LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLsL sLLsLsLsL sLLsLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLsLLsL sLsLsLLsL sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLs LLsLsLsLs LLsLsLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLLsLs LsLsLLsLs LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLsL LsLsLsLsL LsLsLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLLsLsL sLsLLsLsL sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLsLs LsLLsLsLs LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLsLsL sLLsLsLsL sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLsLsLs LLsLsLsLs LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLsLsL LsLs LsLsLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLsLsL LsLsLsLsL sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLsLsLL sLsL sLsLsLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLsLLs LsLs LsLsLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLsLLsL sLsL sLsLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLLsLs LsLs LsLsLLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLLsLsL sLsL sLsLLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLsLs LsLs LsLLsLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLsLsL sLsL sLLsLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLsLsLs LsLs LLsLsLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
Consider for example the [[OTC_2L_8s|OTC 2L+8s]] pajara MODMOS, LsssssLsss -- at P = L/s = 1.885, L+3s forms a just 4/3.  As L/s increases, L gets larger and s smaller; at Q = L/s = 4.827, a just 4/3 is not L+3s, but L+2.5s. Past this point, L+2s will therefore be closer to a just 4/3 than L+3s:
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:126:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc42"&gt;&lt;a name="Scales with two step sizes-22 tones (9+4+9)-10L+12s"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:126 --&gt;&lt;a class="wiki_link" href="/10L%2012s"&gt;10L+12s&lt;/a&gt;&lt;/h3&gt;
Pajara? MODMOS; imperfect; full L/s range good&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:3950:&amp;lt;a href=&amp;quot;/file/view/22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;/file/view/TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png/589274036/TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="/file/view/22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png"&gt;&lt;img src="/file/view/TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png/589274036/TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png" alt="TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png" title="TN_22_10_12_sLsLsLsLs_LsLs_sLsLsLsLs.png" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextLocalImageRule:3950 --&gt;&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 32, 42, 54&lt;br /&gt;
generator = L+s (10.91 to 120.0 cents)&lt;br /&gt;
period = 1/2 octave&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; LsLsLsLsLssLsLsLsLsLss &lt;/tt&gt; (MOS)&lt;br /&gt;
&lt;tt&gt;           ||           &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; LsLsLsLsLsLssLsLsLsLss &lt;/tt&gt; (OTC MODMOS)&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;


[[File:P_Q_C_LsssssLsss.png|alt=P_Q_C_LsssssLsss.png|P_Q_C_LsssssLsss.png]]


&lt;table class="wiki_table"&gt;
For some scales, Q will not exist.  For others, a second Q may exist that is less than P, placing a lower bound on the L/s ratio as well as an upper one.
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLsL sLsLsLsLs sLsLsLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLsLsLs LsLs sLsLsLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLs LsLsLsLss LsLsLsLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLsL sLsLsLssL sLsLsLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLs LsLsLssLs LsLsLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLsL sLsLssLsL sLsLssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLsLsLs sLsLsLsLs sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLs LsLssLsLs LsLssLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLsLss LsLsLsLss LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLsL sLssLsLsL sLssLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLsLssL sLsLsLssL sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLs LssLsLsLs LssLsLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLssLs LsLsLssLs LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLsL ssLsLsLsL ssLsLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLssLsL sLsLssLsL sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsLs sLsLsLsLs sLsLsLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLssLsLs LsLssLsLs LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLsLsL sLssLsLsL sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLsLsLs LssLsLsLs LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsLsLsL ssLsLsLsL sLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLsLsLs sLsL sLsLsLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLsLsLs sLsLsLsLs LsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLsLss LsLs LsLsLsLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLsLssL sLsL sLsLsLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsLssLs LsLs LsLsLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLssLsL sLsL sLsLssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLssLsLs LsLs LsLssLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLsLsL sLsL sLssLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLsLsLs LsLs LssLsLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsLsLsL sLsL ssLsLsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
We can also consider a point C, where the number of steps "crosses" the just 4/3 entirely - in the example above, this corresponds to 4/3 = L+2s.  Q is then halfway between P and C, i.e.
&lt;br /&gt;
&lt;hr /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:128:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Scales with 3 step sizes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:128 --&gt;Scales with 3 step sizes&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:130:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc44"&gt;&lt;a name="Scales with 3 step sizes--22-tone Indian 'sruti' scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:130 --&gt;22-tone Indian 'sruti' scale&lt;/h3&gt;
(5-limit &lt;a class="wiki_link" href="/Just%20intonation"&gt;JI&lt;/a&gt;)&lt;br /&gt;
&lt;br /&gt;


C = 2Q-P


&lt;table class="wiki_table"&gt;
Q = (C+P)/2
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;scale step&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;ratio&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;&lt;strong&gt;cents&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;0.000&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;256/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;90.225&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;111.731&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;182.404&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;203.910&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;32/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;294.135&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;315.641&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;386.314&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;81/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;407.820&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;498.045&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;27/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;519.551&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;45/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;590.224&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;729/512&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;611.730&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;701.955&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;128/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;792.180&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;813.686&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;884.359&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;27/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;905.865&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;996.090&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1017.596&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1088.269&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;243/128&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1109.775&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1200.000&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
P = 2Q-C
A = 256/243&lt;br /&gt;
b = 81/80&lt;br /&gt;
c = 25/24&lt;br /&gt;
A+2b+c = 9/8&lt;br /&gt;
3A+4b+2c = 4/3&lt;br /&gt;
7A+10b+5c = 2/1&lt;br /&gt;
&lt;br /&gt;
modes:&lt;br /&gt;


...which leads to the curious result that, although P is undefined when calculated by the normal method (due to division by zero) for a scale such as blackwood[10] (LsLsLsLsLs), C and Q can be calculated, and thus a value of P = -1 can be found anyway, even though it seems not to be of any use :)


&lt;table class="wiki_table"&gt;
'''"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.
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Abcb AbcbAbcbA AbcbAbcbA &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; AbcbAbcbA bcbA AbcbAbcbA &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; bcbA bcbAbcbAA bcbAbcbAA &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; cbAb cbAbcbAAb cbAbcbAAb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; bAbc bAbcbAAbc bAbcbAAbc &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Abcb AbcbAAbcb AbcbAAbcb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; AbcbAbcbA AbcbAbcbA Abcb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; bcbA bcbAAbcbA bcbAAbcbA &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; bcbAbcbAA bcbAbcbAA bcbA &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; cbAb cbAAbcbAb cbAAbcbAb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; cbAbcbAAb cbAbcbAAb cbAb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; bAbc bAAbcbAbc bAAbcbAbc &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; bAbcbAAbc bAbcbAAbc bAbc &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Abcb AAbcbAbcb AAbcbAbcb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; AbcbAAbcb AbcbAAbcb Abcb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; bcbA AbcbAbcbA AbcbAbcbA &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; bcbAAbcbA bcbAAbcbA bcbA &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; cbAAbcbAb cbAAbcbAb cbAb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; bAAbcbAbc bAAbcbAbc bAbc &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; AAbcbAbcb AAbcbAbcb Abcb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; AbcbAbcbA Abcb AbcbAbcbA &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; AbcbAbcbA AbcbAbcbA bcbA &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; bcbAbcbAA bcbA bcbAbcbAA &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; cbAbcbAAb cbAb cbAbcbAAb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; bAbcbAAbc bAbc bAbcbAAbc &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; AbcbAAbcb Abcb AbcbAAbcb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; bcbAAbcbA bcbA bcbAAbcbA &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; cbAAbcbAb cbAb cbAAbcbAb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; bAAbcbAbc bAbc bAAbcbAbc &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; AAbcbAbcb Abcb AAbcbAbcb &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{{Navbox scale gallery}}
&lt;br /&gt;
[[Category:Omnitetrachordal]]
&lt;hr /&gt;
[[Category:Lists of scales]]
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:132:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc45"&gt;&lt;a name="Definitions and formulas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:132 --&gt;Definitions and formulas&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextAnchorRule:185:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@dual&amp;quot; title=&amp;quot;Anchor: dual&amp;quot;/&amp;gt; --&gt;&lt;a name="dual"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:185 --&gt;&lt;strong&gt;&amp;quot;Dual&amp;quot;&lt;/strong&gt; refers to the &amp;quot;inverse&amp;quot; of a L+s scale pattern, where every L is replaced by s, and vice versa.  For example, &lt;tt&gt; sLssL &lt;/tt&gt; and &lt;tt&gt; LsLLs &lt;/tt&gt; are duals.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextAnchorRule:186:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@perfect&amp;quot; title=&amp;quot;Anchor: perfect&amp;quot;/&amp;gt; --&gt;&lt;a name="perfect"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:186 --&gt;&lt;strong&gt;&amp;quot;Perfect&amp;quot;&lt;/strong&gt; means that values for L and s exist such that L &amp;gt; s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both).  (See also &lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Eigenmonzo subgroup&lt;/a&gt;.)  In this case the value &lt;strong&gt;&amp;quot;P&amp;quot;&lt;/strong&gt; is given, where P = L/s.  For a perfect scale, P &amp;gt; 1.  Note that if a scale &amp;quot;a&amp;quot; is perfect (P&lt;span style="vertical-align: sub;"&gt;a&lt;/span&gt; &lt;!-- ws:start:WikiTextRawRule:00:``=`` --&gt;=&lt;!-- ws:end:WikiTextRawRule:00 --&gt; L/s), its dual &amp;quot;b&amp;quot; will have the value P&lt;span style="vertical-align: sub;"&gt;b&lt;/span&gt; &lt;!-- ws:start:WikiTextRawRule:01:``=`` --&gt;=&lt;!-- ws:end:WikiTextRawRule:01 --&gt; s/L = 1/P&lt;span style="vertical-align: sub;"&gt;a&lt;/span&gt;, and therefore must be imperfect (if P&lt;span style="vertical-align: sub;"&gt;a&lt;/span&gt; &amp;gt; 1, then P&lt;span style="vertical-align: sub;"&gt;b&lt;/span&gt; &amp;lt; 1 ).&lt;br /&gt;
&lt;br /&gt;
In some cases, P may be less than zero.  I'm not yet sure what this means :)&lt;br /&gt;
&lt;br /&gt;
The value of P is calculated as follows:&lt;br /&gt;
&lt;br /&gt;
a = the number of L steps per 2/1&lt;br /&gt;
b = the number of s steps per 2/1&lt;br /&gt;
c = the number of L steps per 3/2&lt;br /&gt;
d = the number of s steps per 3/2&lt;br /&gt;
x = log&lt;span style="vertical-align: sub;"&gt;2&lt;/span&gt;(3/2) = ~0.58496 octaves = ~701.955 cents&lt;br /&gt;
&lt;br /&gt;
aL+bs = log&lt;span style="vertical-align: sub;"&gt;2&lt;/span&gt;(2/1) = 1&lt;br /&gt;
cL+ds = x&lt;br /&gt;
&lt;br /&gt;
s = (c-ax)/(bc-ad)&lt;br /&gt;
L = (x-ds)/c&lt;br /&gt;
P = L/s&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;&amp;quot;L/s range&amp;quot;&lt;/strong&gt;: 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 &amp;quot;full L/s range is good&amp;quot; simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's &amp;quot;goodness&amp;quot; is intended.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;hr /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:134:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc46"&gt;&lt;a name="References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:134 --&gt;References&lt;/h1&gt;
&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextAnchorRule:187:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@ref1&amp;quot; title=&amp;quot;Anchor: ref1&amp;quot;/&amp;gt; --&gt;&lt;a name="ref1"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:187 --&gt;(1) Several of these scales were noted as omnitetrachordal by Paul Erlich in 2002 (if not before). See tuning-math list messages &lt;a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685" rel="nofollow"&gt;3685&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987" rel="nofollow"&gt;10987&lt;/a&gt;.&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 02:58, 28 September 2025


An (incomplete) list of omnitetrachordal (OTC) scales.

Scales with two step sizes

(not necessarily MOS or DE)

These are mostly tempered (irrational) scales. For a few patterns (usually where the generator is close to a perfect 4/3 or 3/2), a Pythagorean (3-limit JI) version with only two step sizes is possible.

In some cases, multiple OTC patterns with the same number of large and small steps exist.

Follow the links for more detailed info on each scale!

3 tones

2L+s (the simplest possible OTC scale; s=9/8, L=4/3)

4 tones

(no OTC scales possible)

5 tones

2L+3s - sLsLs (MOS)

3L+2s - LsLsL (MOS)

6 tones

2L+4s - LsssLs

7 tones

2L+5s - sLsssLs (MOS)

5L+2s - LsLLLsL (MOS)

8 tones

2L+6s - LssssLss

9 tones

2L+7s - LsssssLss

10 tones

2L+8s - LsssssLsss

3L+7s - LsssLsLsss

5L+5s - LsLsLsLsLs (MOS)

7L+3s - sLLLsLLLsL

8L+2s - LLsLLLsLLL

11 tones

2L+9s - LssssssLsss

12 tones

2L+10s - LsssLsssssss (4+4+4), sssLssssLsss (5+2+5)

5L+7s - ssLsLssLsLsL (MOS)

7L+5s - LLsLsLLsLsLs (MOS)

10L+2s - LLLsLLLLsLLL

13 tones

2L+11s - LsssssssLssss

7L+6s - sLLLssLssLLLs

14 tones

2L+12s - LssssssssLssss

5L+9s - sssLsLsssLsLsL

7L+7s - LsLsLsLsLsLsLs (MOS)

12L+2s - LLLLLLLsLLLLLs

15 tones

2L+13s - LssssssssLsssss

7L+8s - LsLLssLsLLssLss, LssLLsLssLLsLss

12L+3s - LsLLLLLsLLLLLsL

16 tones

2L+14s - LsssssssssLsssss

17 tones

2L+15s - LsssssssssLssssss (7+3+7), LssssssssssLsssss (6+5+6)

5L+12s - sLsssLssLssLsssLs (MOS)

7L+10s - sLsLsLssLssLsLsLs, sLssLLssLssLLssLs

10L+7s - LsLsLsLLsLLsLsLsL, LsLLssLLsLLssLLsL

12L+5s - LsLLLsLLsLLsLLLsL (MOS)

18 tones

2L+16s - LssssssssssLssssss

7L+11s - LLsssLsLLsssLsssLs, LsssLLsLsssLLsLsss

19 tones

2L+17s - LsssssssssssLssssss

5L+14s - sLssssLssLssLssssLs

7L+12s - sLssLsLssLssLsLssLs (MOS)

10L+9s - LsLLsssLLsLLsssLLsL

12L+7s - LsLLsLsLLsLLsLsLLsL (MOS)

14L+5s - LLLLsLLsLLLLsLLsLLs

17L+2s - LLLLLsLLLLLLLsLLLLL

20 tones

2L+18s - LsssssssssssLsssssss

7L+13s - sssLsssLssLLsssLssLL, sssLsssLsLsLsssLsLsL, sssLsssLLssLsssLLssL

12L+8s - sLLssLLsLLLssLLsLLLs, sLLssLLLsLLssLLLsLLs, sLsLsLLLsLsLsLLLsLsL

21 tones

2L+19s - LssssssssssssLsssssss

5L+16s - sLsssssLssLssLsssssLs

7L+14s - ssssLssssLsLLssssLsLL, ssssLssssLLsLssssLLsL

22 tones

2L+20s - LssssssssssssLssssssss (9+4+9), LsssssssssssssLsssssss (8+6+8)

5L+17s - ssssLsssLssssLsssLsssL (MOS)

7L+15s - LssLsLsssLssLsLsssLsss, LsssLsLssLsssLsLssLsss, LsssLLsssLsssLLsssLsss

10L+12s - LsLsLsLsLsLssLsLsLsLss

12L+10s - sLsLsLsLsLsLLsLsLsLsLL, sLLsLsLLssLLssLLsLsLLs, sLLssLLLssLLssLLLssLLs

15L+7s - sLLLssLLLsLLLssLLLsLLL

17L+5s - sLLLsLLLsLLLLsLLLsLLLL (MOS)

23 tones

2L+21s - LsssssssssssssLssssssss

7L+16s - ssssLssssLssLLssssLssLL, ssLsLsLssssLssssLsLsLss, ssssLssssLLssLssssLLssL

24 tones

2L+22s - LssssssssssssssLssssssss

5L+19s - sssssLsssLsssssLsssLsssL

7L+17s - sssLsssLssLssLsssLssLssL, sssLsssLsssLsLsssLsssLsL

10L+14s - LssLLssssLLssLLssssLLssL, sssLsLsLsLsssLsLsLsLsLsL

12L+12s - LsLsLsLsLsLsLsLsLsLsLsLs (MOS), ssLsLLssLLssLsLLssLLssLL, ssLLsLssLLssLLsLssLLssLL

14L+10s - LssLLLLssLLssLLssLLLLssL, LLsLsLsLsLsLsLLLsLsLsLsL

15L+9s - LLsssLLLsLLLsLLLsssLLLsL

17L+7s - LLLsLLsLLsLLLsLLsLLsLLLs, LLLsLsLLLsLLLsLLLsLsLLLs

19L+5s - LLLsLLLLLsLLLsLLLLLsLLLs

>24 tones

Many larger OTC L+s scales are believed to exist, but due to exponentially increasing computation time, these have not yet been studied in detail. Scales of the form 2L+ns are known to exist up to size 53, and assumed to exist for any larger size.

L/s matrix

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 L
1 x
2 x x x x x x x
3 x x x
4 x
5 x x x x x x x
6 x x
7 x x x x x x x x
8 x x x
9 x x x x
10 x x x x
11 x x
12 x x x x x
13 x x
14 x x x x
15 x x
16 x x x
17 x x x
18 x
19 x x
20 x
21 x
22 x
23 x
24 x
s                                                                                                    

Scales with 3 step sizes

8 notes

ABCABCAB (Fokker block)

2L+3M+3s - LMsMsLMs, sMLsMsML

10 tones

ABACABACAB (3-SN)

2L+3M+5s - sMsLsMsMsL

2L+5M+3s - MsMLMsMsML

5L+2M+3s - LsLMLsLsLm

11 tones

ABACABACABA (3-SN)

2L+3M+6s - sMsLsMssMsL

2L+6M+3s - MsMLMsMMsML

ABCAABCAABA

2L+3M+6s - sMLssMssMLs, sLMssMssLMs

2L+6M+3s - MsLMMsMMsLM, MLsMMsMMLsM

12 tones

ABABCABABCAB (Fokker block)

5L+2M+5s - LsLsMLsLsLsM, MsLsLsLMsLsL

5L+5M+2s - LMLMsLMLMLMs, sMLMLMLsMLML

13 tones

ABACAABACAABA

2L+3M+8s - sMsLssMssMsLs, sLsMssMssLsMs

2L+8M+3s - MsMLMMsMMsMLM, MLMsMMsMMLMsM

14 tones

ABABACABABACAB (3-SN)

5L+2M+7s - sLsMsLsLsLsMsL

5L+7M+2s - MLMsMLMLMLMsML

15 tones

ABAACAABAACAABA (3-SN)

2L+3M+10s - sMssLssMssMssLs

2L+5M+3s - MsMMLMMsMMsMMLM

10L+2M+3s - LsLLMLLsLLsLLML

17 tones

ABAABACABAABACABA (3-SN)

2L+5M+10s - sMsLsMssMssMsLsMs

2L+10M+5s - MsMLMsMMsMMsMLMsM

5L+2M+10s - sLsMsLssLssLsMsLs

10L+2M+5s - LsLMLsLLsLLsLMLsL

ABAABCAABAABCAABA

2L+5M+10s - sMssMLssMssMLssMs

2L+10M+5s - MsMMsLMMsMMsLMMsM

5L+2M+10s - sLssLMssLssLMssLs

10L+2M+5s - LsLLsMLLsLLsMLLsL

ABACABCABACABCABC (Fokker block)

5L+7M+5s - MLMsMLsMLsMLMsMLs, sLMsMLMsLMsLMsMLM

7L+5M+5s - LMLsLMsLMsLMLsLMs, sMLsLMLsMLsMLsLML

ABCABCAABCABCAABC (Fokker block)

5L+7M+5s - MLsMLsMMLsMLsMMLs, sLMMsLMsLMMsLMsLM

7L+5M+5s - LMsLMsLLMsLMsLLMs, sMLLsMLsMLLsMLsML

19 tones

ABCBAABAABCBAABAABA (3-SN)

ABA=9/8

ABCBA=32/27, BC=256/243

10L+2M+7s: LsMsLLsLLsMsLLsLLsL

ABCABCABABCABCABCAB (Fokker block)

20 tones

ABACABABABABABACABAB

22 tones

ABABCABABABABABABCABAB

ACABBACABACABBACABACAB

AbcbAbcbAAbcbAbcbAbcbA

24 tones

ACABABACABACABABACABACAB (3-SN)

MET-24 has this structure as 5L+12M+7s: MLMsMsMLMsMLMsMsMLMsMLMs

AABAAABAACAABAAABAACAABA (3-SN)

29 tones

BABBABABBABCBABBABABBABCBABBA (3-SN)

2L+10m+17s: smsmssmsLsmssmsmssmsLsmssmsms

31 tones

BABBCBBABABBABABBCBBABABBABABBA (3-SN)

10L+19m+2s: mLmmLmsmLmmLmmLmLmmLmmLmsmLmmLm

10L+2m+19s: sLssLsmsLssLssLsLssLssLsmsLssLs

41 tones

BABCBABBABBABCBABBABCBABBABBABCBABBABCBAB (3-SN)

5L+12M+24s: sMsLsMssMssMsLsMssMsLsMssMssMsLsMssMsLsMs

BBABBBABBABBBABBCBBABBBABBABBBABBCBBABBBA (3-SN)

29L+2M+10s: LsLLLsLLMLLsLLLsLLsLLLsLLsLLLsLLMLLsLLLsL

2L+29M+10s: MsMMMsMMLMMsMMMsMMsMMMsMMsMMMsMMLMMsMMMsM

46 tones

CACACBCACACACBCACACCACACBCACACACBCACACCACACBCA (3-SN)

72 tones

ABAABABABAABABACABABAABABABAABABAABABABAABABAABABABAABABACABABAABABABAAB (3-SN)

29L+2M+41s: sLssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssL

2L+29M+41s: sMssMsMsMssMsMsLsMsMssMsMsMssMsMssMsMsMssMsMssMsMsMssMsMsLsMssMsMsMssM

Definitions and formulas

"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. If a scale is OTC, its dual is often OTC as well, but not always!

"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, or unchanged-interval basis.)

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 (Pa = L/s), its dual "b" will have the value Pb = s/L = 1/Pa, and therefore must be imperfect (if Pa > 1, then Pb < 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 4/3

d = the number of s steps per 4/3

x = log2(4/3) = ~0.41504 octaves = ~498.045 cents

aL+bs = log2(2/1) = 1

cL+ds = x

s = (c-ax)/(bc-ad)

L = (x-ds)/c

P = L/s

Note that the same procedure could be used to calculate the L/s ratio necessary to give any other just interval, such as 5/4, 11/8, etc.

Q is calculated similarly to P, but indicates a limit of sorts -- a point on the L/s continuum beyond which the omnitetrachordality of the scale can be considered to 'break down' in some way.

Consider for example the OTC 2L+8s pajara MODMOS, LsssssLsss -- at P = L/s = 1.885, L+3s forms a just 4/3. As L/s increases, L gets larger and s smaller; at Q = L/s = 4.827, a just 4/3 is not L+3s, but L+2.5s. Past this point, L+2s will therefore be closer to a just 4/3 than L+3s:

P_Q_C_LsssssLsss.png

For some scales, Q will not exist. For others, a second Q may exist that is less than P, placing a lower bound on the L/s ratio as well as an upper one.

We can also consider a point C, where the number of steps "crosses" the just 4/3 entirely - in the example above, this corresponds to 4/3 = L+2s. Q is then halfway between P and C, i.e.

C = 2Q-P

Q = (C+P)/2

P = 2Q-C

...which leads to the curious result that, although P is undefined when calculated by the normal method (due to division by zero) for a scale such as blackwood[10] (LsLsLsLsLs), C and Q can be calculated, and thus a value of P = -1 can be found anyway, even though it seems not to be of any use :)

"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.


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