Meantone family: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 189808872 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 191257462 - 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>2010-12-22 23:03:46 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-05 18:17:34 UTC</tt>.<br>
: The original revision id was <tt>189808872</tt>.<br>
: The original revision id was <tt>191257462</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>
<h4>Original Wikitext content:</h4>
<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">The 5-limit parent [[Comma|comma]] of the meantone family is the Didymos or [[Didymos comma|syntonic comma]], 81/80. This is the one they all temper out. The [[Monzos and Interval Space|monzo]] for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding [[Wedgies and Multivals|wedgie]], &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.
<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">The 5-limit parent [[Comma|comma]] of the [[meantone]] family is the Didymos or [[Didymos comma|syntonic comma]], 81/80. This is the one they all temper out. The [[Monzos and Interval Space|monzo]] for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding [[Wedgies and Multivals|wedgie]], &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.


[[POTE tuning|POTE generator]]: 696.239
[[POTE tuning|POTE generator]]: 696.239
Map: [&lt;1 0 -4|, &lt;0 1 4|]
EDOs: 5, 7, 12, 19, 31, 50, 81
Badness: 0.00736


==Seven limit children==
==Seven limit children==
The 7-limit children of 81/80 are septimal meantone, with normal comma list [|-4 4 -1&gt;, |-13 10 0 -1&gt;], flattone, with normal list [|-4 4 -1&gt;, |-17 9 0 1&gt;], dominant, with normal list [|-4 4 -1&gt;, |6 -2 0 -1&gt;], sharptone, with normal list [|-4 4 -1&gt;, |2 -3 0 1&gt;], injera, with normal list [|-4 4 -1&gt;, |-7 8 0 -2&gt;], mohajira, with normal list [|-4 4 -1&gt;, |-23 11 0 2&gt;], godzilla, with normal list [|-4 4 -1&gt;, |-4 -1 0 2&gt;], mothra, with normal list [|-4 4 -1&gt;, |-10 1 0 3&gt;], squares, with normal list [|-4 4 -1&gt;, |-3 9 0 -4&gt;], and liese, with normal list [|-4 4 -1&gt;, |-9 11 0 -3&gt;].
The 7-limit children of 81/80 are septimal meantone, with normal comma list [|-4 4 -1&gt;, |-13 10 0 -1&gt;], flattone, with normal list [|-4 4 -1&gt;, |-17 9 0 1&gt;], dominant, with normal list [|-4 4 -1&gt;, |6 -2 0 -1&gt;], sharptone, with normal list [|-4 4 -1&gt;, |2 -3 0 1&gt;], injera, with normal list [|-4 4 -1&gt;, |-7 8 0 -2&gt;], mohajira, with normal list [|-4 4 -1&gt;, |-23 11 0 2&gt;], godzilla, with normal list [|-4 4 -1&gt;, |-4 -1 0 2&gt;], mothra, with normal list [|-4 4 -1&gt;, |-10 1 0 3&gt;], squares, with normal list [|-4 4 -1&gt;, |-3 9 0 -4&gt;], and liese, with normal list [|-4 4 -1&gt;, |-9 11 0 -3&gt;].


===Septimal meantone===
==Septimal meantone==
The comma |-13 10 0 -1&gt; for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the 7/4 of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and 7/5, C-F#, the tritone. The [[Wedgies and Multivals|wedgie]] for septimal meantone is &lt;&lt;1 4 10 4 13 12||, again telling us how to get to 5 and 7 in terms of generator steps. The temperament, aside from what is on the normal list, tempers out 126/125 and 225/224, and [[31edo]] is a good tuning for it.
The comma |-13 10 0 -1&gt; for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the 7/4 of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and 7/5, C-F#, the tritone. The [[Wedgies and Multivals|wedgie]] for septimal meantone is &lt;&lt;1 4 10 4 13 12||, again telling us how to get to 5 and 7 in terms of generator steps. The temperament, aside from what is on the normal list, tempers out 126/125 and 225/224, and [[31edo]] is a good tuning for it.


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Map: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]
Map: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]
Generators: 2, 3
Generators: 2, 3
Wedgie: &lt;&lt;1 4 10 4 13 12||
EDOs: 12, 19, 31, 81
Badness: 0.0137


====Unidecimal meantone, aka huyghens====
===Unidecimal meantone, aka huyghens===
Commas: 81/80, 126/125, 99/98
Commas: 81/80, 126/125, 99/98


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Map: [&lt;1 0 -4 -13 -25|, &lt;0 1 4 10 18|]
Map: [&lt;1 0 -4 -13 -25|, &lt;0 1 4 10 18|]
Generators: 2, 3
Generators: 2, 3
EDOs: 7, 12, 31, [[105edo|105]], [[198edo|198]]
Badness: 0.0170


====Meanpop====
====Meanpop====
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Map: [&lt;1 0 -4 -13 24|, &lt;0 1 4 10 -13|]
Map: [&lt;1 0 -4 -13 24|, &lt;0 1 4 10 -13|]
Generators: 2, 3
Generators: 2, 3
EDOs: 12, 19, 31, 81, 112
Badness: 0.0215


===Flattone===
==Flattone==
Commas: 81/80, 525/512
Commas: 81/80, 525/512


Similarly for flattone, the wedgie is &lt;&lt;1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that 7/4 is a diminished minor seventh interval. Other intervals are 7/6, a diminished minor third, and 7/5, a doubly diminshed fifth. Good tunings for flattone are [[26edo]], [[45edo]] and [[64edo]].
The wedgie for flattone is &lt;&lt;1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that 7/4 is a diminished minor seventh interval. Other intervals are 7/6, a diminished minor third, and 7/5, a doubly diminshed fifth. Good tunings for flattone are [[26edo]], [[45edo]] and [[64edo]].


7-limit minimax
7-limit minimax
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Map: [&lt;1 0 -4 17|, &lt;0 1 4 -9|]
Map: [&lt;1 0 -4 17|, &lt;0 1 4 -9|]
Wedgie: &lt;&lt;1 4 -9 4 -17 -32||
Generators: 2, 3
Generators: 2, 3
EDOs: 7, 19, [[45edo|45]], [[64edo|64]]
Badness: 0.0386


===Dominant===
==Dominant==
Commas: 36/35, 64/63
Commas: 36/35, 64/63


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[[POTE tuning|POTE generator]]: 701.573
[[POTE tuning|POTE generator]]: 701.573
Map: [&lt;1 0 -4 6|, &lt;0 1 4 -2|]
Wedgie: &lt;&lt;1 4 -2 4 -6 -16||
EDOs: 5, 7, 12, [[53edo|53]], [[65edo|65]]
Badness: 0.0207


===Sharptone===
===Sharptone===
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[[POTE tuning|POTE generator]]: 700.140
[[POTE tuning|POTE generator]]: 700.140
Map: [&lt;1 0 -4 -2|, &lt;0 1 4 3|]
Wedgie: &lt;&lt;1 4 3 4 2 -4||
EDOs: 5, 12
Badness: 0.0248


===Injera===  
===Injera===  
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[[POTE tuning|POTE generator]]: 694.375
[[POTE tuning|POTE generator]]: 694.375


===Godzilla===
Map: [&lt;2 0 -8 -7|, &lt;0 1 4 4|]
Wedgie: &lt;&lt;2 8 8 8 7 -4||
EDOs: [[12edo|12]], [[26edo|26]], [[38edo|38]], [[140edo|140]], [[178edo|178]]
Badness: 0.0311
 
==Godzilla==
Commas: 49/48, 81/80
Commas: 49/48, 81/80


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Generators: 2, 10/7</pre></div>
Generators: 2, 10/7</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Meantone family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 5-limit parent &lt;a class="wiki_link" href="/Comma"&gt;comma&lt;/a&gt; of the meantone family is the Didymos or &lt;a class="wiki_link" href="/Didymos%20comma"&gt;syntonic comma&lt;/a&gt;, 81/80. This is the one they all temper out. The &lt;a class="wiki_link" href="/Monzos%20and%20Interval%20Space"&gt;monzo&lt;/a&gt; for 81/80 goes |-4 4 -1&amp;gt;, and that can be flipped around to the corresponding &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;, &amp;lt;&amp;lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.&lt;br /&gt;
<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;Meantone family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 5-limit parent &lt;a class="wiki_link" href="/Comma"&gt;comma&lt;/a&gt; of the &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; family is the Didymos or &lt;a class="wiki_link" href="/Didymos%20comma"&gt;syntonic comma&lt;/a&gt;, 81/80. This is the one they all temper out. The &lt;a class="wiki_link" href="/Monzos%20and%20Interval%20Space"&gt;monzo&lt;/a&gt; for 81/80 goes |-4 4 -1&amp;gt;, and that can be flipped around to the corresponding &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;, &amp;lt;&amp;lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 696.239&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 696.239&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -4|, &amp;lt;0 1 4|]&lt;br /&gt;
EDOs: 5, 7, 12, 19, 31, 50, 81&lt;br /&gt;
Badness: 0.00736&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
The 7-limit children of 81/80 are septimal meantone, with normal comma list [|-4 4 -1&amp;gt;, |-13 10 0 -1&amp;gt;], flattone, with normal list [|-4 4 -1&amp;gt;, |-17 9 0 1&amp;gt;], dominant, with normal list [|-4 4 -1&amp;gt;, |6 -2 0 -1&amp;gt;], sharptone, with normal list [|-4 4 -1&amp;gt;, |2 -3 0 1&amp;gt;], injera, with normal list [|-4 4 -1&amp;gt;, |-7 8 0 -2&amp;gt;], mohajira, with normal list [|-4 4 -1&amp;gt;, |-23 11 0 2&amp;gt;], godzilla, with normal list [|-4 4 -1&amp;gt;, |-4 -1 0 2&amp;gt;], mothra, with normal list [|-4 4 -1&amp;gt;, |-10 1 0 3&amp;gt;], squares, with normal list [|-4 4 -1&amp;gt;, |-3 9 0 -4&amp;gt;], and liese, with normal list [|-4 4 -1&amp;gt;, |-9 11 0 -3&amp;gt;].&lt;br /&gt;
The 7-limit children of 81/80 are septimal meantone, with normal comma list [|-4 4 -1&amp;gt;, |-13 10 0 -1&amp;gt;], flattone, with normal list [|-4 4 -1&amp;gt;, |-17 9 0 1&amp;gt;], dominant, with normal list [|-4 4 -1&amp;gt;, |6 -2 0 -1&amp;gt;], sharptone, with normal list [|-4 4 -1&amp;gt;, |2 -3 0 1&amp;gt;], injera, with normal list [|-4 4 -1&amp;gt;, |-7 8 0 -2&amp;gt;], mohajira, with normal list [|-4 4 -1&amp;gt;, |-23 11 0 2&amp;gt;], godzilla, with normal list [|-4 4 -1&amp;gt;, |-4 -1 0 2&amp;gt;], mothra, with normal list [|-4 4 -1&amp;gt;, |-10 1 0 3&amp;gt;], squares, with normal list [|-4 4 -1&amp;gt;, |-3 9 0 -4&amp;gt;], and liese, with normal list [|-4 4 -1&amp;gt;, |-9 11 0 -3&amp;gt;].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Seven limit children-Septimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Septimal meantone&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Septimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Septimal meantone&lt;/h2&gt;
The comma |-13 10 0 -1&amp;gt; for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the 7/4 of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and 7/5, C-F#, the tritone. The &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt; for septimal meantone is &amp;lt;&amp;lt;1 4 10 4 13 12||, again telling us how to get to 5 and 7 in terms of generator steps. The temperament, aside from what is on the normal list, tempers out 126/125 and 225/224, and &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; is a good tuning for it.&lt;br /&gt;
The comma |-13 10 0 -1&amp;gt; for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the 7/4 of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and 7/5, C-F#, the tritone. The &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt; for septimal meantone is &amp;lt;&amp;lt;1 4 10 4 13 12||, again telling us how to get to 5 and 7 in terms of generator steps. The temperament, aside from what is on the normal list, tempers out 126/125 and 225/224, and &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; is a good tuning for it.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Map: [&amp;lt;1 0 -4 -13|, &amp;lt;0 1 4 10|]&lt;br /&gt;
Map: [&amp;lt;1 0 -4 -13|, &amp;lt;0 1 4 10|]&lt;br /&gt;
Generators: 2, 3&lt;br /&gt;
Generators: 2, 3&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 4 10 4 13 12||&lt;br /&gt;
EDOs: 12, 19, 31, 81&lt;br /&gt;
Badness: 0.0137&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc2"&gt;&lt;a name="x-Seven limit children-Septimal meantone-Unidecimal meantone, aka huyghens"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Unidecimal meantone, aka huyghens&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Septimal meantone-Unidecimal meantone, aka huyghens"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Unidecimal meantone, aka huyghens&lt;/h3&gt;
Commas: 81/80, 126/125, 99/98&lt;br /&gt;
Commas: 81/80, 126/125, 99/98&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Map: [&amp;lt;1 0 -4 -13 -25|, &amp;lt;0 1 4 10 18|]&lt;br /&gt;
Map: [&amp;lt;1 0 -4 -13 -25|, &amp;lt;0 1 4 10 18|]&lt;br /&gt;
Generators: 2, 3&lt;br /&gt;
Generators: 2, 3&lt;br /&gt;
EDOs: 7, 12, 31, &lt;a class="wiki_link" href="/105edo"&gt;105&lt;/a&gt;, &lt;a class="wiki_link" href="/198edo"&gt;198&lt;/a&gt;&lt;br /&gt;
Badness: 0.0170&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc3"&gt;&lt;a name="x-Seven limit children-Septimal meantone-Meanpop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Meanpop&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc3"&gt;&lt;a name="x-Septimal meantone-Unidecimal meantone, aka huyghens-Meanpop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Meanpop&lt;/h4&gt;
Commas: 81/80, 126/125, 385/384&lt;br /&gt;
Commas: 81/80, 126/125, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Map: [&amp;lt;1 0 -4 -13 24|, &amp;lt;0 1 4 10 -13|]&lt;br /&gt;
Map: [&amp;lt;1 0 -4 -13 24|, &amp;lt;0 1 4 10 -13|]&lt;br /&gt;
Generators: 2, 3&lt;br /&gt;
Generators: 2, 3&lt;br /&gt;
EDOs: 12, 19, 31, 81, 112&lt;br /&gt;
Badness: 0.0215&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Seven limit children-Flattone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Flattone&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Flattone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Flattone&lt;/h2&gt;
Commas: 81/80, 525/512&lt;br /&gt;
Commas: 81/80, 525/512&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Similarly for flattone, the wedgie is &amp;lt;&amp;lt;1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that 7/4 is a diminished minor seventh interval. Other intervals are 7/6, a diminished minor third, and 7/5, a doubly diminshed fifth. Good tunings for flattone are &lt;a class="wiki_link" href="/26edo"&gt;26edo&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45edo&lt;/a&gt; and &lt;a class="wiki_link" href="/64edo"&gt;64edo&lt;/a&gt;.&lt;br /&gt;
The wedgie for flattone is &amp;lt;&amp;lt;1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that 7/4 is a diminished minor seventh interval. Other intervals are 7/6, a diminished minor third, and 7/5, a doubly diminshed fifth. Good tunings for flattone are &lt;a class="wiki_link" href="/26edo"&gt;26edo&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45edo&lt;/a&gt; and &lt;a class="wiki_link" href="/64edo"&gt;64edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
7-limit minimax&lt;br /&gt;
7-limit minimax&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -4 17|, &amp;lt;0 1 4 -9|]&lt;br /&gt;
Map: [&amp;lt;1 0 -4 17|, &amp;lt;0 1 4 -9|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 4 -9 4 -17 -32||&lt;br /&gt;
Generators: 2, 3&lt;br /&gt;
Generators: 2, 3&lt;br /&gt;
EDOs: 7, 19, &lt;a class="wiki_link" href="/45edo"&gt;45&lt;/a&gt;, &lt;a class="wiki_link" href="/64edo"&gt;64&lt;/a&gt;&lt;br /&gt;
Badness: 0.0386&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-Seven limit children-Dominant"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Dominant&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Dominant"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Dominant&lt;/h2&gt;
Commas: 36/35, 64/63&lt;br /&gt;
Commas: 36/35, 64/63&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.573&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.573&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Seven limit children-Sharptone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Sharptone&lt;/h3&gt;
Map: [&amp;lt;1 0 -4 6|, &amp;lt;0 1 4 -2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 4 -2 4 -6 -16||&lt;br /&gt;
EDOs: 5, 7, 12, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/65edo"&gt;65&lt;/a&gt;&lt;br /&gt;
Badness: 0.0207&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Dominant-Sharptone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Sharptone&lt;/h3&gt;
Commas: 21/20, 28/27&lt;br /&gt;
Commas: 21/20, 28/27&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 288: Line 336:
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 700.140&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 700.140&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Seven limit children-Injera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Injera&lt;/h3&gt;
Map: [&amp;lt;1 0 -4 -2|, &amp;lt;0 1 4 3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 4 3 4 2 -4||&lt;br /&gt;
EDOs: 5, 12&lt;br /&gt;
Badness: 0.0248&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Dominant-Injera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Injera&lt;/h3&gt;
  Commas: 50/49, 81/80&lt;br /&gt;
  Commas: 50/49, 81/80&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 295: Line 348:
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 694.375&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 694.375&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x-Seven limit children-Godzilla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Godzilla&lt;/h3&gt;
Map: [&amp;lt;2 0 -8 -7|, &amp;lt;0 1 4 4|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 8 8 8 7 -4||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/38edo"&gt;38&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/178edo"&gt;178&lt;/a&gt;&lt;br /&gt;
Badness: 0.0311&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-Godzilla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Godzilla&lt;/h2&gt;
Commas: 49/48, 81/80&lt;br /&gt;
Commas: 49/48, 81/80&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 302: Line 360:
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 347.635&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 347.635&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x-Seven limit children-Mohajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Mohajira&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x-Godzilla-Mohajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Mohajira&lt;/h3&gt;
Commas: 81/80, 6144/6125&lt;br /&gt;
Commas: 81/80, 6144/6125&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 318: Line 376:
Generators: 2, 128/105&lt;br /&gt;
Generators: 2, 128/105&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc10"&gt;&lt;a name="x-Seven limit children-Mohajira-11 limit mohajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;11 limit mohajira&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc10"&gt;&lt;a name="x-Godzilla-Mohajira-11 limit mohajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;11 limit mohajira&lt;/h4&gt;
Commas: 81/80, 121/120, 176/175&lt;br /&gt;
Commas: 81/80, 121/120, 176/175&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 331: Line 389:
Generators: 2, 11/9&lt;br /&gt;
Generators: 2, 11/9&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="x-Seven limit children-Mothra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Mothra&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="x-Godzilla-Mothra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Mothra&lt;/h3&gt;
Commas: 81/80, 1029/1024&lt;br /&gt;
Commas: 81/80, 1029/1024&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 347: Line 405:
Generators: 2, 8/7&lt;br /&gt;
Generators: 2, 8/7&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="x-Seven limit children-Squares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Squares&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="x-Godzilla-Squares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Squares&lt;/h3&gt;
Commas: 81/80, 2401/2400&lt;br /&gt;
Commas: 81/80, 2401/2400&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 365: Line 423:
Music:&lt;br /&gt;
Music:&lt;br /&gt;
By Chris Vaisvil&lt;br /&gt;
By Chris Vaisvil&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:243:http://tinyurl.com/25kv7cq --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/25kv7cq" rel="nofollow"&gt;http://tinyurl.com/25kv7cq&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:243 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:284:http://tinyurl.com/25kv7cq --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/25kv7cq" rel="nofollow"&gt;http://tinyurl.com/25kv7cq&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:284 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:244:http://tinyurl.com/24cbxse --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/24cbxse" rel="nofollow"&gt;http://tinyurl.com/24cbxse&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:244 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:285:http://tinyurl.com/24cbxse --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/24cbxse" rel="nofollow"&gt;http://tinyurl.com/24cbxse&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:285 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
11-limit&lt;br /&gt;
11-limit&lt;br /&gt;
Line 376: Line 434:
EDOs: 14, 31, 200&lt;br /&gt;
EDOs: 14, 31, 200&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="x-Seven limit children-Liese"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Liese&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="x-Godzilla-Liese"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Liese&lt;/h3&gt;
Commas: 81/80, 686/675&lt;br /&gt;
Commas: 81/80, 686/675&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;