Semicomma family
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2010-06-20 17:07:45 UTC.
- The original revision id was 149714195.
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Original Wikitext content:
The 5-limit parent comma for the semicomma family is the semicomma, 2109375/2097152 = |-21 3 7>. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor thirds. Orson, the 5-limit temperament tempering it out, has a generator of 75/64. [[53edo]] is an excellent orson tuning, and [[84edo]] makes for a good alternative. These give tunings to the generator which are sharp of 7/6 by less than five cents, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell. ==Seven limit children== The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Adding 64625/65536 leads to orwell, but we could also add 1029/1024, leading to the 31&159 temperament with wedgie <<21 -9 -7 -63 -70 9||, or 67528125/67108864, giving the 31&243 temperament with wedgie <<28 -12 1 -84 -77 36||, or 4375/4374, giving the 53&243 temperament with wedgie <<7 -3 61 -21 77 150||. ===Orwell=== So called because 19/84 (as a [[fraction of the octave]]) is a possible generator of this temperament, orwell divides the interval of a twelfth (a tempered 3/1 frequency ratio) into 7 equal steps. It's compatible with 22, 31 and 53-EDO. It's reasonable in the 7-limit and naturally extends into the 11-limit.
Original HTML content:
<html><head><title>Semicomma family</title></head><body>The 5-limit parent comma for the semicomma family is the semicomma, 2109375/2097152 = |-21 3 7>. This is the amount by which three pure 3/1 twelfths exceed seven pure 8/5 minor thirds. Orson, the 5-limit temperament tempering it out, has a generator of 75/64. <a class="wiki_link" href="/53edo">53edo</a> is an excellent orson tuning, and <a class="wiki_link" href="/84edo">84edo</a> makes for a good alternative. These give tunings to the generator which are sharp of 7/6 by less than five cents, making it hard to treat orson as anything other than an (at least) 7-limit system, leading to orwell.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. Adding 64625/65536 leads to orwell, but we could also add 1029/1024, leading to the 31&159 temperament with wedgie <<21 -9 -7 -63 -70 9||, or 67528125/67108864, giving the 31&243 temperament with wedgie <<28 -12 1 -84 -77 36||, or 4375/4374, giving the 53&243 temperament with wedgie <<7 -3 61 -21 77 150||.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Seven limit children-Orwell"></a><!-- ws:end:WikiTextHeadingRule:2 -->Orwell</h3> So called because 19/84 (as a <a class="wiki_link" href="/fraction%20of%20the%20octave">fraction of the octave</a>) is a possible generator of this temperament, orwell divides the interval of a twelfth (a tempered 3/1 frequency ratio) into 7 equal steps. It's compatible with 22, 31 and 53-EDO. It's reasonable in the 7-limit and naturally extends into the 11-limit.</body></html>