176edo: Difference between revisions

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176edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 6912/6875, [[8019/8000]], [[9801/9800]] and [[16384/16335]] in the 11-limit. Using the [[patent val]], [[351/350]], [[364/363]], [[2080/2079]], [[2197/2187]], and [[4096/4095]] in the 13-limit.

It [[support]]s the [[bison]] temperament and the [[commatic]] temperament, and provides the [[optimal patent val]] for [[countermiracle]] in the 7- and 11-limit, and countermanna, one of the extensions, in the 13-limit.

176edo tempers the [[64/63|Archytas' comma]] to 1/44th of the octave (4 steps) and as a corollary supports the [[ruthenium]] temperament. It [[support]]s the [[bison]] temperament and the [[commatic]] temperament, and provides the [[optimal patent val]] for [[countermiracle]] in the 7- and 11-limit, and countermanna, one of the extensions, in the 13-limit.

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 176 factors into {{factorization|176}}, 176edo has subset edos {{EDOs| 2, 4, 8, 11, 22, 44, and 88 }}.

== Regular temperament properties ==

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 edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| 41 -20 -4 }} ([[undim comma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 6912/6875, [[8019/8000]], [[9801/9800]] and [[16384/16335]] in the 11-limit. Using the [[patent val]], [[351/350]], [[364/363]], [[2080/2079]], [[2197/2187]], and [[4096/4095]] in the 13-limit.
-It [[support]]s the [[bison]] temperament and the [[commatic]] temperament, and provides the [[optimal patent val]] for [[countermiracle]] in the 7- and 11-limit, and countermanna, one of the extensions, in the 13-limit.
+edo tempers the [[64/63|Archytas' comma]] to 1/44th of the octave (4 steps) and as a corollary supports the [[ruthenium]] temperament. It [[support]]s the [[bison]] temperament and the [[commatic]] temperament, and provides the [[optimal patent val]] for [[countermiracle]] in the 7- and 11-limit, and countermanna, one of the extensions, in the 13-limit.
 === Prime harmonics ===
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
 Since 176 factors into {{factorization|176}}, 176edo has subset edos {{EDOs| 2, 4, 8, 11, 22, 44, and 88 }}.
 == Regular temperament properties ==