294edo: Difference between revisions

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294edo 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.

294edo has a very accurate fifth inherited from [[147edo]], 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, rendering it in[[consistent]] in the [[7-odd-limit]].

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]] 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~~]].

In the 5-limit the equal temperament [[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]].

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

=== Prime harmonics ===

=== Subsets and supersets ===

[[Category:~~Equal divisions of the octave|###~~]] ~~~~

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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 {{EDO intro|294}}
-edo 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.
+edo has a very accurate fifth inherited from [[147edo]], 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, rendering it in[[consistent]] in the [[7-odd-limit]].
-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]] 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]].
+In the 5-limit the equal temperament [[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]].
-= 2*3*49, and has divisors 2, 3, 6, 7, 14, 21, 42, 49, 98 and 147.
+=== Prime harmonics ===
+{{Harmonics in equal|294}}
-{{Harmonics in equal|294}}
+=== Subsets and supersets ===
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+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]]