91edo: Difference between revisions
→Theory: a member of the optimal GPV sequence and not optimal patent val |
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The [[concoctic scale]] for 91edo is 27 steps, where two concoctic neutral thirds make a sharp 91b val fifth of 54\91. From a regular temperament theory perspective, there is more than one way to interpret this, as they're all harmonically not very precise. First, in the 13-limit, is to assume that 27\91 is directly equivalent to 16/13 and set a temperament in the 2.3.5.7.16/13 subgroup, which produces a 27 & 91b temperament with the comma basis 91/90, 6272/6075, {{Monzo|84 13 11 -10}}. Second is to directly take the 27 & 91b val in the 13-limit, which can also be taken using the 27e & 91b. | The [[concoctic scale]] for 91edo is 27 steps, where two concoctic neutral thirds make a sharp 91b val fifth of 54\91. From a regular temperament theory perspective, there is more than one way to interpret this, as they're all harmonically not very precise. First, in the 13-limit, is to assume that 27\91 is directly equivalent to 16/13 and set a temperament in the 2.3.5.7.16/13 subgroup, which produces a 27 & 91b temperament with the comma basis 91/90, 6272/6075, {{Monzo|84 13 11 -10}}. Second is to directly take the 27 & 91b val in the 13-limit, which can also be taken using the 27e & 91b. | ||
In the 13-limit, 91edo | In the 13-limit, 91edo is an [[Optimal GPV sequence|optimal GPV tuning]] for [[vidar]] temperament coming after [[87edo|87d]] val and before [[133edo|133d]] val, although it is no longer consistent in the 11-odd-limit. | ||
=== Odd harmonics === | === Odd harmonics === | ||