Temperaments for MOS shapes: Difference between revisions

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**Imported revision 387412848 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 387449248 - 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:genewardsmith|genewardsmith]] and made on <tt>2012-11-29 14:11:20 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-11-29 15:36:13 UTC</tt>.<br>
: The original revision id was <tt>387412848</tt>.<br>
: The original revision id was <tt>387449248</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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==7-limit==
==7-limit==
1L9s &lt;&lt;6 3 8 -9 -4 10|| {25/24, 343/324}
1L9s &lt;&lt;6 3 8 -9 -4 10|| {25/24, 343/324}
2L8s  
2L8s &lt;&lt;2 -4 -4 -11 -12 2|| pajara {50/49, 64/63}
3L7s &lt;&lt;8 -1 4 -20 -16 12|| {49/48, 1875/1792}
3L7s &lt;&lt;8 -1 4 -20 -16 12|| {49/48, 1875/1792}
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}
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&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x10edo-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;7-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x10edo-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;7-limit&lt;/h2&gt;
1L9s &amp;lt;&amp;lt;6 3 8 -9 -4 10|| {25/24, 343/324}&lt;br /&gt;
1L9s &amp;lt;&amp;lt;6 3 8 -9 -4 10|| {25/24, 343/324}&lt;br /&gt;
2L8s &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;8 -1 4 -20 -16 12|| {49/48, 1875/1792}&lt;br /&gt;
3L7s &amp;lt;&amp;lt;8 -1 4 -20 -16 12|| {49/48, 1875/1792}&lt;br /&gt;
4L6s &amp;lt;&amp;lt;4 2 2 -6 -8 -1|| decimal {25/24, 49/48}&lt;br /&gt;
4L6s &amp;lt;&amp;lt;4 2 2 -6 -8 -1|| decimal {25/24, 49/48}&lt;br /&gt;

Revision as of 15:36, 29 November 2012

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2012-11-29 15:36:13 UTC.
The original revision id was 387449248.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

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
2L5s <<1 -3 -2 -7 -6 4|| 
3L4s <<2 1 3 -3 -1 4|| dicot
4L3s <<2 1 -4 -3 -12 -12||
5L2s <<1 4 -2 4 -6 -16|| dominant
6L1s <<3 -2 1 -10 -7 8|| dichotic

==7d==
1L6s <<3 5 2 1 -5 -9|| oxygen 
2L5s <<1 -3 -4 -7 -9 -1|| pelogic
3L4s <<2 1 6 -3 4 11|| sharp 
4L3s <<2 1 -1 -3 -7 -5|| flat
5L2s <<1 4 3 4 2 -4|| sharptone
6L1s <<3 -2 -5 -10 -16 -6||

=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

=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

=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 <<6 3 8 -9 -4 10|| {25/24, 343/324}
2L8s <<2 -4 -4 -11 -12 2|| pajara {50/49, 64/63}
3L7s <<8 -1 4 -20 -16 12|| {49/48, 1875/1792}
4L6s <<4 2 2 -6 -8 -1|| decimal {25/24, 49/48}
5L5s <<10 5 0 -15 -28 -14|| {25/24, 16807/16384}
6L4s 
7L3s 
8L2s <<8 4 -6 -12 -32 -25|| {25/24, 65536/64827}
9L1s <<4 -3 2 -14 -8 13|| negri {49/48, 225/224}

Original HTML content:

<html><head><title>Temperaments for MOS shapes</title></head><body>Below are listed temperaments of least TE complexity which result in a particular MOS shape, where &quot;results in&quot; is taken to mean that the POTE tuning has that shape.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x7edo"></a><!-- ws:end:WikiTextHeadingRule:0 -->7edo</h1>
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x7edo-5-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->5-limit</h2>
1L6s &lt;&lt;3 5 1|| porcupine 250/243<br />
2L5s &lt;&lt;1 -3 -7|| mavila 135/128<br />
3L4s &lt;&lt;2 1 -3|| dicot 25/24<br />
4L3s &lt;&lt;5 6 -2|| sixix 3125/2916<br />
5L2s &lt;&lt;1 4 4|| meantone 81/80<br />
6L1s &lt;&lt;3 -2 -10|| enipucrop 1125/1024<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x7edo-7-limit patent"></a><!-- ws:end:WikiTextHeadingRule:4 -->7-limit patent</h2>
1L6s &lt;&lt;3 5 1 1 -7 -12|| hystrix<br />
2L5s &lt;&lt;1 -3 -2 -7 -6 4|| <br />
3L4s &lt;&lt;2 1 3 -3 -1 4|| dicot<br />
4L3s &lt;&lt;2 1 -4 -3 -12 -12||<br />
5L2s &lt;&lt;1 4 -2 4 -6 -16|| dominant<br />
6L1s &lt;&lt;3 -2 1 -10 -7 8|| dichotic<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x7edo-7d"></a><!-- ws:end:WikiTextHeadingRule:6 -->7d</h2>
1L6s &lt;&lt;3 5 2 1 -5 -9|| oxygen <br />
2L5s &lt;&lt;1 -3 -4 -7 -9 -1|| pelogic<br />
3L4s &lt;&lt;2 1 6 -3 4 11|| sharp <br />
4L3s &lt;&lt;2 1 -1 -3 -7 -5|| flat<br />
5L2s &lt;&lt;1 4 3 4 2 -4|| sharptone<br />
6L1s &lt;&lt;3 -2 -5 -10 -16 -6||<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="x8edo"></a><!-- ws:end:WikiTextHeadingRule:8 -->8edo</h1>
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x8edo-5-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->5-limit</h2>
1L7s &lt;&lt;5 3 -7|| progression 3456/3125<br />
2L6s &lt;&lt;2 6 5|| supersharp 800/729 <br />
3L5s &lt;&lt;7 9 -2|| sensi 78732/78125<br />
4L4s &lt;&lt;4 4 -3|| diminished 648/625<br />
5L3s &lt;&lt;1 -1 -4|| father 16/15<br />
6L2s &lt;&lt;6 2 -11|| 18432/15625<br />
7L1s &lt;&lt;3 5 1|| porcupine 250/243<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="x9edo"></a><!-- ws:end:WikiTextHeadingRule:12 -->9edo</h1>
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x9edo-5-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->5-limit</h2>
1L8s &lt;&lt;4 -3 -14|| negri 16875/16384<br />
2L7s &lt;&lt;1 6 -7|| avila 729/640<br />
3L6s &lt;&lt;3 0 -7|| augmented 128/125<br />
4L5s &lt;&lt;7 6 -7|| 93312/78125<br />
5L4s &lt;&lt;2 3 0|| bug 27/25<br />
6L3s &lt;&lt;3 9 7|| 19683/16000<br />
7L2s &lt;&lt;1 -3 -7|| mavila 135/128<br />
8L1s &lt;&lt;5 3 -7|| progression 3456/3125<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="x10edo"></a><!-- ws:end:WikiTextHeadingRule:16 -->10edo</h1>
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x10edo-5-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->5-limit</h2>
1L9s &lt;&lt;4 7 2|| 2500/2187<br />
2L8s &lt;&lt;2 -4 -11|| srutal 2048/2025<br />
3L7s &lt;&lt;2 11 13|| 204800/177147<br />
4L6s &lt;&lt;14 12 -13|| 6103515625/4353564672<br />
5L5s &lt;&lt;0 5 8|| blackwood 256/243<br />
6L4s &lt;&lt;6 8 -1|| 15625/13122<br />
7L3s &lt;&lt;2 1 -3|| dicot 25/24<br />
8L2s &lt;&lt;2 6 5|| supersharp 800/729<br />
9L1s &lt;&lt;4 -3 -14|| negri 16875/16384<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="x10edo-7-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->7-limit</h2>
1L9s &lt;&lt;6 3 8 -9 -4 10|| {25/24, 343/324}<br />
2L8s &lt;&lt;2 -4 -4 -11 -12 2|| pajara {50/49, 64/63}<br />
3L7s &lt;&lt;8 -1 4 -20 -16 12|| {49/48, 1875/1792}<br />
4L6s &lt;&lt;4 2 2 -6 -8 -1|| decimal {25/24, 49/48}<br />
5L5s &lt;&lt;10 5 0 -15 -28 -14|| {25/24, 16807/16384}<br />
6L4s <br />
7L3s <br />
8L2s &lt;&lt;8 4 -6 -12 -32 -25|| {25/24, 65536/64827}<br />
9L1s &lt;&lt;4 -3 2 -14 -8 13|| negri {49/48, 225/224}</body></html>
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