665edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author JosephRuhf and made on 2016-12-08 14:32:17 UTC.
- The original revision id was 601731906.
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Original Wikitext content:
The //665 equal temperament// divides the octave into 665 equal parts of 1.80451 cents each. It is best known for its extremely accurate fifth, only 0.0001 cents flat. 665edo is the denominator of a convergent to log2(3), after [[41edo]], [[53edo]] and [[306edo]], and before [[15601edo]]. However, it also provides the [[optimal patent val]] for the rank four temperament tempering out 4000/3993. In the 3-limit it tempers out the 'satanic' comma, |-1054 665>; in the 5-limit the enneadeca, |-14 -19 19> and the monzisma, |54 -37 2>; in the 7-limit, 4375/4374 and the meter, | -11 2 7 -3 >; in the 11-limit, 4000/3993 and | 17 -5 0 -2 -1 > and | -1 2 -4 5 -2 >, providing the optimal patent val for 11-limit [[Ragismic microtemperaments#Brahmagupta|brahmagupta temperament]]. In the 13-limit it tempers out 1575/1573, 2080/2079, 4096/4095 and 4225/4224; since it tempers out 1575/1573, the nicola, it supports nicolic tempering and hence the [[nicolic tetrad]], for which it provides an excellent tuning.
Original HTML content:
<html><head><title>665edo</title></head><body>The <em>665 equal temperament</em> divides the octave into 665 equal parts of 1.80451 cents each. It is best known for its extremely accurate fifth, only 0.0001 cents flat. 665edo is the denominator of a convergent to log2(3), after <a class="wiki_link" href="/41edo">41edo</a>, <a class="wiki_link" href="/53edo">53edo</a> and <a class="wiki_link" href="/306edo">306edo</a>, and before <a class="wiki_link" href="/15601edo">15601edo</a>. However, it also provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the rank four temperament tempering out 4000/3993. In the 3-limit it tempers out the 'satanic' comma, |-1054 665>; in the 5-limit the enneadeca, |-14 -19 19> and the monzisma, |54 -37 2>; in the 7-limit, 4375/4374 and the meter, | -11 2 7 -3 >; in the 11-limit, 4000/3993 and | 17 -5 0 -2 -1 > and | -1 2 -4 5 -2 >, providing the optimal patent val for 11-limit <a class="wiki_link" href="/Ragismic%20microtemperaments#Brahmagupta">brahmagupta temperament</a>. In the 13-limit it tempers out 1575/1573, 2080/2079, 4096/4095 and 4225/4224; since it tempers out 1575/1573, the nicola, it supports nicolic tempering and hence the <a class="wiki_link" href="/nicolic%20tetrad">nicolic tetrad</a>, for which it provides an excellent tuning.</body></html>