Semicomma family: Difference between revisions

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Orwell has MOS of size 9, 13, 22 and 31. The 9-note MOS is small enough to be retained in the mind as a genuine scale, is pleasing melodically, and has considerable harmonic resources despite its absence of 5-limit triads. The 13 note MOS has those, and of course the 22 and 31 note MOS are very well supplied with everything.

<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;Semicomma family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 5-limit parent comma for the semicomma family is the semicomma, 2109375/2097152 = |-21 3 7&amp;gt;. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor thirds. Orson, the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; temperament tempering it out, has a &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; of 75/64, which is sharper than 7/6 by 225/224 when untempered, and less sharp than that in any good orson tempering, for example &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; or &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;. These give tunings to the generator which are sharp of 7/6 by less than five &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell.&lt;br /&gt;

The 11-limit version of orwell tempers out 99/98, which means that two of its sharpened 7/6 generators give a flattened 11/8, as well as 121/120, 176/175, 385/384 and 540/539. Despite lowered tuning accuracy, orwell comes into its own in the 11-limit, giving acceptable accuracy and relatively low complexity. Tempering out the orwellisma, 1728/1715, means that orwell interprets three stacked 7/6 generators as an 8/5, and the tempered 1-7/6-11/8-8/5 chord is natural to orwell.&lt;br /&gt;

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