391edo: Difference between revisions

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The ~~'''391~~ equal ~~division''' divides the octave into 391 equal parts of 3.069 cents each. It~~ tempers out 5120/5103 ~~and~~ 420175/419904 in the 7-limit, and provides the [[~~Optimal_patent_val|~~optimal patent val]] for the hemifamity ~~planar~~ temperament and [[~~Hemifamity_temperaments#Septiquarter|~~septiquarter]], the 5&94 temperament. It tempers out ~~6250~~/~~6237~~, 4000/3993, 5632/5625 and ~~3025~~/~~3024~~ 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 [[~~Hemifamity_temperaments#Alphaquarter|~~alphaquarter]]. The 391bcde val provides a tuning for 11-limit miracle very close to the POTE tuning.

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]].

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

=== Odd harmonics ===

=== Subsets and supersets ===

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

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

[[Category:Hemifamity]]

[[Category:Septiquarter]]

[[Category:Alphaquarter]]

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-The '''391 equal division''' divides the octave into 391 equal parts of 3.069 cents each. It tempers out 5120/5103 and 420175/419904 in the 7-limit, and provides the [[Optimal_patent_val|optimal patent val]] for the hemifamity planar temperament and [[Hemifamity_temperaments#Septiquarter|septiquarter]], the 5&amp;94 temperament. It tempers out 6250/6237, 4000/3993, 5632/5625 and 3025/3024 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 [[Hemifamity_temperaments#Alphaquarter|alphaquarter]]. The 391bcde val provides a tuning for 11-limit miracle very close to the POTE tuning.
+{{Infobox ET}}
+{{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]].
+The 391bcde [[val]] provides a tuning for 11-limit miracle very close to the POTE tuning.
+=== Odd harmonics ===
+{{Harmonics in equal|391}}
+=== Subsets and supersets ===
+Since 391 factors into {{factorization|391}}, 391edo contains [[17edo]] and [[23edo]] as subsets.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Hemifamity]]
+[[Category:Septiquarter]]
+[[Category:Alphaquarter]]