346edo: Difference between revisions

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346edo is [[consistent]] to the [[7-odd-limit]], but the errors of [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are all quite large, commending itself as a 2.9.15.21.11 [[subgroup]] temperament. Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[243/242]], [[441/440]], [[540/539]], [[2401/2400]], [[4000/3993]], [[9801/9800]] and [[19683/19600]]. It is ~~an excellent~~ tuning for the 11-limit version of [[harry]], the 72 &~~amp;~~ 274 temperament, as well as the rank-3 temperament [[jove]], which tempers out 243/242 and 441/440.

346edo is [[consistent]] to the [[7-odd-limit]], but the errors of [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are all quite large, commending itself as a 2.9.15.21.11 [[subgroup]] temperament, in which it tempers out [[3025/3024]], [[4375/4374]] and [[5632/5625]], [[support]]ing the 76 & 270 temperament i.e. every other step of [[vishnu]].

Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[243/242]], [[441/440]], [[540/539]], [[2401/2400]], [[4000/3993]], [[9801/9800]] and [[19683/19600]]. It is a possible tuning for the 11-limit version of [[harry]], the 72 & 274 temperament, as well as the rank-3 temperament [[jove]], which tempers out 243/242 and 441/440. The 346e val tempers out [[385/384]] and [[1375/1372]], and provides a possible tuning for [[fibo]], the 103 & 243 temperament.

=== Odd harmonics ===

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=== Subsets and supersets ===

Since 346 factors into {{~~factorization~~|~~346~~}}, 346edo contains [[2edo]] and [[173edo]] as subsets.

Since 346 factors into primes as {{nowrap| 2 × 173 }}, 346edo contains [[2edo]] and [[173edo]] as subsets.

~~[[Category:Nano]]~~

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 {{Infobox ET}}
-{{EDO intro|346}}
+{{ED intro}}
-edo is [[consistent]] to the [[7-odd-limit]], but the errors of [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are all quite large, commending itself as a 2.9.15.21.11 [[subgroup]] temperament. Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[243/242]], [[441/440]], [[540/539]], [[2401/2400]], [[4000/3993]], [[9801/9800]] and [[19683/19600]]. It is an excellent tuning for the 11-limit version of [[harry]], the 72 &amp; 274 temperament, as well as the rank-3 temperament [[jove]], which tempers out 243/242 and 441/440.
+edo is [[consistent]] to the [[7-odd-limit]], but the errors of [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are all quite large, commending itself as a 2.9.15.21.11 [[subgroup]] temperament, in which it tempers out [[3025/3024]], [[4375/4374]] and [[5632/5625]], [[support]]ing the 76 & 270 temperament i.e. every other step of [[vishnu]].
+Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[243/242]], [[441/440]], [[540/539]], [[2401/2400]], [[4000/3993]], [[9801/9800]] and [[19683/19600]]. It is a possible tuning for the 11-limit version of [[harry]], the 72 & 274 temperament, as well as the rank-3 temperament [[jove]], which tempers out 243/242 and 441/440. The 346e val tempers out [[385/384]] and [[1375/1372]], and provides a possible tuning for [[fibo]], the 103 & 243 temperament.
 === Odd harmonics ===
@@ Line 8: / Line 10: @@
 === Subsets and supersets ===
-Since 346 factors into {{factorization|346}}, 346edo contains [[2edo]] and [[173edo]] as subsets.
+Since 346 factors into primes as {{nowrap| 2 × 173 }}, 346edo contains [[2edo]] and [[173edo]] as subsets.
-[[Category:Nano]]