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Gallery of omnitetrachordal scales: Difference between revisions

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Wikispaces>spt3125
**Imported revision 589273442 - Original comment: **
Wikispaces>spt3125
**Imported revision 589280430 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>2016-08-12 21:23:18 UTC</tt>.<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>589273442</tt>.<br>
: The original revision id was <tt>589280430</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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=Scales with two step sizes=
=Scales with two step sizes=
(not necessarily [[MOS]] or [[Distributional Evenness|DE]])
(not necessarily [[MOS]] or [[Distributional Evenness|DE]])
These are mostly tempered (irrational) scales.  In some cases (usually where the generator is close to a perfect 4/3 or 3/2), a Pythagorean (3-limit [[Just intonation|JI]]) version is possible.
[[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)==
==5 tones (2+1+2)==
Line 19: Line 19:
===[[2L 3s|2L+3s]]===
===[[2L 3s|2L+3s]]===
The familiar classic pentatonic scale. Can include [[superpyth]], [[https://en.wikipedia.org/wiki/Pythagorean_tuning|Pythagorean]], [[meantone]], and [[Mavila Temperament Modal Harmony|mavila]] tunings.  Is [[MOS]].  [[{$page}#ref1|(1)]]
The familiar classic pentatonic scale. Can include [[superpyth]], [[https://en.wikipedia.org/wiki/Pythagorean_tuning|Pythagorean]], [[meantone]], and [[Mavila Temperament Modal Harmony|mavila]] tunings.  Is [[MOS]].  [[{$page}#ref1|(1)]]
[[image:TN_05_02_03_sL_s_sL.png link="file:05_02_03_sL_s_sL.png"]]


Pythagorean (3-limit JI): L=[[32_27|32/27]], s=9/8
Pythagorean (3-limit JI): L=[[32_27|32/27]], s=9/8
Line 35: Line 37:
===[[3L 2s|3L+2s]]===
===[[3L 2s|3L+2s]]===
Father? MOS; [[{$page}#perfect|imperfect]]; [[{$page}#ref1|(1)]]
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"]]


generator = L+s (400.0 to 480.0 cents)
generator = L+s (400.0 to 480.0 cents)
Line 51: Line 55:
===[[2L 5s|2L+5s]]===
===[[2L 5s|2L+5s]]===
[[Mavila Temperament Modal Harmony|Mavila]] diatonic MOS.  [[{$page}#perfect|Imperfect]].  [[{$page}#ref1|(1)]]
[[Mavila Temperament Modal Harmony|Mavila]] diatonic MOS.  [[{$page}#perfect|Imperfect]].  [[{$page}#ref1|(1)]]
[[image:TN_07_02_05_sLs_s_sLs.png link="file:07_02_05_sLs_s_sLs.png"]]


generator = L+2s (514.3 to 600.0 cents)
generator = L+2s (514.3 to 600.0 cents)
Line 67: Line 73:
===[[5L 2s|5L+2s]]===
===[[5L 2s|5L+2s]]===
Classic diatonic scale ([[meantone]], Pythagorean, [[superpyth]]); MOS. [[{$page}#ref1|(1)]]
Classic diatonic scale ([[meantone]], Pythagorean, [[superpyth]]); MOS. [[{$page}#ref1|(1)]]
[[image:TN_07_05_02_LsL_L_Ls.png link="file:07_05_02_LsL_L_Ls.png"]]


Pythagorean (3-limit JI): L=9/8, s=[[256_243|256/243]]
Pythagorean (3-limit JI): L=9/8, s=[[256_243|256/243]]
Line 91: Line 99:
* it is its own dual (changing all L to s, and vice versa, gives the same scale)
* 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)
* 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"]]


generator = s (0 to 120 cents)
generator = s (0 to 120 cents)
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===[[7L 3s|7L+3s]]===
===[[7L 3s|7L+3s]]===
[[Mohajira]] / [[Neutral third scales|neutral-thirds]] [[MODMOS]]
[[Mohajira]] / [[Neutral third scales|neutral-thirds]] [[MODMOS]]
[[image:TN_10_07_03_sLLL_sL_sLLL.png link="file:10_07_03_sLLL_sL_sLLL.png"]]


P = 2.5872804832
P = 2.5872804832
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===[[3L 7s|3L+7s]]===
===[[3L 7s|3L+7s]]===
The [[{$page}#dual|dual]] of 7L+3s, this scale pattern barely qualifies as omnitetrachordal.
The [[{$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"]]


notable EDOs: 13, 16b
notable EDOs: 13, 16b
Line 135: Line 149:
===[[2L 8s|2L+8s]]===
===[[2L 8s|2L+8s]]===
[[Pajara]] MODMOS.  Best at lower ratios of L/s.  [[{$page}#ref1|(1)]]
[[Pajara]] MODMOS.  Best at lower ratios of L/s.  [[{$page}#ref1|(1)]]
[[image:TN_10_02_08_sLss_ss_sLss.png link="file:10_02_08_sLss_ss_sLss.png"]]


P = 1.8849491924
P = 1.8849491924
Line 161: Line 177:
===[[8L 2s|8L+2s]]===
===[[8L 2s|8L+2s]]===
The dual of 2L+8s, this scale is imperfect and poorly tuned for 3/2 at any L/s ratio.
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"]]


notable EDOs: 18, 26b
notable EDOs: 18, 26b
Line 171: Line 189:
===[[5L 7s|5L+7s]]===
===[[5L 7s|5L+7s]]===
12-tone MOS of the helmholtz / garibaldi / [[Schismatic family|schismatic]] and [[superpyth]] temperaments (slightly sharp 3/2).  Very usable at any L/s ratio.  Many modes may be pentachordally split in two ways.
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"]]


Pythagorean (3-limit JI): L=2187/2048, s=256/243
Pythagorean (3-limit JI): L=2187/2048, s=256/243
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===[[7L 5s|7L+5s]]===
===[[7L 5s|7L+5s]]===
12-tone MOS of the [[meantone]] and [[Meantone family#Flattone|flattone]] temperaments (slightly flat 3/2).  [[{$page}#perfect|Imperfect]], but very usable at any L/s ratio.  Many modes may be pentachordally split in two ways.
12-tone MOS of the [[meantone]] and [[Meantone family#Flattone|flattone]] temperaments (slightly flat 3/2).  [[{$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"]]


generator = 3L+2s (500.0 to 514.3 cents)
generator = 3L+2s (500.0 to 514.3 cents)
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===[[10L 2s|10L+2s]]===
===[[10L 2s|10L+2s]]===
[[Pajara]] MODMOS.  Good for most any ratio of L to s.
[[Pajara]] MODMOS.  Good for most any ratio of L to s.
[[image:TN_12_10_02_LLsLL_LL_LLsLL.png link="file:12_10_02_LLsLL_LL_LLsLL.png"]]


P = 1.1300083763
P = 1.1300083763
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===[[2L 10s|2L+10s]]===
===[[2L 10s|2L+10s]]===
[[{$page}#dual|Dual]] of 10L+2s.  Probably only useful for small values of L/s.
[[{$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"]]


notable EDOs: 14, 16
notable EDOs: 14, 16
Line 252: Line 278:
===[[7L 6s|7L+6s]]===
===[[7L 6s|7L+6s]]===
[[Tetracot family|Tetracot]] MODMOS.  Best tuned at high values of L/s.
[[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"]]


P = 5.1745609664
P = 5.1745609664
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===[[5L 9s|5L+9s]]===
===[[5L 9s|5L+9s]]===
[[Semaphore and Godzilla|Semaphore / godzilla]] MODMOS.  Usable at any L/s ratio.
[[Semaphore and Godzilla|Semaphore / godzilla]] MODMOS.  Usable at any L/s ratio.
[[image:TN_14_05_09_LsssLs_Ls_LsssLs.png link="file:14_05_09_LsssLs_Ls_LsssLs.png"]]


P = 3.5200335053
P = 3.5200335053
Line 311: Line 341:
===[[12L 2s|12L+2s]]===
===[[12L 2s|12L+2s]]===
[[Injera]] MODMOS.  Imperfect (P&lt;0); best for L/s &gt;= 1.5 [[{$page}#ref1|(1)]]
[[Injera]] MODMOS.  Imperfect (P&lt;0); best for L/s &gt;= 1.5 [[{$page}#ref1|(1)]]
[[image:TN_14_12_02_sLLLLL_LL_sLLLLL.png link="file:14_12_02_sLLLLL_LL_sLLLLL.png"]]


generator = L (85.7 to 100.0 cents)
generator = L (85.7 to 100.0 cents)
Line 341: Line 373:
===[[7L 8s|7L+8s]]===
===[[7L 8s|7L+8s]]===
[[Porcupine]] MODMOS
[[Porcupine]] MODMOS
[[image:TN_15_07_08_ssLsLL_ssL_ssLsLL.png link="file:15_07_08_ssLsLL_ssL_ssLsLL.png"]]


[[{$page}#perfect|P]] = 3.3809207248
[[{$page}#perfect|P]] = 3.3809207248
Line 370: Line 404:
===[[12L 3s|12L+3s]]===
===[[12L 3s|12L+3s]]===
[[Augmented]] MODMOS.  Best at higher L/s ratios.
[[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"]]


P = 12.5377181246
P = 12.5377181246
Line 402: Line 438:
===[[5L 12s|5L+12s]]===
===[[5L 12s|5L+12s]]===
[[Superpyth]] / ultrapyth MOS.  Imperfect, best at low L/s.  Many modes may be split two ways.
[[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"]]


generator = 2L+5s (480.0 to 494.1 cents)
generator = 2L+5s (480.0 to 494.1 cents)
Line 428: Line 466:
===[[12L 5s|12L+5s]]===
===[[12L 5s|12L+5s]]===
Helmholtz / [[Schismatic family|schismatic]] MOS; full L/s range very good [[{$page}#ref1|(1)]]
Helmholtz / [[Schismatic family|schismatic]] MOS; full L/s range very good [[{$page}#ref1|(1)]]
[[image:TN_17_12_05_LLLsLLs_LLs_LLLsLLs.png link="file:17_12_05_LLLsLLs_LLs_LLLsLLs.png"]]


Pythagorean (3-limit JI): L=256/243, s=531441/524288
Pythagorean (3-limit JI): L=256/243, s=531441/524288
Line 456: Line 496:
===[[7L 10s|7L+10s]]===
===[[7L 10s|7L+10s]]===
[[Mohajira]] / [[Neutral third scales|neutral-thirds]] MODMOS; full L/s range good
[[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"]]


P = 1.5872804832
P = 1.5872804832
Line 487: Line 529:
===[[10L 7s|10L+7s]]===
===[[10L 7s|10L+7s]]===
Beatles? / [[Dicot family|dicot]]? MODMOS; imperfect; full L/s range mostly good
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)
generator = 3L+2s (352.9 to 360.0 cents)
Line 519: Line 563:
===[[7L 11s|7L+11s]]===
===[[7L 11s|7L+11s]]===
Sixix?; best for L/s&gt;2
Sixix?; best for L/s&gt;2
[[image:TN_18_07_11_sssLsLL_sssL_sssLsLL.png link="file:18_07_11_sssLsLL_sssL_sssLsLL.png"]]


P = 5.968201208
P = 5.968201208
Line 553: Line 599:
===[[7L 12s|7L+12s]]===
===[[7L 12s|7L+12s]]===
[[Meantone family#Flattone|Flattone]] MOS; [[{$page}#perfect|P]]&lt;0; [[{$page}#ref1|(1)]]
[[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"]]


generator = 3L+5s (505.3 to 514.3 cents)
generator = 3L+5s (505.3 to 514.3 cents)
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===[[12L 7s|12L+7s]]===
===[[12L 7s|12L+7s]]===
[[Meantone]] MOS; [[{$page}#perfect|P]]&lt;0 (oddly, neither this scale nor its [[{$page}#dual|dual]] can be tuned with a perfect 3/2!)  [[{$page}#ref1|(1)]]
[[Meantone]] MOS; [[{$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)
generator = 5L+3s (500.0 to 505.3 cents)
Line 609: Line 659:
===[[5L 14s|5L+14s]]===
===[[5L 14s|5L+14s]]===
Godzilla? MODMOS; full L/s range good
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
P = 2.5200335053
Line 642: Line 694:
===[[14L 5s|14L+5s]]===
===[[14L 5s|14L+5s]]===
[[Semaphore and godzilla|Semaphore / godzilla]] MODMOS; imperfect; full L/s range good
[[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)
generator = 3L+s (252.6 to 257.1 cents)
Line 676: Line 730:
===[[7L 15s|7L+15s]]===
===[[7L 15s|7L+15s]]===
[[Porcupine]] MODMOS; full L/s range good
[[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
P = 2.3809207248
Line 712: Line 768:
===[[15L 7s|15L+7s]]===
===[[15L 7s|15L+7s]]===
[[Porcupine]] MODMOS; imperfect; full L/s range mostly good
[[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)
generator = 2L+s (160.0 to 163.6 cents)
Line 747: Line 805:
===[[12L 10s|12L+10s]]===
===[[12L 10s|12L+10s]]===
[[Pajara]] / [[Diaschismic family|srutal (diaschismic)]] MODMOS [[{$page}#ref1|(1)]]  
[[Pajara]] / [[Diaschismic family|srutal (diaschismic)]] MODMOS [[{$page}#ref1|(1)]]  
[[image:TN_22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png link="file:22_12_10_LsLsLsLsL_sLsL_LsLsLsLsL.png"]]


P = 7.6918120831
P = 7.6918120831
Line 784: Line 844:
===[[10L 12s|10L+12s]]===
===[[10L 12s|10L+12s]]===
Pajara? MODMOS; imperfect; full L/s range good
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
notable EDOs: 32, 42, 54
Line 971: Line 1,033:
&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;
&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;
(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;
These are mostly tempered (irrational) scales.  In some cases (usually where the generator is close to a perfect 4/3 or 3/2), a Pythagorean (3-limit &lt;a class="wiki_link" href="/Just%20intonation"&gt;JI&lt;/a&gt;) version is possible.&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;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;!-- 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;
Line 977: Line 1,039:
&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;
&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:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:03 --&gt;&lt;br /&gt;
The familiar classic pentatonic scale. Can include &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt;, &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Pythagorean_tuning" rel="nofollow"&gt;Pythagorean&lt;/a&gt;, &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;, and &lt;a class="wiki_link" href="/Mavila%20Temperament%20Modal%20Harmony"&gt;mavila&lt;/a&gt; tunings.  Is &lt;a class="wiki_link" href="/MOS"&gt;MOS&lt;/a&gt;.  &lt;!-- ws:start:WikiTextVariableComponentRule:03:[[{$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;
&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;
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;
Line 1,033: Line 1,097:
&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;
&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;
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;
&lt;br /&gt;
generator = L+s (400.0 to 480.0 cents)&lt;br /&gt;
generator = L+s (400.0 to 480.0 cents)&lt;br /&gt;
Line 1,089: Line 1,155:
&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;!-- 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;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;
&lt;br /&gt;
generator = L+2s (514.3 to 600.0 cents)&lt;br /&gt;
generator = L+2s (514.3 to 600.0 cents)&lt;br /&gt;
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&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;
&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:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:015 --&gt;&lt;br /&gt;
Classic diatonic scale (&lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;, Pythagorean, &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt;); MOS. &lt;!-- ws:start:WikiTextVariableComponentRule:015:[[{$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;
&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;
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;
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Blackwood MOS.  This omnitetrachordal scale has some unusual properties:&lt;br /&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;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;
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;
&lt;a class="wiki_link" href="/periods%20and%20generators"&gt;period&lt;/a&gt; = 1/5 octave&lt;br /&gt;
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&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;!-- 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;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;
&lt;br /&gt;
P = 2.5872804832&lt;br /&gt;
P = 2.5872804832&lt;br /&gt;
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&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;
&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:[[{$page}#dual|dual]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual"&gt;dual&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:017 --&gt; of 7L+3s, this scale pattern barely qualifies as omnitetrachordal.&lt;br /&gt;
The &lt;!-- ws:start:WikiTextVariableComponentRule:017:[[{$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;
&lt;br /&gt;
notable EDOs: 13, 16b&lt;br /&gt;
notable EDOs: 13, 16b&lt;br /&gt;
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&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;!-- 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:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:019 --&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Pajara"&gt;Pajara&lt;/a&gt; MODMOS.  Best at lower ratios of L/s.  &lt;!-- ws:start:WikiTextVariableComponentRule:019:[[{$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;
&lt;br /&gt;
P = 1.8849491924&lt;br /&gt;
P = 1.8849491924&lt;br /&gt;
Line 1,506: Line 1,584:
&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;
&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;
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;
&lt;br /&gt;
notable EDOs: 18, 26b&lt;br /&gt;
notable EDOs: 18, 26b&lt;br /&gt;
Line 1,516: Line 1,596:
&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;
&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;
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;
&lt;br /&gt;
Pythagorean (3-limit JI): L=2187/2048, s=256/243&lt;br /&gt;
Pythagorean (3-limit JI): L=2187/2048, s=256/243&lt;br /&gt;
Line 1,628: Line 1,710:
&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;
&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:[[{$page}#perfect|Imperfect]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;Imperfect&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:021 --&gt;, but very usable at any L/s ratio.  Many modes may be pentachordally split in two ways.&lt;br /&gt;
12-tone MOS of the &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; and &lt;a class="wiki_link" href="/Meantone%20family#Flattone"&gt;flattone&lt;/a&gt; temperaments (slightly flat 3/2).  &lt;!-- ws:start:WikiTextVariableComponentRule:021:[[{$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;
&lt;br /&gt;
generator = 3L+2s (500.0 to 514.3 cents)&lt;br /&gt;
generator = 3L+2s (500.0 to 514.3 cents)&lt;br /&gt;
Line 1,736: Line 1,820:
&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;!-- 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;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;
&lt;br /&gt;
P = 1.1300083763&lt;br /&gt;
P = 1.1300083763&lt;br /&gt;
Line 1,852: Line 1,938:
&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: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:[[{$page}#dual|Dual]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual"&gt;Dual&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:023 --&gt; of 10L+2s.  Probably only useful for small values of L/s.&lt;br /&gt;
&lt;!-- ws:start:WikiTextVariableComponentRule:023:[[{$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;
&lt;br /&gt;
notable EDOs: 14, 16&lt;br /&gt;
notable EDOs: 14, 16&lt;br /&gt;
Line 1,862: Line 1,950:
&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;!-- 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;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;
&lt;br /&gt;
P = 5.1745609664&lt;br /&gt;
P = 5.1745609664&lt;br /&gt;
Line 1,988: Line 2,078:
&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;!-- 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;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;
&lt;br /&gt;
P = 3.5200335053&lt;br /&gt;
P = 3.5200335053&lt;br /&gt;
Line 2,120: Line 2,212:
&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;!-- 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:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:025 --&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Injera"&gt;Injera&lt;/a&gt; MODMOS.  Imperfect (P&amp;lt;0); best for L/s &amp;gt;= 1.5 &lt;!-- ws:start:WikiTextVariableComponentRule:025:[[{$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;
&lt;br /&gt;
generator = L (85.7 to 100.0 cents)&lt;br /&gt;
generator = L (85.7 to 100.0 cents)&lt;br /&gt;
Line 2,253: Line 2,347:
&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;!-- 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;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;br /&gt;
&lt;!-- ws:start:WikiTextVariableComponentRule:027:[[{$page}#perfect|P]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:027 --&gt; = 3.3809207248&lt;br /&gt;
&lt;!-- ws:start:WikiTextVariableComponentRule:027:[[{$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;
Line 2,392: Line 2,488:
&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;!-- 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;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;
&lt;br /&gt;
P = 12.5377181246&lt;br /&gt;
P = 12.5377181246&lt;br /&gt;
Line 2,534: Line 2,632:
&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;!-- 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;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;
&lt;br /&gt;
generator = 2L+5s (480.0 to 494.1 cents)&lt;br /&gt;
generator = 2L+5s (480.0 to 494.1 cents)&lt;br /&gt;
Line 2,684: Line 2,784:
&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;
&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:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:029 --&gt;&lt;br /&gt;
Helmholtz / &lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic&lt;/a&gt; MOS; full L/s range very good &lt;!-- ws:start:WikiTextVariableComponentRule:029:[[{$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;
&lt;br /&gt;
Pythagorean (3-limit JI): L=256/243, s=531441/524288&lt;br /&gt;
Pythagorean (3-limit JI): L=256/243, s=531441/524288&lt;br /&gt;
Line 2,836: Line 2,938:
&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;!-- 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;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;
&lt;br /&gt;
P = 1.5872804832&lt;br /&gt;
P = 1.5872804832&lt;br /&gt;
Line 2,991: Line 3,095:
&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;
&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;
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;
&lt;br /&gt;
generator = 3L+2s (352.9 to 360.0 cents)&lt;br /&gt;
generator = 3L+2s (352.9 to 360.0 cents)&lt;br /&gt;
Line 3,147: Line 3,253:
&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;
&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;
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;
&lt;br /&gt;
P = 5.968201208&lt;br /&gt;
P = 5.968201208&lt;br /&gt;
Line 3,312: Line 3,420:
&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;!-- 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;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;
&lt;br /&gt;
generator = 3L+5s (505.3 to 514.3 cents)&lt;br /&gt;
generator = 3L+5s (505.3 to 514.3 cents)&lt;br /&gt;
Line 3,478: Line 3,588:
&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;!-- 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:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:039 --&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Meantone"&gt;Meantone&lt;/a&gt; MOS; &lt;!-- ws:start:WikiTextVariableComponentRule:035:[[{$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;
&lt;br /&gt;
generator = 5L+3s (500.0 to 505.3 cents)&lt;br /&gt;
generator = 5L+3s (500.0 to 505.3 cents)&lt;br /&gt;
Line 3,644: Line 3,756:
&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;
&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;
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;
&lt;br /&gt;
P = 2.5200335053&lt;br /&gt;
P = 2.5200335053&lt;br /&gt;
Line 3,815: Line 3,929:
&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;!-- 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;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;
&lt;br /&gt;
generator = 3L+s (252.6 to 257.1 cents)&lt;br /&gt;
generator = 3L+s (252.6 to 257.1 cents)&lt;br /&gt;
Line 3,987: Line 4,103:
&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;!-- 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;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;
&lt;br /&gt;
P = 2.3809207248&lt;br /&gt;
P = 2.3809207248&lt;br /&gt;
Line 4,182: Line 4,300:
&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;!-- 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;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;
&lt;br /&gt;
generator = 2L+s (160.0 to 163.6 cents)&lt;br /&gt;
generator = 2L+s (160.0 to 163.6 cents)&lt;br /&gt;
Line 4,376: Line 4,496:
&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;!-- 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:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:041 --&gt; &lt;br /&gt;
&lt;a class="wiki_link" href="/Pajara"&gt;Pajara&lt;/a&gt; / &lt;a class="wiki_link" href="/Diaschismic%20family"&gt;srutal (diaschismic)&lt;/a&gt; MODMOS &lt;!-- ws:start:WikiTextVariableComponentRule:041:[[{$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;
&lt;br /&gt;
P = 7.6918120831&lt;br /&gt;
P = 7.6918120831&lt;br /&gt;
Line 4,572: Line 4,694:
&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;
&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;
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;
&lt;br /&gt;
notable EDOs: 32, 42, 54&lt;br /&gt;
notable EDOs: 32, 42, 54&lt;br /&gt;
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