294edo: Difference between revisions

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The 294 equal division divides the octave into 294 parts of 4.082 cents each. It has a very accurate fifth, only 0.086 cents sharp, but it has a 5/4 which is 1.441 cents sharp and a 7/4 which is 1.479 cents flat, so that 7/5 is 2.920 cents flat. In the 5-limit it tempers out 393216/390625, the wuerschmidt comma, and |54 -37 2>, the monzisma. The patent val tempers out 10976/10935, the hemimage comma, and 50421/50000, the trimyna comma, and supplies the [[Optimal_patent_val|optimal patent val]] for [[Trimyna_family|trymyna temperament]] tempering out the trymyna, as well as its 11-limit extension, and also supplies the optimal patent val for the rank four temperament tempering out 3773/3750. The 294d val tempers out 16875/16807 and 19683/19600 instead, supporting [[Mirkwai_clan#Mirkat|mirkat temperament]], whereas 294c tempers out 126/125 and 1029/1024, supporting [[Starling_temperaments#Valentine temperament|valentine temperament]].

294 = 2*3*49, ~~and~~ has ~~divisors~~ 2, 3, 6, 7, 14, 21, 42, 49, 98 and 147.

294edo has a very accurate fifth inherited from [[147edo]], only 0.086{{c}} sharp, but it has a [[5/4]] which is 1.441{{c}} sharp and a [[7/4]] which is 1.479{{c}} flat, so that 7/5 is 2.920{{c}} flat, rendering it in[[consistent]] in the [[7-odd-limit]].

In the 5-limit 294edo [[tempering out|tempers out]] 393216/390625, the [[würschmidt comma]], and {{monzo| 54 -37 2 }}, the [[monzisma]]. The [[patent val]] tempers out 10976/10935, the [[hemimage comma]], and 50421/50000, the [[trimyna comma]], and supplies the [[optimal patent val]] for [[trimyna]] temperament, as well as its 11-limit [[extension]], and also supplies the optimal patent val for the rank-4 temperament tempering out [[3773/3750]]. The 294d val tempers out [[16875/16807]] and [[19683/19600]] instead, supporting [[mirkat]], whereas 294c tempers out [[126/125]] and [[1029/1024]], supporting [[valentine]].

=== Prime harmonics ===

=== Subsets and supersets ===

Since 294 factors into 2 × 3 × 49, 294edo has {{EDOs| 2, 3, 6, 7, 14, 21, 42, 49, 98, and 147 }} as its subsets.

[[Category:Trimyna]]

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-The 294 equal division divides the octave into 294 parts of 4.082 cents each. It has a very accurate fifth, only 0.086 cents sharp, but it has a 5/4 which is 1.441 cents sharp and a 7/4 which is 1.479 cents flat, so that 7/5 is 2.920 cents flat. In the 5-limit it tempers out 393216/390625, the wuerschmidt comma, and |54 -37 2&gt;, the monzisma. The patent val tempers out 10976/10935, the hemimage comma, and 50421/50000, the trimyna comma, and supplies the [[Optimal_patent_val|optimal patent val]] for [[Trimyna_family|trymyna temperament]] tempering out the trymyna, as well as its 11-limit extension, and also supplies the optimal patent val for the rank four temperament tempering out 3773/3750. The 294d val tempers out 16875/16807 and 19683/19600 instead, supporting [[Mirkwai_clan#Mirkat|mirkat temperament]], whereas 294c tempers out 126/125 and 1029/1024, supporting [[Starling_temperaments#Valentine temperament|valentine temperament]].
+{{Infobox ET}}
+{{ED intro}}
-= 2*3*49, and has divisors 2, 3, 6, 7, 14, 21, 42, 49, 98 and 147.
+edo has a very accurate fifth inherited from [[147edo]], only 0.086{{c}} sharp, but it has a [[5/4]] which is 1.441{{c}} sharp and a [[7/4]] which is 1.479{{c}} flat, so that 7/5 is 2.920{{c}} flat, rendering it in[[consistent]] in the [[7-odd-limit]].
+In the 5-limit 294edo [[tempering out|tempers out]] 393216/390625, the [[würschmidt comma]], and {{monzo| 54 -37 2 }}, the [[monzisma]]. The [[patent val]] tempers out 10976/10935, the [[hemimage comma]], and 50421/50000, the [[trimyna comma]], and supplies the [[optimal patent val]] for [[trimyna]] temperament, as well as its 11-limit [[extension]], and also supplies the optimal patent val for the rank-4 temperament tempering out [[3773/3750]]. The 294d val tempers out [[16875/16807]] and [[19683/19600]] instead, supporting [[mirkat]], whereas 294c tempers out [[126/125]] and [[1029/1024]], supporting [[valentine]].
+=== Prime harmonics ===
+{{Harmonics in equal|294}}
+=== Subsets and supersets ===
+Since 294 factors into 2 × 3 × 49, 294edo has {{EDOs| 2, 3, 6, 7, 14, 21, 42, 49, 98, and 147 }} as its subsets.
+[[Category:Trimyna]]