Temperaments for MOS shapes: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Below are listed temperaments of least TE complexity which result in a particular MOS shape, where "results in" is taken to mean that the POTE tuning has that shape.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-12-01 15:11:27 UTC</tt>.<br>
: The original revision id was <tt>388030896</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">Below are listed temperaments of least TE complexity which result in a particular MOS shape, where "results in" is taken to mean that the POTE tuning has that shape.


=7edo=
=7edo=
==5-limit==
==5-limit==
1L6s &lt;&lt;3 5 1|| porcupine 250/243
1L6s &lt;&lt;3 5 1|| porcupine 250/243
2L5s &lt;&lt;1 -3 -7|| mavila 135/128
2L5s &lt;&lt;1 -3 -7|| mavila 135/128
3L4s &lt;&lt;2 1 -3|| dicot 25/24
3L4s &lt;&lt;2 1 -3|| dicot 25/24
4L3s &lt;&lt;5 6 -2|| sixix 3125/2916
4L3s &lt;&lt;5 6 -2|| sixix 3125/2916
5L2s &lt;&lt;1 4 4|| meantone 81/80
5L2s &lt;&lt;1 4 4|| meantone 81/80
6L1s &lt;&lt;3 -2 -10|| enipucrop 1125/1024
6L1s &lt;&lt;3 -2 -10|| enipucrop 1125/1024


==7-limit patent==
==7-limit patent==
1L6s &lt;&lt;3 5 1 1 -7 -12|| hystrix {36/35, 160/147}
1L6s &lt;&lt;3 5 1 1 -7 -12|| hystrix {36/35, 160/147}
2L5s &lt;&lt;1 -3 -2 -7 -6 4|| {15/14, 64/63}
2L5s &lt;&lt;1 -3 -2 -7 -6 4|| {15/14, 64/63}
3L4s &lt;&lt;2 1 -4 -3 -12 -12|| dichotic {25/24, 64/63}
3L4s &lt;&lt;2 1 -4 -3 -12 -12|| dichotic {25/24, 64/63}
4L3s &lt;&lt;2 1 3 -3 -1 4|| dicot {15/14, 25/24}
4L3s &lt;&lt;2 1 3 -3 -1 4|| dicot {15/14, 25/24}
5L2s &lt;&lt;1 4 -2 4 -6 -16|| dominant {36/35, 64/63}
5L2s &lt;&lt;1 4 -2 4 -6 -16|| dominant {36/35, 64/63}
6L1s &lt;&lt;3 -2 1 -10 -7 8|| {15/14, 256/245}
6L1s &lt;&lt;3 -2 1 -10 -7 8|| {15/14, 256/245}


==7d==
==7d==
1L6s &lt;&lt;3 5 2 1 -5 -9|| oxygen {21/20, 175/162}
1L6s &lt;&lt;3 5 2 1 -5 -9|| oxygen {21/20, 175/162}
2L5s &lt;&lt;1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}
2L5s &lt;&lt;1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}
3L4s &lt;&lt;2 1 6 -3 4 11|| sharp {25/24, 28/27}
3L4s &lt;&lt;2 1 6 -3 4 11|| sharp {25/24, 28/27}
4L3s &lt;&lt;2 1 -1 -3 -7 -5|| flat {21/20, 25/24}
4L3s &lt;&lt;2 1 -1 -3 -7 -5|| flat {21/20, 25/24}
5L2s &lt;&lt;1 4 3 4 2 -4|| sharptone {21/20, 28/27}
5L2s &lt;&lt;1 4 3 4 2 -4|| sharptone {21/20, 28/27}
6L1s &lt;&lt;4 2 5 -6 -3 6|| {25/24, 49/45}
6L1s &lt;&lt;4 2 5 -6 -3 6|| {25/24, 49/45}


=8edo=
=8edo=
==5-limit==
==5-limit==
1L7s &lt;&lt;5 3 -7|| progression 3456/3125
1L7s &lt;&lt;5 3 -7|| progression 3456/3125
2L6s &lt;&lt;2 6 5|| supersharp 800/729  
2L6s &lt;&lt;2 6 5|| supersharp 800/729  
3L5s &lt;&lt;7 9 -2|| sensi 78732/78125
3L5s &lt;&lt;7 9 -2|| sensi 78732/78125
4L4s &lt;&lt;4 4 -3|| diminished 648/625
4L4s &lt;&lt;4 4 -3|| diminished 648/625
5L3s &lt;&lt;1 -1 -4|| father 16/15
5L3s &lt;&lt;1 -1 -4|| father 16/15
6L2s &lt;&lt;6 2 -11|| 18432/15625
6L2s &lt;&lt;6 2 -11|| 18432/15625
7L1s &lt;&lt;3 5 1|| porcupine 250/243
7L1s &lt;&lt;3 5 1|| porcupine 250/243


==7-limit 8d==
==7-limit 8d==
1L7s &lt;&lt;5 3 7 -7 -3 8|| progression {36/35, 392/375}  
1L7s &lt;&lt;5 3 7 -7 -3 8|| progression {36/35, 392/375}  
2L6s &lt;&lt;2 -2 -2 -8 -9 1|| walid {16/15, 50/49}
2L6s &lt;&lt;2 -2 -2 -8 -9 1|| walid {16/15, 50/49}
3L5s &lt;&lt;1 -1 -5 -4 -11 -9|| pater {16/15, 126/125}
3L5s &lt;&lt;1 -1 -5 -4 -11 -9|| pater {16/15, 126/125}
4L4s &lt;&lt;4 4 4 -3 -5 -2|| diminished {36/35, 50/49}
4L4s &lt;&lt;4 4 4 -3 -5 -2|| diminished {36/35, 50/49}
5L3s &lt;&lt;1 -1 3 -4 2 10|| father {16/15, 28/27}
5L3s &lt;&lt;1 -1 3 -4 2 10|| father {16/15, 28/27}
6L2s &lt;&lt;6 2 2 -11 -14 -1|| {50/49, 192/175}
6L2s &lt;&lt;6 2 2 -11 -14 -1|| {50/49, 192/175}
7L1s &lt;&lt;3 5 1 1 -7 -12|| hystrix {36/35, 160/147}
7L1s &lt;&lt;3 5 1 1 -7 -12|| hystrix {36/35, 160/147}


=9edo=
=9edo=
==5-limit==
==5-limit==
1L8s &lt;&lt;4 -3 -14|| negri 16875/16384
1L8s &lt;&lt;4 -3 -14|| negri 16875/16384
2L7s &lt;&lt;1 6 -7|| avila 729/640
2L7s &lt;&lt;1 6 -7|| avila 729/640
3L6s &lt;&lt;3 0 -7|| augmented 128/125
3L6s &lt;&lt;3 0 -7|| augmented 128/125
4L5s &lt;&lt;7 6 -7|| 93312/78125
4L5s &lt;&lt;7 6 -7|| 93312/78125
5L4s &lt;&lt;2 3 0|| bug 27/25
5L4s &lt;&lt;2 3 0|| bug 27/25
6L3s &lt;&lt;3 9 7|| 19683/16000
6L3s &lt;&lt;3 9 7|| 19683/16000
7L2s &lt;&lt;1 -3 -7|| mavila 135/128
7L2s &lt;&lt;1 -3 -7|| mavila 135/128
8L1s &lt;&lt;5 3 -7|| progression 3456/3125
8L1s &lt;&lt;5 3 -7|| progression 3456/3125


==7-limit==
==7-limit==
1L8s &lt;&lt;4 -3 2 -14 -8 13|| negri {49/48, 225/224}
1L8s &lt;&lt;4 -3 2 -14 -8 13|| negri {49/48, 225/224}
2L7s &lt;&lt;1 6 5 7 5 -5|| {21/20, 243/224}
2L7s &lt;&lt;1 6 5 7 5 -5|| {21/20, 243/224}
3L6s &lt;&lt;3 0 6 -7 1 14|| august {36/35, 128/125}
3L6s &lt;&lt;3 0 6 -7 1 14|| august {36/35, 128/125}
4L5s &lt;&lt;7 6 8 -7 -7 2|| {36/35, 686/625}
4L5s &lt;&lt;7 6 8 -7 -7 2|| {36/35, 686/625}
5L4s &lt;&lt;2 3 1 0 -4 -6|| beep {21/20, 27/25}
5L4s &lt;&lt;2 3 1 0 -4 -6|| beep {21/20, 27/25}
6L3s &lt;&lt;3 9 6 7 1 -11|| {21/20, 729/686}
6L3s &lt;&lt;3 9 6 7 1 -11|| {21/20, 729/686}
7L2s &lt;&lt;1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}
7L2s &lt;&lt;1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}
8L1s &lt;&lt;5 3 7 -7 -3 8|| progression {36/35, 392/375}  
8L1s &lt;&lt;5 3 7 -7 -3 8|| progression {36/35, 392/375}  


=10edo=
=10edo=
==5-limit==
==5-limit==
1L9s &lt;&lt;4 7 2|| 2500/2187
1L9s &lt;&lt;4 7 2|| 2500/2187
2L8s &lt;&lt;2 -4 -11|| srutal 2048/2025
2L8s &lt;&lt;2 -4 -11|| srutal 2048/2025
3L7s &lt;&lt;2 11 13|| 204800/177147
3L7s &lt;&lt;2 11 13|| 204800/177147
4L6s &lt;&lt;14 12 -13|| 6103515625/4353564672
4L6s &lt;&lt;14 12 -13|| 6103515625/4353564672
5L5s &lt;&lt;0 5 8|| blackwood 256/243
5L5s &lt;&lt;0 5 8|| blackwood 256/243
6L4s &lt;&lt;6 8 -1|| 15625/13122
6L4s &lt;&lt;6 8 -1|| 15625/13122
7L3s &lt;&lt;2 1 -3|| dicot 25/24
7L3s &lt;&lt;2 1 -3|| dicot 25/24
8L2s &lt;&lt;2 6 5|| supersharp 800/729
8L2s &lt;&lt;2 6 5|| supersharp 800/729
9L1s &lt;&lt;4 -3 -14|| negri 16875/16384
9L1s &lt;&lt;4 -3 -14|| negri 16875/16384


==7-limit==
==7-limit==
1L9s &lt;&lt;4 7 2 2 -8 -15|| {49/48, 175/162}
1L9s &lt;&lt;4 7 2 2 -8 -15|| {49/48, 175/162}
2L8s &lt;&lt;2 -4 -4 -11 -12 2|| pajara {50/49, 64/63}
2L8s &lt;&lt;2 -4 -4 -11 -12 2|| pajara {50/49, 64/63}
3L7s &lt;&lt;2 11 6 13 4 -17|| {28/27, 2401/2400}
3L7s &lt;&lt;2 11 6 13 4 -17|| {28/27, 2401/2400}
4L6s &lt;&lt;4 2 2 -6 -8 -1|| decimal {25/24, 49/48}
4L6s &lt;&lt;4 2 2 -6 -8 -1|| decimal {25/24, 49/48}
5L5s  &lt;&lt;0 5 0 8 0 -14|| blacksmith {28/27, 49/48}
5L5s  &lt;&lt;0 5 0 8 0 -14|| blacksmith {28/27, 49/48}
6L4s &lt;&lt;6 8 8 -1 -4 -4|| {50/49, 175/162}
6L4s &lt;&lt;6 8 8 -1 -4 -4|| {50/49, 175/162}
7L3s &lt;&lt;2 1 6 -3 4 11|| sharp {25/24, 28/27}
7L3s &lt;&lt;2 1 6 -3 4 11|| sharp {25/24, 28/27}
8L2s &lt;&lt;2 6 6 5 4 -3|| octokaidecal {28/27, 50/49}
8L2s &lt;&lt;2 6 6 5 4 -3|| octokaidecal {28/27, 50/49}
9L1s &lt;&lt;4 -3 2 -14 -8 13|| negri {49/48, 225/224}
9L1s &lt;&lt;4 -3 2 -14 -8 13|| negri {49/48, 225/224}


==11-limit==
==11-limit==
1L9s &lt;&lt;4 7 2 5 2 -8 -6 -15 -13 7|| {35/33, 49/48, 55/54}
1L9s &lt;&lt;4 7 2 5 2 -8 -6 -15 -13 7|| {35/33, 49/48, 55/54}
2L8s &lt;&lt;2 -4 6 0 -11 4 -7 25 14 -21|| {28/27, 35/33, 128/121}
2L8s &lt;&lt;2 -4 6 0 -11 4 -7 25 14 -21|| {28/27, 35/33, 128/121}
3L7s &lt;&lt;2 1 -4 -5 -3 -12 -15 -12 -15 0|| dichosis {25/24, 35/33, 64/63}
3L7s &lt;&lt;2 1 -4 -5 -3 -12 -15 -12 -15 0|| dichosis {25/24, 35/33, 64/63}
4l6s &lt;&lt;4 2 2 0 -6 -8 -14 -1 -7 -7|| decibel {25/24, 35/33, 49/48}
4l6s &lt;&lt;4 2 2 0 -6 -8 -14 -1 -7 -7|| decibel {25/24, 35/33, 49/48}
5L5s &lt;&lt;0 5 0 5 8 0 8 -14 -6 14|| ferrum {28/27, 35/33, 49/48}
5L5s &lt;&lt;0 5 0 5 8 0 8 -14 -6 14|| ferrum {28/27, 35/33, 49/48}
6L4s &lt;&lt;6 8 8 10 -1 -4 -5 -4 -5 0|| {35/33, 50/49, 55/54}
6L4s &lt;&lt;6 8 8 10 -1 -4 -5 -4 -5 0|| {35/33, 50/49, 55/54}
7L3s &lt;&lt;2 1 6 5 -3 4 1 11 8 -7|| sharp {25/24, 28/27, 35/33}
7L3s &lt;&lt;2 1 6 5 -3 4 1 11 8 -7|| sharp {25/24, 28/27, 35/33}
8L2s  &lt;&lt;2 6 6 10 5 4 9 -3 2 7|| {28/27, 35/33, 50/49}
8L2s  &lt;&lt;2 6 6 10 5 4 9 -3 2 7|| {28/27, 35/33, 50/49}
9L1s &lt;&lt;4 -3 2 5 -14 -8 -6 13 22 7|| negri {45/44, 49/48, 56/55}
9L1s &lt;&lt;4 -3 2 5 -14 -8 -6 13 22 7|| negri {45/44, 49/48, 56/55}


=11edo=
=11edo=
==5-limit 11b==
==5-limit 11b==
1L10s &lt;&lt;7 4 -10|| 82944/78125
1L10s &lt;&lt;7 4 -10|| 82944/78125
2L9s &lt;&lt;3 8 6|| 8000/6561
2L9s &lt;&lt;3 8 6|| 8000/6561
3L8s &lt;&lt;10 1 -22|| 12582912/9765625
3L8s &lt;&lt;10 1 -22|| 12582912/9765625
4L7s &lt;&lt;6 5 -6|| hanson 15625/15552
4L7s &lt;&lt;6 5 -6|| hanson 15625/15552
5L6s &lt;&lt;2 9 10|| 25600/19683
5L6s &lt;&lt;2 9 10|| 25600/19683
6L5s &lt;&lt;9 2 -18|| 2359296/1953125
6L5s &lt;&lt;9 2 -18|| 2359296/1953125
7L4s &lt;&lt;5 6 -2|| sixix 3125/2916
7L4s &lt;&lt;5 6 -2|| sixix 3125/2916
8L3s &lt;&lt;1 10 14|| 81920/59049
8L3s &lt;&lt;1 10 14|| 81920/59049
9L2s &lt;&lt;8 3 -14|| 442368/390625
9L2s &lt;&lt;8 3 -14|| 442368/390625
10L1s &lt;&lt;4 7 2|| 2500/2187
10L1s &lt;&lt;4 7 2|| 2500/2187


==5-limit 11c==
==5-limit 11c==
1L10s &lt;&lt;5 8 1|| ripple 6561/6250
1L10s &lt;&lt;5 8 1|| ripple 6561/6250
2L9s &lt;&lt;1 -5 -10|| 1215/1024
2L9s &lt;&lt;1 -5 -10|| 1215/1024
3L8s &lt;&lt;4 13 11|| 1594323/1280000
3L8s &lt;&lt;4 13 11|| 1594323/1280000
4L7s &lt;&lt;9 10 -5|| 1953125/1889568
4L7s &lt;&lt;9 10 -5|| 1953125/1889568
5L6s &lt;&lt;3 7 4|| laconic 2187/2000
5L6s &lt;&lt;3 7 4|| laconic 2187/2000
6L5s &lt;&lt;8 15 5|| 14348907/12500000
6L5s &lt;&lt;8 15 5|| 14348907/12500000
7L4s &lt;&lt;13 12 -11|| 1220703125/1088391168
7L4s &lt;&lt;13 12 -11|| 1220703125/1088391168
8L3s &lt;&lt;7 9 -2|| sensi 78732/78125
8L3s &lt;&lt;7 9 -2|| sensi 78732/78125
9L2s &lt;&lt;1 6 7|| avila 729/640
9L2s &lt;&lt;1 6 7|| avila 729/640
10L1s &lt;&lt;5 -14 -33|| 14946778125/8589934592</pre></div>
 
<h4>Original HTML content:</h4>
10L1s &lt;&lt;5 -14 -33|| 14946778125/8589934592
<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;Temperaments for MOS shapes&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are listed temperaments of least TE complexity which result in a particular MOS shape, where &amp;quot;results in&amp;quot; is taken to mean that the POTE tuning has that shape.&lt;br /&gt;
[[Category:todo:link]]
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x7edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;7edo&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x7edo-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;5-limit&lt;/h2&gt;
1L6s &amp;lt;&amp;lt;3 5 1|| porcupine 250/243&lt;br /&gt;
2L5s &amp;lt;&amp;lt;1 -3 -7|| mavila 135/128&lt;br /&gt;
3L4s &amp;lt;&amp;lt;2 1 -3|| dicot 25/24&lt;br /&gt;
4L3s &amp;lt;&amp;lt;5 6 -2|| sixix 3125/2916&lt;br /&gt;
5L2s &amp;lt;&amp;lt;1 4 4|| meantone 81/80&lt;br /&gt;
6L1s &amp;lt;&amp;lt;3 -2 -10|| enipucrop 1125/1024&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x7edo-7-limit patent"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;7-limit patent&lt;/h2&gt;
1L6s &amp;lt;&amp;lt;3 5 1 1 -7 -12|| hystrix {36/35, 160/147}&lt;br /&gt;
2L5s &amp;lt;&amp;lt;1 -3 -2 -7 -6 4|| {15/14, 64/63}&lt;br /&gt;
3L4s &amp;lt;&amp;lt;2 1 -4 -3 -12 -12|| dichotic {25/24, 64/63}&lt;br /&gt;
4L3s &amp;lt;&amp;lt;2 1 3 -3 -1 4|| dicot {15/14, 25/24}&lt;br /&gt;
5L2s &amp;lt;&amp;lt;1 4 -2 4 -6 -16|| dominant {36/35, 64/63}&lt;br /&gt;
6L1s &amp;lt;&amp;lt;3 -2 1 -10 -7 8|| {15/14, 256/245}&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x7edo-7d"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;7d&lt;/h2&gt;
1L6s &amp;lt;&amp;lt;3 5 2 1 -5 -9|| oxygen {21/20, 175/162}&lt;br /&gt;
2L5s &amp;lt;&amp;lt;1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}&lt;br /&gt;
3L4s &amp;lt;&amp;lt;2 1 6 -3 4 11|| sharp {25/24, 28/27}&lt;br /&gt;
4L3s &amp;lt;&amp;lt;2 1 -1 -3 -7 -5|| flat {21/20, 25/24}&lt;br /&gt;
5L2s &amp;lt;&amp;lt;1 4 3 4 2 -4|| sharptone {21/20, 28/27}&lt;br /&gt;
6L1s &amp;lt;&amp;lt;4 2 5 -6 -3 6|| {25/24, 49/45}&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="x8edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;8edo&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x8edo-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;5-limit&lt;/h2&gt;
1L7s &amp;lt;&amp;lt;5 3 -7|| progression 3456/3125&lt;br /&gt;
2L6s &amp;lt;&amp;lt;2 6 5|| supersharp 800/729 &lt;br /&gt;
3L5s &amp;lt;&amp;lt;7 9 -2|| sensi 78732/78125&lt;br /&gt;
4L4s &amp;lt;&amp;lt;4 4 -3|| diminished 648/625&lt;br /&gt;
5L3s &amp;lt;&amp;lt;1 -1 -4|| father 16/15&lt;br /&gt;
6L2s &amp;lt;&amp;lt;6 2 -11|| 18432/15625&lt;br /&gt;
7L1s &amp;lt;&amp;lt;3 5 1|| porcupine 250/243&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x8edo-7-limit 8d"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;7-limit 8d&lt;/h2&gt;
1L7s &amp;lt;&amp;lt;5 3 7 -7 -3 8|| progression {36/35, 392/375} &lt;br /&gt;
2L6s &amp;lt;&amp;lt;2 -2 -2 -8 -9 1|| walid {16/15, 50/49}&lt;br /&gt;
3L5s &amp;lt;&amp;lt;1 -1 -5 -4 -11 -9|| pater {16/15, 126/125}&lt;br /&gt;
4L4s &amp;lt;&amp;lt;4 4 4 -3 -5 -2|| diminished {36/35, 50/49}&lt;br /&gt;
5L3s &amp;lt;&amp;lt;1 -1 3 -4 2 10|| father {16/15, 28/27}&lt;br /&gt;
6L2s &amp;lt;&amp;lt;6 2 2 -11 -14 -1|| {50/49, 192/175}&lt;br /&gt;
7L1s &amp;lt;&amp;lt;3 5 1 1 -7 -12|| hystrix {36/35, 160/147}&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="x9edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;9edo&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x9edo-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;5-limit&lt;/h2&gt;
1L8s &amp;lt;&amp;lt;4 -3 -14|| negri 16875/16384&lt;br /&gt;
2L7s &amp;lt;&amp;lt;1 6 -7|| avila 729/640&lt;br /&gt;
3L6s &amp;lt;&amp;lt;3 0 -7|| augmented 128/125&lt;br /&gt;
4L5s &amp;lt;&amp;lt;7 6 -7|| 93312/78125&lt;br /&gt;
5L4s &amp;lt;&amp;lt;2 3 0|| bug 27/25&lt;br /&gt;
6L3s &amp;lt;&amp;lt;3 9 7|| 19683/16000&lt;br /&gt;
7L2s &amp;lt;&amp;lt;1 -3 -7|| mavila 135/128&lt;br /&gt;
8L1s &amp;lt;&amp;lt;5 3 -7|| progression 3456/3125&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x9edo-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;7-limit&lt;/h2&gt;
1L8s &amp;lt;&amp;lt;4 -3 2 -14 -8 13|| negri {49/48, 225/224}&lt;br /&gt;
2L7s &amp;lt;&amp;lt;1 6 5 7 5 -5|| {21/20, 243/224}&lt;br /&gt;
3L6s &amp;lt;&amp;lt;3 0 6 -7 1 14|| august {36/35, 128/125}&lt;br /&gt;
4L5s &amp;lt;&amp;lt;7 6 8 -7 -7 2|| {36/35, 686/625}&lt;br /&gt;
5L4s &amp;lt;&amp;lt;2 3 1 0 -4 -6|| beep {21/20, 27/25}&lt;br /&gt;
6L3s &amp;lt;&amp;lt;3 9 6 7 1 -11|| {21/20, 729/686}&lt;br /&gt;
7L2s &amp;lt;&amp;lt;1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}&lt;br /&gt;
8L1s &amp;lt;&amp;lt;5 3 7 -7 -3 8|| progression {36/35, 392/375} &lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="x10edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;10edo&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="x10edo-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;5-limit&lt;/h2&gt;
1L9s &amp;lt;&amp;lt;4 7 2|| 2500/2187&lt;br /&gt;
2L8s &amp;lt;&amp;lt;2 -4 -11|| srutal 2048/2025&lt;br /&gt;
3L7s &amp;lt;&amp;lt;2 11 13|| 204800/177147&lt;br /&gt;
4L6s &amp;lt;&amp;lt;14 12 -13|| 6103515625/4353564672&lt;br /&gt;
5L5s &amp;lt;&amp;lt;0 5 8|| blackwood 256/243&lt;br /&gt;
6L4s &amp;lt;&amp;lt;6 8 -1|| 15625/13122&lt;br /&gt;
7L3s &amp;lt;&amp;lt;2 1 -3|| dicot 25/24&lt;br /&gt;
8L2s &amp;lt;&amp;lt;2 6 5|| supersharp 800/729&lt;br /&gt;
9L1s &amp;lt;&amp;lt;4 -3 -14|| negri 16875/16384&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="x10edo-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;7-limit&lt;/h2&gt;
1L9s &amp;lt;&amp;lt;4 7 2 2 -8 -15|| {49/48, 175/162}&lt;br /&gt;
2L8s &amp;lt;&amp;lt;2 -4 -4 -11 -12 2|| pajara {50/49, 64/63}&lt;br /&gt;
3L7s &amp;lt;&amp;lt;2 11 6 13 4 -17|| {28/27, 2401/2400}&lt;br /&gt;
4L6s &amp;lt;&amp;lt;4 2 2 -6 -8 -1|| decimal {25/24, 49/48}&lt;br /&gt;
5L5s  &amp;lt;&amp;lt;0 5 0 8 0 -14|| blacksmith {28/27, 49/48}&lt;br /&gt;
6L4s &amp;lt;&amp;lt;6 8 8 -1 -4 -4|| {50/49, 175/162}&lt;br /&gt;
7L3s &amp;lt;&amp;lt;2 1 6 -3 4 11|| sharp {25/24, 28/27}&lt;br /&gt;
8L2s &amp;lt;&amp;lt;2 6 6 5 4 -3|| octokaidecal {28/27, 50/49}&lt;br /&gt;
9L1s &amp;lt;&amp;lt;4 -3 2 -14 -8 13|| negri {49/48, 225/224}&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="x10edo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;11-limit&lt;/h2&gt;
1L9s &amp;lt;&amp;lt;4 7 2 5 2 -8 -6 -15 -13 7|| {35/33, 49/48, 55/54}&lt;br /&gt;
2L8s &amp;lt;&amp;lt;2 -4 6 0 -11 4 -7 25 14 -21|| {28/27, 35/33, 128/121}&lt;br /&gt;
3L7s &amp;lt;&amp;lt;2 1 -4 -5 -3 -12 -15 -12 -15 0|| dichosis {25/24, 35/33, 64/63}&lt;br /&gt;
4l6s &amp;lt;&amp;lt;4 2 2 0 -6 -8 -14 -1 -7 -7|| decibel {25/24, 35/33, 49/48}&lt;br /&gt;
5L5s &amp;lt;&amp;lt;0 5 0 5 8 0 8 -14 -6 14|| ferrum {28/27, 35/33, 49/48}&lt;br /&gt;
6L4s &amp;lt;&amp;lt;6 8 8 10 -1 -4 -5 -4 -5 0|| {35/33, 50/49, 55/54}&lt;br /&gt;
7L3s &amp;lt;&amp;lt;2 1 6 5 -3 4 1 11 8 -7|| sharp {25/24, 28/27, 35/33}&lt;br /&gt;
8L2s  &amp;lt;&amp;lt;2 6 6 10 5 4 9 -3 2 7|| {28/27, 35/33, 50/49}&lt;br /&gt;
9L1s &amp;lt;&amp;lt;4 -3 2 5 -14 -8 -6 13 22 7|| negri {45/44, 49/48, 56/55}&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="x11edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11edo&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="x11edo-5-limit 11b"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;5-limit 11b&lt;/h2&gt;
1L10s &amp;lt;&amp;lt;7 4 -10|| 82944/78125&lt;br /&gt;
2L9s &amp;lt;&amp;lt;3 8 6|| 8000/6561&lt;br /&gt;
3L8s &amp;lt;&amp;lt;10 1 -22|| 12582912/9765625&lt;br /&gt;
4L7s &amp;lt;&amp;lt;6 5 -6|| hanson 15625/15552&lt;br /&gt;
5L6s &amp;lt;&amp;lt;2 9 10|| 25600/19683&lt;br /&gt;
6L5s &amp;lt;&amp;lt;9 2 -18|| 2359296/1953125&lt;br /&gt;
7L4s &amp;lt;&amp;lt;5 6 -2|| sixix 3125/2916&lt;br /&gt;
8L3s &amp;lt;&amp;lt;1 10 14|| 81920/59049&lt;br /&gt;
9L2s &amp;lt;&amp;lt;8 3 -14|| 442368/390625&lt;br /&gt;
10L1s &amp;lt;&amp;lt;4 7 2|| 2500/2187&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="x11edo-5-limit 11c"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;5-limit 11c&lt;/h2&gt;
1L10s &amp;lt;&amp;lt;5 8 1|| ripple 6561/6250&lt;br /&gt;
2L9s &amp;lt;&amp;lt;1 -5 -10|| 1215/1024&lt;br /&gt;
3L8s &amp;lt;&amp;lt;4 13 11|| 1594323/1280000&lt;br /&gt;
4L7s &amp;lt;&amp;lt;9 10 -5|| 1953125/1889568&lt;br /&gt;
5L6s &amp;lt;&amp;lt;3 7 4|| laconic 2187/2000&lt;br /&gt;
6L5s &amp;lt;&amp;lt;8 15 5|| 14348907/12500000&lt;br /&gt;
7L4s &amp;lt;&amp;lt;13 12 -11|| 1220703125/1088391168&lt;br /&gt;
8L3s &amp;lt;&amp;lt;7 9 -2|| sensi 78732/78125&lt;br /&gt;
9L2s &amp;lt;&amp;lt;1 6 7|| avila 729/640&lt;br /&gt;
10L1s &amp;lt;&amp;lt;5 -14 -33|| 14946778125/8589934592&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

Below are listed temperaments of least TE complexity which result in a particular MOS shape, where "results in" is taken to mean that the POTE tuning has that shape.

7edo

5-limit

1L6s <<3 5 1|| porcupine 250/243

2L5s <<1 -3 -7|| mavila 135/128

3L4s <<2 1 -3|| dicot 25/24

4L3s <<5 6 -2|| sixix 3125/2916

5L2s <<1 4 4|| meantone 81/80

6L1s <<3 -2 -10|| enipucrop 1125/1024

7-limit patent

1L6s <<3 5 1 1 -7 -12|| hystrix {36/35, 160/147}

2L5s <<1 -3 -2 -7 -6 4|| {15/14, 64/63}

3L4s <<2 1 -4 -3 -12 -12|| dichotic {25/24, 64/63}

4L3s <<2 1 3 -3 -1 4|| dicot {15/14, 25/24}

5L2s <<1 4 -2 4 -6 -16|| dominant {36/35, 64/63}

6L1s <<3 -2 1 -10 -7 8|| {15/14, 256/245}

7d

1L6s <<3 5 2 1 -5 -9|| oxygen {21/20, 175/162}

2L5s <<1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}

3L4s <<2 1 6 -3 4 11|| sharp {25/24, 28/27}

4L3s <<2 1 -1 -3 -7 -5|| flat {21/20, 25/24}

5L2s <<1 4 3 4 2 -4|| sharptone {21/20, 28/27}

6L1s <<4 2 5 -6 -3 6|| {25/24, 49/45}

8edo

5-limit

1L7s <<5 3 -7|| progression 3456/3125

2L6s <<2 6 5|| supersharp 800/729

3L5s <<7 9 -2|| sensi 78732/78125

4L4s <<4 4 -3|| diminished 648/625

5L3s <<1 -1 -4|| father 16/15

6L2s <<6 2 -11|| 18432/15625

7L1s <<3 5 1|| porcupine 250/243

7-limit 8d

1L7s <<5 3 7 -7 -3 8|| progression {36/35, 392/375}

2L6s <<2 -2 -2 -8 -9 1|| walid {16/15, 50/49}

3L5s <<1 -1 -5 -4 -11 -9|| pater {16/15, 126/125}

4L4s <<4 4 4 -3 -5 -2|| diminished {36/35, 50/49}

5L3s <<1 -1 3 -4 2 10|| father {16/15, 28/27}

6L2s <<6 2 2 -11 -14 -1|| {50/49, 192/175}

7L1s <<3 5 1 1 -7 -12|| hystrix {36/35, 160/147}

9edo

5-limit

1L8s <<4 -3 -14|| negri 16875/16384

2L7s <<1 6 -7|| avila 729/640

3L6s <<3 0 -7|| augmented 128/125

4L5s <<7 6 -7|| 93312/78125

5L4s <<2 3 0|| bug 27/25

6L3s <<3 9 7|| 19683/16000

7L2s <<1 -3 -7|| mavila 135/128

8L1s <<5 3 -7|| progression 3456/3125

7-limit

1L8s <<4 -3 2 -14 -8 13|| negri {49/48, 225/224}

2L7s <<1 6 5 7 5 -5|| {21/20, 243/224}

3L6s <<3 0 6 -7 1 14|| august {36/35, 128/125}

4L5s <<7 6 8 -7 -7 2|| {36/35, 686/625}

5L4s <<2 3 1 0 -4 -6|| beep {21/20, 27/25}

6L3s <<3 9 6 7 1 -11|| {21/20, 729/686}

7L2s <<1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}

8L1s <<5 3 7 -7 -3 8|| progression {36/35, 392/375}

10edo

5-limit

1L9s <<4 7 2|| 2500/2187

2L8s <<2 -4 -11|| srutal 2048/2025

3L7s <<2 11 13|| 204800/177147

4L6s <<14 12 -13|| 6103515625/4353564672

5L5s <<0 5 8|| blackwood 256/243

6L4s <<6 8 -1|| 15625/13122

7L3s <<2 1 -3|| dicot 25/24

8L2s <<2 6 5|| supersharp 800/729

9L1s <<4 -3 -14|| negri 16875/16384

7-limit

1L9s <<4 7 2 2 -8 -15|| {49/48, 175/162}

2L8s <<2 -4 -4 -11 -12 2|| pajara {50/49, 64/63}

3L7s <<2 11 6 13 4 -17|| {28/27, 2401/2400}

4L6s <<4 2 2 -6 -8 -1|| decimal {25/24, 49/48}

5L5s <<0 5 0 8 0 -14|| blacksmith {28/27, 49/48}

6L4s <<6 8 8 -1 -4 -4|| {50/49, 175/162}

7L3s <<2 1 6 -3 4 11|| sharp {25/24, 28/27}

8L2s <<2 6 6 5 4 -3|| octokaidecal {28/27, 50/49}

9L1s <<4 -3 2 -14 -8 13|| negri {49/48, 225/224}

11-limit

1L9s <<4 7 2 5 2 -8 -6 -15 -13 7|| {35/33, 49/48, 55/54}

2L8s <<2 -4 6 0 -11 4 -7 25 14 -21|| {28/27, 35/33, 128/121}

3L7s <<2 1 -4 -5 -3 -12 -15 -12 -15 0|| dichosis {25/24, 35/33, 64/63}

4l6s <<4 2 2 0 -6 -8 -14 -1 -7 -7|| decibel {25/24, 35/33, 49/48}

5L5s <<0 5 0 5 8 0 8 -14 -6 14|| ferrum {28/27, 35/33, 49/48}

6L4s <<6 8 8 10 -1 -4 -5 -4 -5 0|| {35/33, 50/49, 55/54}

7L3s <<2 1 6 5 -3 4 1 11 8 -7|| sharp {25/24, 28/27, 35/33}

8L2s <<2 6 6 10 5 4 9 -3 2 7|| {28/27, 35/33, 50/49}

9L1s <<4 -3 2 5 -14 -8 -6 13 22 7|| negri {45/44, 49/48, 56/55}

11edo

5-limit 11b

1L10s <<7 4 -10|| 82944/78125

2L9s <<3 8 6|| 8000/6561

3L8s <<10 1 -22|| 12582912/9765625

4L7s <<6 5 -6|| hanson 15625/15552

5L6s <<2 9 10|| 25600/19683

6L5s <<9 2 -18|| 2359296/1953125

7L4s <<5 6 -2|| sixix 3125/2916

8L3s <<1 10 14|| 81920/59049

9L2s <<8 3 -14|| 442368/390625

10L1s <<4 7 2|| 2500/2187

5-limit 11c

1L10s <<5 8 1|| ripple 6561/6250

2L9s <<1 -5 -10|| 1215/1024

3L8s <<4 13 11|| 1594323/1280000

4L7s <<9 10 -5|| 1953125/1889568

5L6s <<3 7 4|| laconic 2187/2000

6L5s <<8 15 5|| 14348907/12500000

7L4s <<13 12 -11|| 1220703125/1088391168

8L3s <<7 9 -2|| sensi 78732/78125

9L2s <<1 6 7|| avila 729/640

10L1s <<5 -14 -33|| 14946778125/8589934592

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