59edo
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-04-03 03:08:29 UTC.
- The original revision id was 216554264.
- The revision comment was:
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Original Wikitext content:
The //59 equal division// divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its major third is nearly pure. It is a good [[Porcupine family]] porcupine tuning, giving in fact the [[optimal patent val]] for 11-limit porcupine. This patent val tempers out 250/243 in the 5-limit, 64/63 and 16875/16807 in the 7-limit, and 55/54, 100/99 and 176/175 in the 11-limit. 59edo an excelent tuning for the 2.9.5.21.11 subgroup, on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 2.9.5.21.11.39.17.57 subgroup, for which the 50&59 temperament with a subminor third generator provides an interesting temperament. Using the flat fifth instead of the sharp one allows for the 12&35 temperament, which is a kind of bizarre cousin to [[Schismatic family|garibaldi temperament]] with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth.
Original HTML content:
<html><head><title>59edo</title></head><body>The <em>59 equal division</em> divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its major third is nearly pure. It is a good <a class="wiki_link" href="/Porcupine%20family">Porcupine family</a> porcupine tuning, giving in fact the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11-limit porcupine. This patent val tempers out 250/243 in the 5-limit, 64/63 and 16875/16807 in the 7-limit, and 55/54, 100/99 and 176/175 in the 11-limit. 59edo an excelent tuning for the 2.9.5.21.11 subgroup, on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 2.9.5.21.11.39.17.57 subgroup, for which the 50&59 temperament with a subminor third generator provides an interesting temperament.<br /> <br /> Using the flat fifth instead of the sharp one allows for the 12&35 temperament, which is a kind of bizarre cousin to <a class="wiki_link" href="/Schismatic%20family">garibaldi temperament</a> with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth.</body></html>