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 xenwolf and made on 2011-05-30 03:55:20 UTC.
- The original revision id was 232828628.
- 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 //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 is an excelent tuning for the 2.9.5.21.11 11-limit [[k*N subgroups|2*59 subgroup]], on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, 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 <a class="wiki_link" href="/major%20third">major third</a> is nearly pure. It is a good <a class="wiki_link" href="/Porcupine%20family">porcupine</a> tuning, giving in fact the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="/11-limit">11-limit</a> porcupine. This patent val tempers out 250/243 in the <a class="wiki_link" href="/5-limit">5-limit</a>, 64/63 and 16875/16807 in the <a class="wiki_link" href="/7-limit">7-limit</a>, and 55/54, 100/99 and 176/175 in the <a class="wiki_link" href="/11-limit">11-limit</a>. 59edo is an excelent tuning for the 2.9.5.21.11 11-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*59 subgroup</a>, on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, 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>