Temperaments for MOS shapes: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Below are listed [[temperament]]s 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>2012-11-28 22:11:23 UTC</tt>.<br>
: The original revision id was <tt>387160930</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">
=7edo=
==5-limit==
1L6s &lt;&lt;3 5 1|| porcupine 250/243
2L5s &lt;&lt;1 -3 -7|| mavila 135/128
3L4s &lt;&lt;2 1 -3|| dicot 25/24
4L3s &lt;&lt;5 6 -2|| sixix 3125/2916
5L2s &lt;&lt;1 4 4|| meantone 81/80
6L1s &lt;&lt;3 -2 -10|| enipucpop 1125/1024


==7-limit patent==
== 7edo ==
1L6s &lt;&lt;3 5 1 1 -7 -12|| hystrix
=== 5-limit ===
2L5s &lt;&lt;1 -3 -2 -7 -6 4||  
{| class="wikitable center-1"
3L4s &lt;&lt;2 1 3 -3 -1 4|| dicot
|-
4L3s &lt;&lt;2 1 -4 -3 -12 -12||
! Mos !! Temperament !! Comma list
5L2s &lt;&lt;1 4 -2 4 -6 -16|| dominant
|-
6L1s &lt;&lt;3 -2 1 -10 -7 8|| dichotic
| 1L 6s || [[Porcupine]] || 250/243
|-
| 2L 5s || [[Mavila]] || 135/128
|-
| 3L 4s || [[Dicot]] || 25/24
|-
| 4L 3s || [[Sixix]] || 3125/2916
|-
| 5L 2s || [[Meantone]] || 81/80
|-
| 6L 1s || [[Enipucrop]] || 1125/1024
|}


==7d==
=== 7-limit patent ===
1L6s &lt;&lt;3 5 2 1 -5 -9|| oxygen
{| class="wikitable center-1"
2L5s &lt;&lt;1 -3 -4 -7 -9 -1|| pelogic
|-
3L4s &lt;&lt;2 1 6 -3 4 11|| sharp
! Mos !! Temperament !! Comma list
4L3s &lt;&lt;2 1 -1 -3 -7 -5|| flat
|-
5L2s &lt;&lt;1 4 3 4 2 -4|| sharptone
| 1L 6s || [[Hystrix]] || 36/35, 160/147
6L1s &lt;&lt;3 -2 -5 -10 -16 -6||
|-
| 2L 5s || [[Medusa]] || 15/14, 64/63
|-
| 3L 4s || [[Dichotic]] || 25/24, 64/63
|-
| 4L 3s || [[Dicot]] || 15/14, 25/24
|-
| 5L 2s || [[Dominant (temperament)|Dominant]] || 36/35, 64/63
|-
| 6L 1s ||  || 15/14, 256/245
|}


=8edo=
=== 7d ===
==5-limit==
{| class="wikitable center-1"
1L7s &lt;&lt;5 3 -7|| 3456/3125
|-
2L6s &lt;&lt;2 6 5|| supersharp 800/729  
! Mos !! Temperament !! Comma list
3L5s &lt;&lt;7 9 -2|| sensi 78732/78125
|-
4L4s &lt;&lt;4 4 -3|| diminished 648/625
| 1L 6s || [[Oxygen]] || 21/20, 175/162
5L3s &lt;&lt;1 -1 -4|| father 16/15
|-
6L2s &lt;&lt;6 2 -11|| 18432/15625
| 2L 5s || [[Pelogic]] || 21/20, 135/128
7L1s &lt;&lt;3 5 1|| porcupine 250/243</pre></div>
|-
<h4>Original HTML content:</h4>
| 3L 4s || [[Sharpie]] || 25/24, 28/27
<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;&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;
| 4L 3s || [[Flattie]] || 21/20, 25/24
&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;
| 5L 2s || [[Sharptone]] || 21/20, 28/27
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;
| 6L 1s ||  || 25/24, 49/45
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|| enipucpop 1125/1024&lt;br /&gt;
== 8edo ==
&lt;br /&gt;
=== 5-limit ===
&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;
{| class="wikitable center-1"
1L6s &amp;lt;&amp;lt;3 5 1 1 -7 -12|| hystrix&lt;br /&gt;
|-
2L5s &amp;lt;&amp;lt;1 -3 -2 -7 -6 4|| &lt;br /&gt;
! Mos !! Temperament !! Comma list
3L4s &amp;lt;&amp;lt;2 1 3 -3 -1 4|| dicot&lt;br /&gt;
|-
4L3s &amp;lt;&amp;lt;2 1 -4 -3 -12 -12||&lt;br /&gt;
| 1L 7s || [[Progression]] || 3456/3125
5L2s &amp;lt;&amp;lt;1 4 -2 4 -6 -16|| dominant&lt;br /&gt;
|-
6L1s &amp;lt;&amp;lt;3 -2 1 -10 -7 8|| dichotic&lt;br /&gt;
| 2L 6s || [[Supersharp]] || 800/729  
&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;
| 3L 5s || [[Sensipent]] || 78732/78125
1L6s &amp;lt;&amp;lt;3 5 2 1 -5 -9|| oxygen &lt;br /&gt;
|-
2L5s &amp;lt;&amp;lt;1 -3 -4 -7 -9 -1|| pelogic&lt;br /&gt;
| 4L 4s || [[Diminished (temperament)|Diminished]] || 648/625
3L4s &amp;lt;&amp;lt;2 1 6 -3 4 11|| sharp &lt;br /&gt;
|-
4L3s &amp;lt;&amp;lt;2 1 -1 -3 -7 -5|| flat&lt;br /&gt;
| 5L 3s || [[Father]] || 16/15
5L2s &amp;lt;&amp;lt;1 4 3 4 2 -4|| sharptone&lt;br /&gt;
|-
6L1s &amp;lt;&amp;lt;3 -2 -5 -10 -16 -6||&lt;br /&gt;
| 6L 2s ||  || 18432/15625
&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;
| 7L 1s || [[Porcupine]] || 250/243
&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|| 3456/3125&lt;br /&gt;
 
2L6s &amp;lt;&amp;lt;2 6 5|| supersharp 800/729 &lt;br /&gt;
=== 7-limit 8d ===
3L5s &amp;lt;&amp;lt;7 9 -2|| sensi 78732/78125&lt;br /&gt;
{| class="wikitable center-1"
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;
! Mos !! Temperament !! Comma list
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;/body&gt;&lt;/html&gt;</pre></div>
| 1L 7s || [[Progression]] || 36/35, 392/375
|-
| 2L 6s || [[Walid]] || 16/15, 50/49
|-
| 3L 5s || [[Pater]] || 16/15, 126/125
|-
| 4L 4s || [[Diminished (temperament)|Diminished]] || 36/35, 50/49
|-
| 5L 3s || [[Father]] || 16/15, 28/27
|-
| 6L 2s ||  || 50/49, 192/175
|-
| 7L 1s || [[Hystrix]] || 36/35, 160/147
|}
 
== 9edo ==
=== 5-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 8s || [[Negri]] || 16875/16384
|-
| 2L 7s || [[Avila]] || 729/640
|-
| 3L 6s || [[Augmented (temperament)|Augmented]] || 128/125
|-
| 4L 5s ||  || 93312/78125
|-
| 5L 4s || [[Bug]] || 27/25
|-
| 6L 3s ||  || 19683/16000
|-
| 7L 2s || [[Mavila]] || 135/128
|-
| 8L 1s || [[Progression]] || 3456/3125
|}
 
=== 7-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 8s || [[Negri]] || 49/48, 225/224
|-
| 2L 7s ||  || 21/20, 243/224
|-
| 3L 6s || [[August]] || 36/35, 128/125
|-
| 4L 5s ||  || 36/35, 686/625
|-
| 5L 4s || [[Beep]] || 21/20, 27/25
|-
| 6L 3s ||  || 21/20, 729/686
|-
| 7L 2s || [[Pelogic]] || 21/20, 135/128
|-
| 8L 1s || [[Progression]] || 36/35, 392/375
|}
 
== 10edo ==
=== 5-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 9s ||  || 2500/2187
|-
| 2L 8s || [[Diaschismic]] || 2048/2025
|-
| 3L 7s ||  || 204800/177147
|-
| 4L 6s ||  || 6103515625/4353564672
|-
| 5L 5s || [[Blackwood]] || 256/243
|-
| 6L 4s ||  || 15625/13122
|-
| 7L 3s || [[Dicot]] || 25/24
|-
| 8L 2s || [[Supersharp]] || 800/729
|-
| 9L 1s || [[Negri]] || 16875/16384
|}
 
=== 7-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 9s ||  || 49/48, 175/162
|-
| 2L 8s || [[Pajara]] || 50/49, 64/63
|-
| 3L 7s ||  || 28/27, 2401/2400
|-
| 4L 6s || [[Decimal]] || 25/24, 49/48
|-
| 5L 5s || [[Blackwood]] || 28/27, 49/48
|-
| 6L 4s ||  || 50/49, 175/162
|-
| 7L 3s || [[Sharpie]] || 25/24, 28/27
|-
| 8L 2s || [[Octokaidecal]] || 28/27, 50/49
|-
| 9L 1s || [[Negri]] || 49/48, 225/224
|}
 
=== 11-limit ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 9s ||  || 35/33, 49/48, 55/54
|-
| 2L 8s ||  || 28/27, 35/33, 128/121
|-
| 3L 7s || [[Dichosis]] || 25/24, 35/33, 64/63
|-
| 4L 6s || [[Decibel]] || 25/24, 35/33, 49/48
|-
| 5L 5s || [[Ferrum]] || 28/27, 35/33, 49/48
|-
| 6L 4s ||  || 35/33, 50/49, 55/54
|-
| 7L 3s || [[Sharpie]] || 25/24, 28/27, 35/33
|-
| 8L 2s ||  || 28/27, 35/33, 50/49
|-
| 9L 1s || [[Negri]] || 45/44, 49/48, 56/55
|}
 
== 11edo ==
=== 5-limit 11b ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 10s ||  || 82944/78125
|-
| 2L 9s ||  || 8000/6561
|-
| 3L 8s ||  || 12582912/9765625
|-
| 4L 7s || [[Hanson]] || 15625/15552
|-
| 5L 6s ||  || 25600/19683
|-
| 6L 5s ||  || 2359296/1953125
|-
| 7L 4s || [[Sixix]] || 3125/2916
|-
| 8L 3s ||  || 81920/59049
|-
| 9L 2s ||  || 442368/390625
|-
| 10L 1s ||  || 2500/2187
|}
 
=== 5-limit 11c ===
{| class="wikitable center-1"
|-
! Mos !! Temperament !! Comma list
|-
| 1L 10s || [[Ripple]] || 6561/6250
|-
| 2L 9s ||  || 1215/1024
|-
| 3L 8s ||  || 1594323/1280000
|-
| 4L 7s ||  || 1953125/1889568
|-
| 5L 6s || [[Laconic]] || 2187/2000
|-
| 6L 5s ||  || 14348907/12500000
|-
| 7L 4s ||  || 1220703125/1088391168
|-
| 8L 3s || [[Sensipent]] || 78732/78125
|-
| 9L 2s || [[Avila]] || 729/640
|-
| 10L 1s || || 14946778125/8589934592
|}
 
[[Category:Lists of temperaments]]
[[Category:MOS scale]]
{{todo|expand}}

Latest revision as of 23:34, 8 April 2026

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

Mos Temperament Comma list
1L 6s Porcupine 250/243
2L 5s Mavila 135/128
3L 4s Dicot 25/24
4L 3s Sixix 3125/2916
5L 2s Meantone 81/80
6L 1s Enipucrop 1125/1024

7-limit patent

Mos Temperament Comma list
1L 6s Hystrix 36/35, 160/147
2L 5s Medusa 15/14, 64/63
3L 4s Dichotic 25/24, 64/63
4L 3s Dicot 15/14, 25/24
5L 2s Dominant 36/35, 64/63
6L 1s 15/14, 256/245

7d

Mos Temperament Comma list
1L 6s Oxygen 21/20, 175/162
2L 5s Pelogic 21/20, 135/128
3L 4s Sharpie 25/24, 28/27
4L 3s Flattie 21/20, 25/24
5L 2s Sharptone 21/20, 28/27
6L 1s 25/24, 49/45

8edo

5-limit

Mos Temperament Comma list
1L 7s Progression 3456/3125
2L 6s Supersharp 800/729
3L 5s Sensipent 78732/78125
4L 4s Diminished 648/625
5L 3s Father 16/15
6L 2s 18432/15625
7L 1s Porcupine 250/243

7-limit 8d

Mos Temperament Comma list
1L 7s Progression 36/35, 392/375
2L 6s Walid 16/15, 50/49
3L 5s Pater 16/15, 126/125
4L 4s Diminished 36/35, 50/49
5L 3s Father 16/15, 28/27
6L 2s 50/49, 192/175
7L 1s Hystrix 36/35, 160/147

9edo

5-limit

Mos Temperament Comma list
1L 8s Negri 16875/16384
2L 7s Avila 729/640
3L 6s Augmented 128/125
4L 5s 93312/78125
5L 4s Bug 27/25
6L 3s 19683/16000
7L 2s Mavila 135/128
8L 1s Progression 3456/3125

7-limit

Mos Temperament Comma list
1L 8s Negri 49/48, 225/224
2L 7s 21/20, 243/224
3L 6s August 36/35, 128/125
4L 5s 36/35, 686/625
5L 4s Beep 21/20, 27/25
6L 3s 21/20, 729/686
7L 2s Pelogic 21/20, 135/128
8L 1s Progression 36/35, 392/375

10edo

5-limit

Mos Temperament Comma list
1L 9s 2500/2187
2L 8s Diaschismic 2048/2025
3L 7s 204800/177147
4L 6s 6103515625/4353564672
5L 5s Blackwood 256/243
6L 4s 15625/13122
7L 3s Dicot 25/24
8L 2s Supersharp 800/729
9L 1s Negri 16875/16384

7-limit

Mos Temperament Comma list
1L 9s 49/48, 175/162
2L 8s Pajara 50/49, 64/63
3L 7s 28/27, 2401/2400
4L 6s Decimal 25/24, 49/48
5L 5s Blackwood 28/27, 49/48
6L 4s 50/49, 175/162
7L 3s Sharpie 25/24, 28/27
8L 2s Octokaidecal 28/27, 50/49
9L 1s Negri 49/48, 225/224

11-limit

Mos Temperament Comma list
1L 9s 35/33, 49/48, 55/54
2L 8s 28/27, 35/33, 128/121
3L 7s Dichosis 25/24, 35/33, 64/63
4L 6s Decibel 25/24, 35/33, 49/48
5L 5s Ferrum 28/27, 35/33, 49/48
6L 4s 35/33, 50/49, 55/54
7L 3s Sharpie 25/24, 28/27, 35/33
8L 2s 28/27, 35/33, 50/49
9L 1s Negri 45/44, 49/48, 56/55

11edo

5-limit 11b

Mos Temperament Comma list
1L 10s 82944/78125
2L 9s 8000/6561
3L 8s 12582912/9765625
4L 7s Hanson 15625/15552
5L 6s 25600/19683
6L 5s 2359296/1953125
7L 4s Sixix 3125/2916
8L 3s 81920/59049
9L 2s 442368/390625
10L 1s 2500/2187

5-limit 11c

Mos Temperament Comma list
1L 10s Ripple 6561/6250
2L 9s 1215/1024
3L 8s 1594323/1280000
4L 7s 1953125/1889568
5L 6s Laconic 2187/2000
6L 5s 14348907/12500000
7L 4s 1220703125/1088391168
8L 3s Sensipent 78732/78125
9L 2s Avila 729/640
10L 1s 14946778125/8589934592
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