639edo: Difference between revisions
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== Theory == | == Theory == | ||
639edo is [[consistency|distinctly consistent]] in the [[17-odd-limit]]. It has a sharp tendency, with [[harmonic]]s | 639edo is [[consistency|distinctly consistent]] in the [[17-odd-limit]]. It has a sharp tendency, with [[harmonic]]s 3 to 17 all tuned sharp. The 639h [[val]] gives a reasonable approximation of [[19/1|harmonic 19]], in which the edo is almost consistent up to the [[25-odd-limit]], with the exception of [[19/16]] and [[25/16]] themselves and their [[octave complement]]s. | ||
Using this val, the equal temperament [[tempering out|tempers out]] {{monzo| 1 27 -18 }} ([[ennealimma]]) and {{monzo| 55 -1 -23 }} ([[counterwürschmidt comma]]) in the 5-limit; [[2401/2400]] and [[4375/4374]] in the 7-limit; [[5632/5625]] and [[19712/19683]] in the 11-limit; [[2080/2079]] and [[4459/4455]] in the 13-limit; [[1156/1155]], [[2058/2057]], and [[2601/2600]] in the 17-limit; [[1216/1215]], [[1445/1444]], [[1540/1539]], [[2376/2375]], and [[2926/2925]] in the 19-limit. It [[support]]s [[ennealimmal]] and its 13-limit extension enneabiotic. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 639 | Since 639 factors into primes as {{nowrap| 3<sup>2</sup> × 71 }}, 639edo has subset edos {{EDOs| 3, 9, 71, and 213 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||