Kleismic rank-3 family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 166297969 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 166519265 - Original comment: some links added** |
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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: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-09-29 17:02:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>166519265</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>some links added</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
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7 and 9 limit minimax | 7 and 9 limit minimax | ||
[|1 0 0 0>, |0 1 0 0>, |1 5/6 0 0>, |0 0 0 1>] | [|1 0 0 0>, |0 1 0 0>, |1 5/6 0 0>, |0 0 0 1>] | ||
Eigenmonzos: 2, 7/6, 4/3 | [[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 4/3 | ||
Map: [<1 0 1 0|, <0 6 5 0|, <0 0 0 1|] | Map: [<1 0 1 0|, <0 6 5 0|, <0 0 0 1|] | ||
Generators: 2, 6/5, 7 | [[Generator|Generators]]: 2, 6/5, 7 | ||
Edos: 15, 19, 23, 34, 53, 68, 72, 87, 121, 125, 140, 212, 333, 405 | [[edo|Edos]]: [[15edo|15]], [[19edo|19]], [[23edo|23]], [[34edo|34]], [[53edo|53]], [[68edo|68]], [[72edo|72]], [[87edo|87]], [[121edo|121]], [[125edo|125]], [[140edo|140]], [[212edo|212]], 333, 405 | ||
===Enlil=== | ===Enlil=== | ||
Commas: 15625/15552, 385/384 | [[Comma|Commas]]: 15625/15552, 385/384 | ||
Minimax tuning | [[Minimax tuning]] | ||
[|1 0 0 0 0>, |0 1 0 0 0>, |1 5/6 0 0 0>, | [|1 0 0 0 0>, |0 1 0 0 0>, |1 5/6 0 0 0>, | ||
|3 1/12 0 1/2 -1/2>, |3 1/12 0 -1/2 1/2>] | |3 1/12 0 1/2 -1/2>, |3 1/12 0 -1/2 1/2>] | ||
Eigenmonzos: 2, 4/3, 14/11 | [[Eigenmonzo|Eigenmonzos]]: 2, 4/3, 14/11 | ||
Map: [<1 0 1 0 6|, <0 6 5 0 1|, <0 0 0 1 -1|] | Map: [<1 0 1 0 6|, <0 6 5 0 1|, <0 0 0 1 -1|] | ||
Generators: 2, 6/5, 7 | [[Generator|Generators]]: 2, 6/5, 7 | ||
13-limit | 13-limit | ||
Commas: 15625/15552, 385/384, 325/324 | [[Comma|Commas]]: 15625/15552, 385/384, 325/324 | ||
13 and 15 limit minimax tuning | 13 and 15 limit minimax tuning | ||
| Line 36: | Line 36: | ||
|28/9 0 0 -14/27 13/27 1/27>, | |28/9 0 0 -14/27 13/27 1/27>, | ||
|28/9 0 0 -14/27 -14/27 28/27>] | |28/9 0 0 -14/27 -14/27 28/27>] | ||
Eigenmonzos: 2, 13/11, 14/11 | [[Eigenmonzo|Eigenmonzos]]: 2, 13/11, 14/11 | ||
Map: [<1 0 1 0 6 0|, <0 6 5 0 1 14|, <0 0 0 1 -1 0|] | Map: [<1 0 1 0 6 0|, <0 6 5 0 1 14|, <0 0 0 1 -1 0|] | ||
Generators: 2, 6/5, 7 | [[Generator|Generators]]: 2, 6/5, 7 | ||
Edos: 15, 19, 34, 53, 57, 68, 72, 87, 159, 212, 284, 299 | [[edo|Edos]]: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[57edo|57]], [[68edo|68]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[212edo|212]], 284, 299 | ||
===Enki=== | ===Enki=== | ||
Commas: 15625/15552, 3025/3024 | [[Comma|Commas]]: 15625/15552, 3025/3024 | ||
Minimax tuning | [[Minimax tuning]] | ||
[|1 0 0 0 0>, |-18/13 0 6/13 -6/13 12/13>, | [|1 0 0 0 0>, |-18/13 0 6/13 -6/13 12/13>, | ||
|-2/13 0 5/13 -5/13 10/13>, | |-2/13 0 5/13 -5/13 10/13>, | ||
|-2/13 0 -8/13 8/13 10/13>, |0 0 0 0 1>] | |-2/13 0 -8/13 8/13 10/13>, |0 0 0 0 1>] | ||
Eigenmonzos: 2, 11/8, 7/5 | [[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 7/5 | ||
Map: [<1 0 1 0 1|, <0 6 5 0 4|, <0 0 0 2 1|] | Map: [<1 0 1 0 1|, <0 6 5 0 4|, <0 0 0 2 1|] | ||
Generators: 2, 6/5, 66/25 | [[Generator|Generators]]: 2, 6/5, 66/25 | ||
Edos: 15, 49, 57, 72, 87, 159, 193, 231, 265, 280, 337, 352, 439 | [[edo|Edos]]: [[15edo|15]], [[49edo|49]], [[57edo|57]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], [[231|231]], 265, 280, 337, 352, 439 | ||
13-limit | 13-limit | ||
Commas: 15625/15552, 3025/3024, 325/324 | [[Comma|Commas]]: 15625/15552, 3025/3024, 325/324 | ||
13 and 15 limit | 13 and 15 limit | ||
| Line 63: | Line 63: | ||
|13/9 0 -4/9 1/2 0 4/9>, | |13/9 0 -4/9 1/2 0 4/9>, | ||
|14/9 0 -14/9 0 0 14/9>] | |14/9 0 -14/9 0 0 14/9>] | ||
Eigenmonzos: 2, 8/7 13/10 | [[Eigenmonzo|Eigenmonzos]]: 2, 8/7 13/10 | ||
Map: [<1 0 1 0 1 0|, <0 6 5 0 4 14|, <0 0 0 2 1 0|] | Map: [<1 0 1 0 1 0|, <0 6 5 0 4 14|, <0 0 0 2 1 0|] | ||
Generators: 2, 6/5, 66/25 | [[Generator|Generators]]: 2, 6/5, 66/25 | ||
Edos: 15, 72, 87, 159, 193, 280, 439</pre></div> | [[edo|Edos]]: [[15edo|15]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], 280, 439</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Kleismic rank three family</title></head><body>These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.<br /> | <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"><html><head><title>Kleismic rank three family</title></head><body>These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.<br /> | ||
| Line 73: | Line 73: | ||
7 and 9 limit minimax<br /> | 7 and 9 limit minimax<br /> | ||
[|1 0 0 0&gt;, |0 1 0 0&gt;, |1 5/6 0 0&gt;, |0 0 0 1&gt;]<br /> | [|1 0 0 0&gt;, |0 1 0 0&gt;, |1 5/6 0 0&gt;, |0 0 0 1&gt;]<br /> | ||
Eigenmonzos: 2, 7/6, 4/3<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6, 4/3<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 0|, &lt;0 6 5 0|, &lt;0 0 0 1|]<br /> | Map: [&lt;1 0 1 0|, &lt;0 6 5 0|, &lt;0 0 0 1|]<br /> | ||
Generators: 2, 6/5, 7<br /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 7<br /> | ||
Edos: 15, 19, 23, 34, 53, 68, 72, 87, 121, 125, 140, 212, 333, 405<br /> | <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/23edo">23</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/125edo">125</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a>, 333, 405<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Enlil"></a><!-- ws:end:WikiTextHeadingRule:0 -->Enlil</h3> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Enlil"></a><!-- ws:end:WikiTextHeadingRule:0 -->Enlil</h3> | ||
Commas: 15625/15552, 385/384<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 385/384<br /> | ||
<br /> | <br /> | ||
Minimax tuning<br /> | <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> | ||
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1 5/6 0 0 0&gt;, <br /> | [|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1 5/6 0 0 0&gt;, <br /> | ||
|3 1/12 0 1/2 -1/2&gt;, |3 1/12 0 -1/2 1/2&gt;]<br /> | |3 1/12 0 1/2 -1/2&gt;, |3 1/12 0 -1/2 1/2&gt;]<br /> | ||
Eigenmonzos: 2, 4/3, 14/11<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 4/3, 14/11<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 0 6|, &lt;0 6 5 0 1|, &lt;0 0 0 1 -1|]<br /> | Map: [&lt;1 0 1 0 6|, &lt;0 6 5 0 1|, &lt;0 0 0 1 -1|]<br /> | ||
Generators: 2, 6/5, 7<br /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 7<br /> | ||
<br /> | <br /> | ||
13-limit<br /> | 13-limit<br /> | ||
Commas: 15625/15552, 385/384, 325/324<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 385/384, 325/324<br /> | ||
<br /> | <br /> | ||
13 and 15 limit minimax tuning<br /> | 13 and 15 limit minimax tuning<br /> | ||
| Line 99: | Line 99: | ||
|28/9 0 0 -14/27 13/27 1/27&gt;, <br /> | |28/9 0 0 -14/27 13/27 1/27&gt;, <br /> | ||
|28/9 0 0 -14/27 -14/27 28/27&gt;]<br /> | |28/9 0 0 -14/27 -14/27 28/27&gt;]<br /> | ||
Eigenmonzos: 2, 13/11, 14/11<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 13/11, 14/11<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 0 6 0|, &lt;0 6 5 0 1 14|, &lt;0 0 0 1 -1 0|]<br /> | Map: [&lt;1 0 1 0 6 0|, &lt;0 6 5 0 1 14|, &lt;0 0 0 1 -1 0|]<br /> | ||
Generators: 2, 6/5, 7<br /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 7<br /> | ||
Edos: 15, 19, 34, 53, 57, 68, 72, 87, 159, 212, 284, 299<br /> | <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/212edo">212</a>, 284, 299<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x--Enki"></a><!-- ws:end:WikiTextHeadingRule:2 -->Enki</h3> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x--Enki"></a><!-- ws:end:WikiTextHeadingRule:2 -->Enki</h3> | ||
Commas: 15625/15552, 3025/3024<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 3025/3024<br /> | ||
<br /> | <br /> | ||
Minimax tuning<br /> | <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> | ||
[|1 0 0 0 0&gt;, |-18/13 0 6/13 -6/13 12/13&gt;, <br /> | [|1 0 0 0 0&gt;, |-18/13 0 6/13 -6/13 12/13&gt;, <br /> | ||
|-2/13 0 5/13 -5/13 10/13&gt;, <br /> | |-2/13 0 5/13 -5/13 10/13&gt;, <br /> | ||
|-2/13 0 -8/13 8/13 10/13&gt;, |0 0 0 0 1&gt;]<br /> | |-2/13 0 -8/13 8/13 10/13&gt;, |0 0 0 0 1&gt;]<br /> | ||
Eigenmonzos: 2, 11/8, 7/5<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/8, 7/5<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 0 1|, &lt;0 6 5 0 4|, &lt;0 0 0 2 1|]<br /> | Map: [&lt;1 0 1 0 1|, &lt;0 6 5 0 4|, &lt;0 0 0 2 1|]<br /> | ||
Generators: 2, 6/5, 66/25<br /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 66/25<br /> | ||
Edos: 15, 49, 57, 72, 87, 159, 193, 231, 265, 280, 337, 352, 439 <br /> | <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/193edo">193</a>, <a class="wiki_link" href="/231">231</a>, 265, 280, 337, 352, 439 <br /> | ||
<br /> | <br /> | ||
13-limit<br /> | 13-limit<br /> | ||
Commas: 15625/15552, 3025/3024, 325/324<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 3025/3024, 325/324<br /> | ||
<br /> | <br /> | ||
13 and 15 limit<br /> | 13 and 15 limit<br /> | ||
| Line 126: | Line 126: | ||
|13/9 0 -4/9 1/2 0 4/9&gt;, <br /> | |13/9 0 -4/9 1/2 0 4/9&gt;, <br /> | ||
|14/9 0 -14/9 0 0 14/9&gt;]<br /> | |14/9 0 -14/9 0 0 14/9&gt;]<br /> | ||
Eigenmonzos: 2, 8/7 13/10<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 8/7 13/10<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 1 0 1 0|, &lt;0 6 5 0 4 14|, &lt;0 0 0 2 1 0|]<br /> | Map: [&lt;1 0 1 0 1 0|, &lt;0 6 5 0 4 14|, &lt;0 0 0 2 1 0|]<br /> | ||
Generators: 2, 6/5, 66/25<br /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 66/25<br /> | ||
Edos: 15, 72, 87, 159, 193, 280, 439</body></html></pre></div> | <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/193edo">193</a>, 280, 439</body></html></pre></div> | ||
Revision as of 17:02, 29 September 2010
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenwolf and made on 2010-09-29 17:02:01 UTC.
- The original revision id was 166519265.
- The revision comment was: some links added
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth. 7 and 9 limit minimax [|1 0 0 0>, |0 1 0 0>, |1 5/6 0 0>, |0 0 0 1>] [[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 4/3 Map: [<1 0 1 0|, <0 6 5 0|, <0 0 0 1|] [[Generator|Generators]]: 2, 6/5, 7 [[edo|Edos]]: [[15edo|15]], [[19edo|19]], [[23edo|23]], [[34edo|34]], [[53edo|53]], [[68edo|68]], [[72edo|72]], [[87edo|87]], [[121edo|121]], [[125edo|125]], [[140edo|140]], [[212edo|212]], 333, 405 ===Enlil=== [[Comma|Commas]]: 15625/15552, 385/384 [[Minimax tuning]] [|1 0 0 0 0>, |0 1 0 0 0>, |1 5/6 0 0 0>, |3 1/12 0 1/2 -1/2>, |3 1/12 0 -1/2 1/2>] [[Eigenmonzo|Eigenmonzos]]: 2, 4/3, 14/11 Map: [<1 0 1 0 6|, <0 6 5 0 1|, <0 0 0 1 -1|] [[Generator|Generators]]: 2, 6/5, 7 13-limit [[Comma|Commas]]: 15625/15552, 385/384, 325/324 13 and 15 limit minimax tuning [|1 0 0 0 0 0>, |4/3 0 0 -2/9 -2/9 4/9>, |19/9 0 0 -5/27 -5/27 10/27>, |28/9 0 0 13/27 -14/27 1/27>, |28/9 0 0 -14/27 13/27 1/27>, |28/9 0 0 -14/27 -14/27 28/27>] [[Eigenmonzo|Eigenmonzos]]: 2, 13/11, 14/11 Map: [<1 0 1 0 6 0|, <0 6 5 0 1 14|, <0 0 0 1 -1 0|] [[Generator|Generators]]: 2, 6/5, 7 [[edo|Edos]]: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[57edo|57]], [[68edo|68]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[212edo|212]], 284, 299 ===Enki=== [[Comma|Commas]]: 15625/15552, 3025/3024 [[Minimax tuning]] [|1 0 0 0 0>, |-18/13 0 6/13 -6/13 12/13>, |-2/13 0 5/13 -5/13 10/13>, |-2/13 0 -8/13 8/13 10/13>, |0 0 0 0 1>] [[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 7/5 Map: [<1 0 1 0 1|, <0 6 5 0 4|, <0 0 0 2 1|] [[Generator|Generators]]: 2, 6/5, 66/25 [[edo|Edos]]: [[15edo|15]], [[49edo|49]], [[57edo|57]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], [[231|231]], 265, 280, 337, 352, 439 13-limit [[Comma|Commas]]: 15625/15552, 3025/3024, 325/324 13 and 15 limit [|1 0 0 0 0 0>, |2/3 0 -2/3 0 0 2/3>, |14/9 0 -5/9 0 0 5/9>, |0 0 0 1 0 0>, |13/9 0 -4/9 1/2 0 4/9>, |14/9 0 -14/9 0 0 14/9>] [[Eigenmonzo|Eigenmonzos]]: 2, 8/7 13/10 Map: [<1 0 1 0 1 0|, <0 6 5 0 4 14|, <0 0 0 2 1 0|] [[Generator|Generators]]: 2, 6/5, 66/25 [[edo|Edos]]: [[15edo|15]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], 280, 439
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<html><head><title>Kleismic rank three family</title></head><body>These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.<br /> <br /> 7 and 9 limit minimax<br /> [|1 0 0 0>, |0 1 0 0>, |1 5/6 0 0>, |0 0 0 1>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6, 4/3<br /> <br /> Map: [<1 0 1 0|, <0 6 5 0|, <0 0 0 1|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 7<br /> <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/23edo">23</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/125edo">125</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a>, 333, 405<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h3> --><h3 id="toc0"><a name="x--Enlil"></a><!-- ws:end:WikiTextHeadingRule:0 -->Enlil</h3> <a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 385/384<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> [|1 0 0 0 0>, |0 1 0 0 0>, |1 5/6 0 0 0>, <br /> |3 1/12 0 1/2 -1/2>, |3 1/12 0 -1/2 1/2>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 4/3, 14/11<br /> <br /> Map: [<1 0 1 0 6|, <0 6 5 0 1|, <0 0 0 1 -1|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 7<br /> <br /> 13-limit<br /> <a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 385/384, 325/324<br /> <br /> 13 and 15 limit minimax tuning<br /> [|1 0 0 0 0 0>, |4/3 0 0 -2/9 -2/9 4/9>, <br /> |19/9 0 0 -5/27 -5/27 10/27>, <br /> |28/9 0 0 13/27 -14/27 1/27>, <br /> |28/9 0 0 -14/27 13/27 1/27>, <br /> |28/9 0 0 -14/27 -14/27 28/27>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 13/11, 14/11<br /> <br /> Map: [<1 0 1 0 6 0|, <0 6 5 0 1 14|, <0 0 0 1 -1 0|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 7<br /> <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/212edo">212</a>, 284, 299<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x--Enki"></a><!-- ws:end:WikiTextHeadingRule:2 -->Enki</h3> <a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 3025/3024<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br /> [|1 0 0 0 0>, |-18/13 0 6/13 -6/13 12/13>, <br /> |-2/13 0 5/13 -5/13 10/13>, <br /> |-2/13 0 -8/13 8/13 10/13>, |0 0 0 0 1>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/8, 7/5<br /> <br /> Map: [<1 0 1 0 1|, <0 6 5 0 4|, <0 0 0 2 1|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 66/25<br /> <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/193edo">193</a>, <a class="wiki_link" href="/231">231</a>, 265, 280, 337, 352, 439 <br /> <br /> 13-limit<br /> <a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 3025/3024, 325/324<br /> <br /> 13 and 15 limit<br /> [|1 0 0 0 0 0>, |2/3 0 -2/3 0 0 2/3>, <br /> |14/9 0 -5/9 0 0 5/9>, |0 0 0 1 0 0>, <br /> |13/9 0 -4/9 1/2 0 4/9>, <br /> |14/9 0 -14/9 0 0 14/9>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 8/7 13/10<br /> <br /> Map: [<1 0 1 0 1 0|, <0 6 5 0 4 14|, <0 0 0 2 1 0|]<br /> <a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 66/25<br /> <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/193edo">193</a>, 280, 439</body></html>