369edo: Difference between revisions

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== Theory ==

369 = 9 × 41, and it shares the fifth with [[41edo]]. It has a sharp tendency, with [[harmonic]]s 3 through 11 all tuned sharp. It tempers out [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it ~~supports~~ the [[ennealimmal]] temperament; in the 11-limit, [[4000/3993]], [[5632/5625]] and [[16384/16335]]. It provides the [[optimal patent val]] for the 11-limit 130&239 temperament, the 65&152 temperament, and the rank-4 temperament tempering out 16384/16335, the semiporwellisma, as well as the no-7 subgroup version of it.

369 = 9 × 41, and it shares the fifth with [[41edo]]. It has a sharp tendency, with [[harmonic]]s 3 through 11 all tuned sharp. It tempers out [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament; in the 11-limit, [[4000/3993]], [[5632/5625]] and [[16384/16335]]. It provides the [[optimal patent val]] for the 11-limit 130&239 temperament, the 65&152 temperament, and the rank-4 temperament tempering out 16384/16335, the semiporwellisma, as well as the no-7 subgroup version of it.

Extension to the 13-limit is viable by the 369f val, tempering out [[1575/1573]], [[2080/2079]], [[2200/2197]], and 3584/3575. The optimal tuning of this temperament is consistent in the 15-integer-limit.

@@ Line 9: / Line 9: @@
 == Theory ==
-= 9 × 41, and it shares the fifth with [[41edo]]. It has a sharp tendency, with [[harmonic]]s 3 through 11 all tuned sharp. It tempers out [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it supports the [[ennealimmal]] temperament; in the 11-limit, [[4000/3993]], [[5632/5625]] and [[16384/16335]]. It provides the [[optimal patent val]] for the 11-limit 130&amp;239 temperament, the 65&amp;152 temperament, and the rank-4 temperament tempering out 16384/16335, the semiporwellisma, as well as the no-7 subgroup version of it.
+= 9 × 41, and it shares the fifth with [[41edo]]. It has a sharp tendency, with [[harmonic]]s 3 through 11 all tuned sharp. It tempers out [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament; in the 11-limit, [[4000/3993]], [[5632/5625]] and [[16384/16335]]. It provides the [[optimal patent val]] for the 11-limit 130&amp;239 temperament, the 65&amp;152 temperament, and the rank-4 temperament tempering out 16384/16335, the semiporwellisma, as well as the no-7 subgroup version of it.
 Extension to the 13-limit is viable by the 369f val, tempering out [[1575/1573]], [[2080/2079]], [[2200/2197]], and 3584/3575. The optimal tuning of this temperament is consistent in the 15-integer-limit.