68edo

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Revision as of 11:04, 7 December 2016 by Wikispaces>JosephRuhf (**Imported revision 601622606 - Original comment: **)
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This revision was by author JosephRuhf and made on 2016-12-07 11:04:55 UTC.
The original revision id was 601622606.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

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.

Diatonic scales:
Negative comma: [[tel:14 14 -1 14 14 14 -1|14 14 -1 14 14 14 -1]] (E is sharper than F, and B is sharper than C5)
Superpyth: [[tel:12 12 4 12 12 12 4|12 12 4 12 12 12 4]]
Flattone: [[tel:10 10 9 10 10 10 9|10 10 9 10 10 10 9]]
Inverse: 8 [[tel:8 14 8 8 8 14|8 14 8 8 8 14]]

Original HTML content:

<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 />
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 comma: <a class="wiki_link" href="http://tel.wikispaces.com/14%2014%20-1%2014%2014%2014%20-1">14 14 -1 14 14 14 -1</a> (E is sharper than F, and B is sharper than C5)<br />
Superpyth: <a class="wiki_link" href="http://tel.wikispaces.com/12%2012%204%2012%2012%2012%204">12 12 4 12 12 12 4</a><br />
Flattone: <a class="wiki_link" href="http://tel.wikispaces.com/10%2010%209%2010%2010%2010%209">10 10 9 10 10 10 9</a><br />
Inverse: 8 <a class="wiki_link" href="http://tel.wikispaces.com/8%2014%208%208%208%2014">8 14 8 8 8 14</a></body></html>