Temperaments for MOS shapes: Difference between revisions

Revision as of 22:59, 30 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 2012-11-30 22:59:01 UTC.

The original revision id was 387909630.

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 {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}

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 {36/35, 160/147}<br />
2L5s &lt;&lt;1 -3 -2 -7 -6 4|| {15/14, 64/63}<br />
3L4s &lt;&lt;2 1 -4 -3 -12 -12|| dichotic {25/24, 64/63}<br />
4L3s &lt;&lt;2 1 3 -3 -1 4|| dicot {15/14, 25/24}<br />
5L2s &lt;&lt;1 4 -2 4 -6 -16|| dominant {36/35, 64/63}<br />
6L1s &lt;&lt;3 -2 1 -10 -7 8|| {15/14, 256/245}<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 {21/20, 175/162}<br />
2L5s &lt;&lt;1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}<br />
3L4s &lt;&lt;2 1 6 -3 4 11|| sharp {25/24, 28/27}<br />
4L3s &lt;&lt;2 1 -1 -3 -7 -5|| flat {21/20, 25/24}<br />
5L2s &lt;&lt;1 4 3 4 2 -4|| sharptone {21/20, 28/27}<br />
6L1s &lt;&lt;4 2 5 -6 -3 6|| {25/24, 49/45}<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;h2&gt; --><h2 id="toc6"><a name="x8edo-7-limit 8d"></a><!-- ws:end:WikiTextHeadingRule:12 -->7-limit 8d</h2>
1L7s &lt;&lt;5 3 7 -7 -3 8|| progression {36/35, 392/375} <br />
2L6s &lt;&lt;2 -2 -2 -8 -9 1|| walid {16/15, 50/49}<br />
3L5s &lt;&lt;1 -1 -5 -4 -11 -9|| pater {16/15, 126/125}<br />
4L4s &lt;&lt;4 4 4 -3 -5 -2|| diminished {36/35, 50/49}<br />
5L3s &lt;&lt;1 -1 3 -4 2 10|| father {16/15, 28/27}<br />
6L2s &lt;&lt;6 2 2 -11 -14 -1|| {50/49, 192/175}<br />
7L1s &lt;&lt;3 5 1 1 -7 -12|| hystrix {36/35, 160/147}<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="x9edo"></a><!-- ws:end:WikiTextHeadingRule:14 -->9edo</h1>
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x9edo-5-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->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:18:&lt;h2&gt; --><h2 id="toc9"><a name="x9edo-7-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->7-limit</h2>
1L8s &lt;&lt;4 -3 2 -14 -8 13|| negri {49/48, 225/224}<br />
2L7s &lt;&lt;1 6 5 7 5 -5|| {21/20, 243/224}<br />
3L6s &lt;&lt;3 0 6 -7 1 14|| august {36/35, 128/125}<br />
4L5s &lt;&lt;7 6 8 -7 -7 2|| {36/35, 686/625}<br />
5L4s &lt;&lt;2 3 1 0 -4 -6|| beep {21/20, 27/25}<br />
6L3s &lt;&lt;3 9 6 7 1 -11|| {21/20, 729/686}<br />
7L2s &lt;&lt;1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}<br />
8L1s &lt;&lt;5 3 7 -7 -3 8|| progression {36/35, 392/375} <br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="x10edo"></a><!-- ws:end:WikiTextHeadingRule:20 -->10edo</h1>
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="x10edo-5-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->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:24:&lt;h2&gt; --><h2 id="toc12"><a name="x10edo-7-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->7-limit</h2>
1L9s &lt;&lt;4 7 2 2 -8 -15|| {49/48, 175/162}<br />
2L8s &lt;&lt;2 -4 -4 -11 -12 2|| pajara {50/49, 64/63}<br />
3L7s &lt;&lt;2 11 6 13 4 -17|| {28/27, 2401/2400}<br />
4L6s &lt;&lt;4 2 2 -6 -8 -1|| decimal {25/24, 49/48}<br />
5L5s  &lt;&lt;0 5 0 8 0 -14|| blacksmith {28/27, 49/48}<br />
6L4s &lt;&lt;6 8 8 -1 -4 -4|| {50/49, 175/162}<br />
7L3s &lt;&lt;2 1 6 -3 4 11|| sharp {25/24, 28/27}<br />
8L2s &lt;&lt;2 6 6 5 4 -3|| octokaidecal {28/27, 50/49}<br />
9L1s &lt;&lt;4 -3 2 -14 -8 13|| negri {49/48, 225/224}<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="x10edo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h2>
1L9s &lt;&lt;4 7 2 5 2 -8 -6 -15 -13 7|| {35/33, 49/48, 55/54}<br />
2L8s &lt;&lt;2 -4 6 0 -11 4 -7 25 14 -21|| {28/27, 35/33, 128/121}<br />
3L7s &lt;&lt;2 1 -4 -5 -3 -12 -15 -12 -15 0|| dichosis {25/24, 35/33, 64/63}<br />
4l6s &lt;&lt;4 2 2 0 -6 -8 -14 -1 -7 -7|| decibel {25/24, 35/33, 49/48}<br />
5L5s &lt;&lt;0 5 0 5 8 0 8 -14 -6 14|| ferrum {28/27, 35/33, 49/48}<br />
6L4s &lt;&lt;6 8 8 10 -1 -4 -5 -4 -5 0|| {35/33, 50/49, 55/54}<br />
7L3s &lt;&lt;2 1 6 5 -3 4 1 11 8 -7|| sharp {25/24, 28/27, 35/33}<br />
8L2s  &lt;&lt;2 6 6 10 5 4 9 -3 2 7|| {28/27, 35/33, 50/49}<br />
9L1s &lt;&lt;4 -3 2 5 -14 -8 -6 13 22 7|| negri {45/44, 49/48, 56/55}</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2012-11-30 22:43:01 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-11-30 22:59:01 UTC</tt>.<br>
-: The original revision id was <tt>387907868</tt>.<br>
+: The original revision id was <tt>387909630</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>
@@ Line 26: / Line 26: @@
 ==7d==
-L6s &lt;&lt;3 5 2 1 -5 -9|| oxygen
+L6s &lt;&lt;3 5 2 1 -5 -9|| oxygen {21/20, 175/162}
-L5s &lt;&lt;1 -3 -4 -7 -9 -1|| pelogic
+L5s &lt;&lt;1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}
-L4s &lt;&lt;2 1 6 -3 4 11|| sharp
+L4s &lt;&lt;2 1 6 -3 4 11|| sharp {25/24, 28/27}
-L3s &lt;&lt;2 1 -1 -3 -7 -5|| flat
+L3s &lt;&lt;2 1 -1 -3 -7 -5|| flat {21/20, 25/24}
-L2s &lt;&lt;1 4 3 4 2 -4|| sharptone
+L2s &lt;&lt;1 4 3 4 2 -4|| sharptone {21/20, 28/27}
-L1s &lt;&lt;3 -2 -5 -10 -16 -6||
+L1s &lt;&lt;4 2 5 -6 -3 6|| {25/24, 49/45}
 =8edo=
@@ Line 127: / Line 127: @@
 &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;
-L6s &amp;lt;&amp;lt;3 5 2 1 -5 -9|| oxygen &lt;br /&gt;
+L6s &amp;lt;&amp;lt;3 5 2 1 -5 -9|| oxygen {21/20, 175/162}&lt;br /&gt;
-L5s &amp;lt;&amp;lt;1 -3 -4 -7 -9 -1|| pelogic&lt;br /&gt;
+L5s &amp;lt;&amp;lt;1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}&lt;br /&gt;
-L4s &amp;lt;&amp;lt;2 1 6 -3 4 11|| sharp &lt;br /&gt;
+L4s &amp;lt;&amp;lt;2 1 6 -3 4 11|| sharp {25/24, 28/27}&lt;br /&gt;
-L3s &amp;lt;&amp;lt;2 1 -1 -3 -7 -5|| flat&lt;br /&gt;
+L3s &amp;lt;&amp;lt;2 1 -1 -3 -7 -5|| flat {21/20, 25/24}&lt;br /&gt;
-L2s &amp;lt;&amp;lt;1 4 3 4 2 -4|| sharptone&lt;br /&gt;
+L2s &amp;lt;&amp;lt;1 4 3 4 2 -4|| sharptone {21/20, 28/27}&lt;br /&gt;
-L1s &amp;lt;&amp;lt;3 -2 -5 -10 -16 -6||&lt;br /&gt;
+L1s &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;

Temperaments for MOS shapes: Difference between revisions

Revision as of 22:59, 30 November 2012

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search