68edo
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author PiotrGrochowski and made on 2016-09-17 04:36:46 UTC.
- The original revision id was 592459868.
- 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 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
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 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>