764edo: Difference between revisions
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== Theory == | == Theory == | ||
764edo is a very strong 17-limit system [[ | 764edo is a very strong 17-limit system, [[consistent]] to the [[17-odd-limit]] or the no-19 no-29 [[41-odd-limit]]. It is the fourteenth [[zeta integral edo]]. In the 5-limit it [[tempering out|tempers out]] the hemithirds comma, {{monzo| 38 -2 -15 }}; in the 7-limit [[4375/4374]]; in the 11-limit [[3025/3024]] and [[9801/9800]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; and in the 17-limit [[2431/2430]], [[2500/2499]], [[4914/4913]] and [[5832/5831]]. It provides the [[optimal patent val]] for the [[abigail]] temperament in the 11-limit. | ||
In higher limits, it is a strong no-19 and no-29 37-limit tuning, and an exceptional 2.11.23.31.37 subgroup system, with errors less than 2%. | In higher limits, it is a strong no-19 and no-29 37-limit tuning, and an exceptional 2.11.23.31.37 subgroup system, with errors less than 2%. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|764|columns= | {{Harmonics in equal|764|columns=15}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 764 factors into {{factorization|764}}, 764edo has subset edos 2, 4, 191, and 382. In addition, one step of 764edo is exactly 22 [[jinn]]s ([[16808edo|22\16808]]). | Since 764 factors into {{factorization|764}}, 764edo has subset edos 2, 4, 191, and 382. In addition, one step of 764edo is exactly 22 [[jinn]]s ([[16808edo|22\16808]]). | ||
== Regular temperament properties == | == Regular temperament properties == | ||