Meantone family: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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<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">&lt;span style="display: block; text-align: right;"&gt;[[toc]]

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The [[5-limit]] parent [[Comma|comma]] of the [[meantone]] family is the Didymus or [[http://en.wikipedia.org/wiki/Syntonic_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.

=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|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|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.

=Mohajira=  

[[Comma]]s: 81/80, 6144/6125

=Maqamic=  

Main article: [[Maqamic]]

[[Comma]]s: 81/80, 36/35, 121/120

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The &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; 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 Didymus or &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow"&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;

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&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Septimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Septimal meantone&lt;/h1&gt;

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&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 126/125&lt;br /&gt;

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&lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Mohajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;Mohajira&lt;/h1&gt;

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Mohajira, with wedgie &amp;lt;&amp;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. &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 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.&lt;br /&gt;

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&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc48"&gt;&lt;a name="Maqamic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;Maqamic&lt;/h1&gt;

&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 36/35, 121/120&lt;br /&gt;

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