Diaschismic family
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2010-06-02 21:01:40 UTC.
- The original revision id was 146624707.
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Original Wikitext content:
The 5-limit parent comma for the diaschismic family is 2048/2025, the diaschisma. Its monzo is |11 -4 -2>, and flipping that yields <<2 -4 -11|| for the wedgie. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. [[34edo]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]] or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities. =Seven limit children== The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Pajara derives from 64/63 and is a popular and well-known choice. Diaschismic adds 2097152/2066715 to obtain 7-limit harmony by more complex methods, but with greater accuracy. Keen adds 2240/2187, and shrutar 245/243, the sensamagic comma. The other temperaments all keep the same 1/2 octave period and fifth generator, but shrutar has a generator of a quarter-tone (which can be taken as 36/35, the septimal quarter-tone.)
Original HTML content:
<html><head><title>Diaschismic family</title></head><body>The 5-limit parent comma for the diaschismic family is 2048/2025, the diaschisma. Its monzo is |11 -4 -2>, and flipping that yields <<2 -4 -11|| for the wedgie. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. <a class="wiki_link" href="/34edo">34edo</a> is a good tuning choice, with <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/56edo">56edo</a>, <a class="wiki_link" href="/58edo">58edo</a> or <a class="wiki_link" href="/80edo">80edo</a> being other possibilities. Both <a class="wiki_link" href="/12edo">12edo</a> and <a class="wiki_link" href="/22edo">22edo</a> support it, and retuning them to a MOS of diaschismic gives two scale possibilities.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Seven limit children="></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children=</h1> 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. Pajara derives from 64/63 and is a popular and well-known choice. Diaschismic adds 2097152/2066715 to obtain 7-limit harmony by more complex methods, but with greater accuracy. Keen adds 2240/2187, and shrutar 245/243, the sensamagic comma. The other temperaments all keep the same 1/2 octave period and fifth generator, but shrutar has a generator of a quarter-tone (which can be taken as 36/35, the septimal quarter-tone.)</body></html>