68edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 262696162 - Original comment: ** |
Wikispaces>PiotrGrochowski **Imported revision 592459868 - 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: | : This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09-17 04:36:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>592459868</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> | ||
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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">The //68 equal temperament//, often abbreviated 68-tET, 68-EDO, or 68-ET, is the scale derived by dividing the octave into 68 equally-sized steps. Each step represents a frequency ratio of 17.65 cents; this is half of the step size of [[34edo]], which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of [[17edo]], which does well in the [[3-limit]], but not so well in the [[5-limit]]. The luck continues; 68 is a strong [[7-limit]] system, but does not do as well for in [[11-limit]]; though it's certainly usable for that purpose, it does not represent the 11-limit diamond [[consistent]]ly. | <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 //68 equal temperament//, often abbreviated 68-tET, 68-EDO, or 68-ET, is the scale derived by dividing the octave into 68 equally-sized steps. Each step represents a frequency ratio of 17.65 cents; this is half of the step size of [[34edo]], which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of [[17edo]], which does well in the [[3-limit]], but not so well in the [[5-limit]]. The luck continues; 68 is a strong [[7-limit]] system, but does not do as well for in [[11-limit]]; though it's certainly usable for that purpose, it does not represent the 11-limit diamond [[consistent]]ly. | ||
As a 7-limit system it tempers out 2048/2025, 245/243, 4000/3969, 15625/15552, 3136/3125, 6144/6125 and 2401/2400. It supports octacot, shrutar, hemiwuerschmidt, hemikleismic, clyde and neptune temperaments, and supplies the optimal patent val for 11-limit hemikleismic. It is a sharp-tending system, with the third, fifth and seventh harmonics all sharp.</pre></div> | As a 7-limit system it tempers out 2048/2025, 245/243, 4000/3969, 15625/15552, 3136/3125, 6144/6125 and 2401/2400. It supports octacot, shrutar, hemiwuerschmidt, hemikleismic, clyde and neptune temperaments, and supplies the optimal patent val for 11-limit hemikleismic. It is a sharp-tending system, with the third, fifth and seventh harmonics all sharp. | ||
Diatonic scales: | |||
Negative semitone: 14 14 -1 14 14 14 -1 (E is sharper than F, and B is sharper than C5) | |||
Superpyth: 12 12 4 12 12 12 4 | |||
Flattone: 10 10 9 10 10 10 9 | |||
Inverse: 8 8 14 8 8 8 14</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"><html><head><title>68edo</title></head><body>The <em>68 equal temperament</em>, often abbreviated 68-tET, 68-EDO, or 68-ET, is the scale derived by dividing the octave into 68 equally-sized steps. Each step represents a frequency ratio of 17.65 cents; this is half of the step size of <a class="wiki_link" href="/34edo">34edo</a>, which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of <a class="wiki_link" href="/17edo">17edo</a>, which does well in the <a class="wiki_link" href="/3-limit">3-limit</a>, but not so well in the <a class="wiki_link" href="/5-limit">5-limit</a>. The luck continues; 68 is a strong <a class="wiki_link" href="/7-limit">7-limit</a> system, but does not do as well for in <a class="wiki_link" href="/11-limit">11-limit</a>; though it's certainly usable for that purpose, it does not represent the 11-limit diamond <a class="wiki_link" href="/consistent">consistent</a>ly.<br /> | <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"><html><head><title>68edo</title></head><body>The <em>68 equal temperament</em>, often abbreviated 68-tET, 68-EDO, or 68-ET, is the scale derived by dividing the octave into 68 equally-sized steps. Each step represents a frequency ratio of 17.65 cents; this is half of the step size of <a class="wiki_link" href="/34edo">34edo</a>, which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of <a class="wiki_link" href="/17edo">17edo</a>, which does well in the <a class="wiki_link" href="/3-limit">3-limit</a>, but not so well in the <a class="wiki_link" href="/5-limit">5-limit</a>. The luck continues; 68 is a strong <a class="wiki_link" href="/7-limit">7-limit</a> system, but does not do as well for in <a class="wiki_link" href="/11-limit">11-limit</a>; though it's certainly usable for that purpose, it does not represent the 11-limit diamond <a class="wiki_link" href="/consistent">consistent</a>ly.<br /> | ||
<br /> | <br /> | ||
As a 7-limit system it tempers out 2048/2025, 245/243, 4000/3969, 15625/15552, 3136/3125, 6144/6125 and 2401/2400. It supports octacot, shrutar, hemiwuerschmidt, hemikleismic, clyde and neptune temperaments, and supplies the optimal patent val for 11-limit hemikleismic. It is a sharp-tending system, with the third, fifth and seventh harmonics all sharp.</body></html></pre></div> | As a 7-limit system it tempers out 2048/2025, 245/243, 4000/3969, 15625/15552, 3136/3125, 6144/6125 and 2401/2400. It supports octacot, shrutar, hemiwuerschmidt, hemikleismic, clyde and neptune temperaments, and supplies the optimal patent val for 11-limit hemikleismic. It is a sharp-tending system, with the third, fifth and seventh harmonics all sharp.<br /> | ||
<br /> | |||
Diatonic scales:<br /> | |||
Negative semitone: 14 14 -1 14 14 14 -1 (E is sharper than F, and B is sharper than C5)<br /> | |||
Superpyth: 12 12 4 12 12 12 4<br /> | |||
Flattone: 10 10 9 10 10 10 9<br /> | |||
Inverse: 8 8 14 8 8 8 14</body></html></pre></div> | |||