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:genewardsmith|genewardsmith]] and made on <tt>2011-10-07 15:46:37 UTC</tt>.<br>
: 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>262696162</tt>.<br>
: 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">&lt;html&gt;&lt;head&gt;&lt;title&gt;68edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;68 equal temperament&lt;/em&gt;, 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 &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt;, which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;, which does well in the &lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt;, but not so well in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;. The luck continues; 68 is a strong &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; system, but does not do as well for in &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;; though it's certainly usable for that purpose, it does not represent the 11-limit diamond &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt;ly.&lt;br /&gt;
<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;68edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;68 equal temperament&lt;/em&gt;, 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 &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt;, which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;, which does well in the &lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt;, but not so well in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;. The luck continues; 68 is a strong &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; system, but does not do as well for in &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;; though it's certainly usable for that purpose, it does not represent the 11-limit diamond &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt;ly.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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.&lt;/body&gt;&lt;/html&gt;</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.&lt;br /&gt;
&lt;br /&gt;
Diatonic scales:&lt;br /&gt;
Negative semitone: 14 14 -1 14 14 14 -1 (E is sharper than F, and B is sharper than C5)&lt;br /&gt;
Superpyth: 12 12 4 12 12 12 4&lt;br /&gt;
Flattone: 10 10 9 10 10 10 9&lt;br /&gt;
Inverse: 8 8 14 8 8 8 14&lt;/body&gt;&lt;/html&gt;</pre></div>