Meantone family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 179212561 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 179220449 - 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>2010-11-13 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-11-13 17:25:16 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>179220449</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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===Mohajira=== | ===Mohajira=== | ||
Mohajira, with wedgie <<2 8 -11 8 -23 -48||, really makes more sense as an 11-limit temperament. It has a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 128/105. Mohajira tempers out 6144/6125, the porwell comma. [[31edo]] makes for an excellent (7-limit) mohajira tuning, with generator 9/31. It has a 7-note MOS with three larger steps and four smaller ones, going sLsLsLs. | Mohajira, with wedgie <<2 8 -11 8 -23 -48||, really makes more sense as an 11-limit temperament. It has a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 128/105. Mohajira tempers out 6144/6125, the porwell comma. [[31edo]] makes for an excellent (7-limit) mohajira tuning, with generator 9/31. It has a 7-note MOS with three larger steps and four smaller ones, going sLsLsLs. | ||
Commas: 81/80, 6144/6125 | |||
7 and 9 limit minimax 1/4 comma | |||
[|1 0 0 0>, |1 0 1/4 0>, |0 0 1 0>, |6 0 -11/8 0>] | |||
Eigenmonzos: 2, 5 | |||
Algebraic generator: Mohabis, real root of 3x^3-3x^2-1, 348.6067 cents. Corresponding recurrence converges quickly. | |||
Map: [<1 1 0 6|, <0 2 8 -11|] | |||
Generators: 2, 128/105 | |||
====11 limit mohajira==== | |||
Commas: 81/80, 121/120, 176/175 | |||
11-limit minimax 1/4 comma | |||
[|1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>, | |||
|6 0 -11/8 0 0>, |2 0 5/8 0 0>] | |||
Eigenmonzos: 2, 5 | |||
Map: [<1 1 0 6 2|, <0 2 8 -11 5|] | |||
Generators: 2, 11/9 | |||
===Mothra=== | ===Mothra=== | ||
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Mohajira, with wedgie &lt;&lt;2 8 -11 8 -23 -48||, really makes more sense as an 11-limit temperament. It has a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 128/105. Mohajira tempers out 6144/6125, the porwell comma. <a class="wiki_link" href="/31edo">31edo</a> makes for an excellent (7-limit) mohajira tuning, with generator 9/31. It has a 7-note MOS with three larger steps and four smaller ones, going sLsLsLs.<br /> | Mohajira, with wedgie &lt;&lt;2 8 -11 8 -23 -48||, really makes more sense as an 11-limit temperament. It has a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 128/105. Mohajira tempers out 6144/6125, the porwell comma. <a class="wiki_link" href="/31edo">31edo</a> makes for an excellent (7-limit) mohajira tuning, with generator 9/31. It has a 7-note MOS with three larger steps and four smaller ones, going sLsLsLs.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id=" | Commas: 81/80, 6144/6125<br /> | ||
<br /> | |||
7 and 9 limit minimax 1/4 comma<br /> | |||
[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |6 0 -11/8 0&gt;]<br /> | |||
Eigenmonzos: 2, 5<br /> | |||
<br /> | |||
Algebraic generator: Mohabis, real root of 3x^3-3x^2-1, 348.6067 cents. Corresponding recurrence converges quickly.<br /> | |||
<br /> | |||
Map: [&lt;1 1 0 6|, &lt;0 2 8 -11|]<br /> | |||
Generators: 2, 128/105<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h4&gt; --><h4 id="toc8"><a name="x-Seven limit children-Mohajira-11 limit mohajira"></a><!-- ws:end:WikiTextHeadingRule:16 -->11 limit mohajira</h4> | |||
Commas: 81/80, 121/120, 176/175<br /> | |||
<br /> | |||
11-limit minimax 1/4 comma<br /> | |||
[|1 0 0 0 0&gt;, |1 0 1/4 0 0&gt;, |0 0 1 0 0&gt;, <br /> | |||
|6 0 -11/8 0 0&gt;, |2 0 5/8 0 0&gt;]<br /> | |||
Eigenmonzos: 2, 5<br /> | |||
<br /> | |||
Map: [&lt;1 1 0 6 2|, &lt;0 2 8 -11 5|]<br /> | |||
Generators: 2, 11/9<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x-Seven limit children-Mothra"></a><!-- ws:end:WikiTextHeadingRule:18 -->Mothra</h3> | |||
Mothra, with wedgie &lt;&lt;3 12 -1 12 -10 -36||, splits the fifth into three 8/7 generators. It uses 1029/1024, the gamelisma, to accomplish this deed and also tempers out 1728/1715, the orwell comma. Using <a class="wiki_link" href="/31edo">31edo</a> with a generator of 6/31 is an excellent tuning choice. Once again something other than a MOS should be used as a scale to get the most out of mothra.<br /> | Mothra, with wedgie &lt;&lt;3 12 -1 12 -10 -36||, splits the fifth into three 8/7 generators. It uses 1029/1024, the gamelisma, to accomplish this deed and also tempers out 1728/1715, the orwell comma. Using <a class="wiki_link" href="/31edo">31edo</a> with a generator of 6/31 is an excellent tuning choice. Once again something other than a MOS should be used as a scale to get the most out of mothra.<br /> | ||
<br /> | <br /> | ||
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Generators: 2, 8/7<br /> | Generators: 2, 8/7<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="x-Seven limit children-Squares"></a><!-- ws:end:WikiTextHeadingRule:20 -->Squares</h3> | ||
Squares, with wedgie &lt;&lt;4 16 9 16 3 -24||, splits the interval of an eleventh, or 8/3, into four supermajor third (9/7) intervals, and uses it for a generator. <a class="wiki_link" href="/31edo">31edo</a>, with a generator of 11/31, makes for a good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out 2401/2400, the breedsma, as well as 2430/2401.<br /> | Squares, with wedgie &lt;&lt;4 16 9 16 3 -24||, splits the interval of an eleventh, or 8/3, into four supermajor third (9/7) intervals, and uses it for a generator. <a class="wiki_link" href="/31edo">31edo</a>, with a generator of 11/31, makes for a good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out 2401/2400, the breedsma, as well as 2430/2401.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="x-Seven limit children-Liese"></a><!-- ws:end:WikiTextHeadingRule:22 -->Liese</h3> | ||
Liese, with wedgie &lt;&lt;3 12 11 12 9 -8||, splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. <a class="wiki_link" href="/74edo">74edo</a> makes for a good liese tuning, though <a class="wiki_link" href="/19edo">19edo</a> can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55.</body></html></pre></div> | Liese, with wedgie &lt;&lt;3 12 11 12 9 -8||, splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. <a class="wiki_link" href="/74edo">74edo</a> makes for a good liese tuning, though <a class="wiki_link" href="/19edo">19edo</a> can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55.</body></html></pre></div> | ||