391edo: Difference between revisions

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391edo has a sharp tendency, with [[prime harmonic]]s 3 to 13 all tuned sharp. The equal temperament [[tempering out|tempers out]] [[5120/5103]], 420175/419904, and 29360128/29296875 in the 7-limit, and provides the [[optimal patent val]] for the [[hemifamity]] temperament, and [[septiquarter]], the {{nowrap|99 & 292}} temperament. It tempers out [[3025/3024]], [[4000/3993]], [[5632/5625]], and [[6250/6237]] in the 11-limit; and [[676/675]], [[1716/1715]] and [[4225/4224]] in the 13-limit, and provides further optimal patent vals for temperaments tempering out 5120/5103 such as [[alphaquarter]].

391edo has a sharp tendency, with [[prime harmonic]]s 3 to 13 all tuned sharp.

The 391bcde [[val]] provides a tuning for 11-limit miracle very close to the POTE tuning.

As an equal temperament, it [[tempering out|tempers out]] [[5120/5103]], [[420175/419904]], and [[29360128/29296875]] in the [[7-limit]], and provides the [[optimal patent val]] for the [[aberschismic]] temperament, and [[septiquarter]], the {{nowrap| 99 & 292 }} temperament. It tempers out [[3025/3024]], [[4000/3993]], [[5632/5625]], and [[6250/6237]] in the [[11-limit]]; and [[676/675]], [[1716/1715]] and [[4225/4224]] in the [[13-limit]], and provides further optimal patent vals for temperaments tempering out 5120/5103 such as [[alphaquarter]].

The 391bcde [[val]] provides a tuning for 11-limit miracle very close to the [[POTE tuning]].

=== Odd harmonics ===

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=== Subsets and supersets ===

Since 391 factors into {{~~factorization~~|~~391~~}}, 391edo contains [[17edo]] and [[23edo]] as subsets.

Since 391 factors into primes as {{nowrap| 17 × 23}}, 391edo contains [[17edo]] and [[23edo]] as subsets.

[[Category:Aberschismic]]

[[Category:Septiquarter]]

[[Category:Alphaquarter]]

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 {{ED intro}}
-edo has a sharp tendency, with [[prime harmonic]]s 3 to 13 all tuned sharp. The equal temperament [[tempering out|tempers out]] [[5120/5103]], 420175/419904, and 29360128/29296875 in the 7-limit, and provides the [[optimal patent val]] for the [[hemifamity]] temperament, and [[septiquarter]], the {{nowrap|99 &amp; 292}} temperament. It tempers out [[3025/3024]], [[4000/3993]], [[5632/5625]], and [[6250/6237]] in the 11-limit; and [[676/675]], [[1716/1715]] and [[4225/4224]] in the 13-limit, and provides further optimal patent vals for temperaments tempering out 5120/5103 such as [[alphaquarter]].
+edo has a sharp tendency, with [[prime harmonic]]s 3 to 13 all tuned sharp.
-The 391bcde [[val]] provides a tuning for 11-limit miracle very close to the POTE tuning.
+As an equal temperament, it [[tempering out|tempers out]] [[5120/5103]], [[420175/419904]], and [[29360128/29296875]] in the [[7-limit]], and provides the [[optimal patent val]] for the [[aberschismic]] temperament, and [[septiquarter]], the {{nowrap| 99 & 292 }} temperament. It tempers out [[3025/3024]], [[4000/3993]], [[5632/5625]], and [[6250/6237]] in the [[11-limit]]; and [[676/675]], [[1716/1715]] and [[4225/4224]] in the [[13-limit]], and provides further optimal patent vals for temperaments tempering out 5120/5103 such as [[alphaquarter]].
+The 391bcde [[val]] provides a tuning for 11-limit miracle very close to the [[POTE tuning]].
 === Odd harmonics ===
@@ Line 10: / Line 12: @@
 === Subsets and supersets ===
-Since 391 factors into {{factorization|391}}, 391edo contains [[17edo]] and [[23edo]] as subsets.
+Since 391 factors into primes as {{nowrap| 17 × 23}}, 391edo contains [[17edo]] and [[23edo]] as subsets.
 [[Category:Aberschismic]]
 [[Category:Septiquarter]]
 [[Category:Alphaquarter]]