639edo: Difference between revisions

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== Theory ==

639edo is [[consistency|distinctly consistent]] in the [[17-odd-limit]]. It has a sharp tendency, with [[harmonic]]s of 3 to 17 all tuned sharp. The 639h [[val]] gives a reasonable approximation of [[19/1|harmonic 19]], where it [[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 ~~supports~~ 11-limit [[ennealimmal]] and its 13-limit extension ennealimmalis.

639edo is [[consistency|distinctly consistent]] in the [[17-odd-limit]]. It has a sharp tendency, with [[harmonic]]s of 3 to 17 all tuned sharp. The 639h [[val]] gives a reasonable approximation of [[19/1|harmonic 19]], where it [[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 11-limit [[ennealimmal]] and its 13-limit extension ennealimmalis.

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 639 = ~~3<sup>2</sup> × 71~~, it has subset edos {{EDOs| 3, 9, 71, and 213 }}.

Since 639 = {{factorization|639}}, it has subset edos {{EDOs| 3, 9, 71, and 213 }}.

== Regular temperament properties ==

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 == Theory ==
-edo is [[consistency|distinctly consistent]] in the [[17-odd-limit]]. It has a sharp tendency, with [[harmonic]]s of 3 to 17 all tuned sharp. The 639h [[val]] gives a reasonable approximation of [[19/1|harmonic 19]], where it [[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 supports 11-limit [[ennealimmal]] and its 13-limit extension ennealimmalis.
+edo is [[consistency|distinctly consistent]] in the [[17-odd-limit]]. It has a sharp tendency, with [[harmonic]]s of 3 to 17 all tuned sharp. The 639h [[val]] gives a reasonable approximation of [[19/1|harmonic 19]], where it [[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 11-limit [[ennealimmal]] and its 13-limit extension ennealimmalis.
 === Prime harmonics ===
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 === Subsets and supersets ===
-Since 639 = 3<sup>2</sup> × 71, it has subset edos {{EDOs| 3, 9, 71, and 213 }}.
+Since 639 = {{factorization|639}}, it has subset edos {{EDOs| 3, 9, 71, and 213 }}.
 == Regular temperament properties ==