72ed5: Difference between revisions
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== Theory == | == Theory == | ||
72ed5 is related to [[31edo]], but with the 5/1 rather than the [[2/1]] being just. The octave is slightly compressed (about 0.3372 cents). | 72ed5 is related to [[31edo]], but with the 5/1 rather than the [[2/1]] being just. The octave is slightly compressed (about 0.3372 cents). Like 31edo, 72ed5 is [[consistent]] through the [[integer limit|12-integer-limit]], but it has a flat tendency, with [[prime harmonic]]s 2, [[3/1|3]], [[7/1|7]], and [[11/1|11]] all tuned flat. It [[support]]s [[meantone]] as the number of divisions of the 5th harmonic is multiple of 4. | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|72|5|1|intervals=integer|columns=11}} | {{Harmonics in equal|72|5|1|intervals=integer|columns=11}} | ||
{{Harmonics in equal|72|5|1|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 72ed5 (continued)}} | {{Harmonics in equal|72|5|1|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 72ed5 (continued)}} | ||
=== Subsets and supersets === | |||
72 is a [[largely composite]] number. Since it factors into primes as {{nowrap| 2<sup>3</sup> × 3<sup>2</sup> }}, 72ed5 has subset ed5's {{EDs|equave=5| 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36 }}. | |||
== Intervals == | == Intervals == | ||
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* [[80ed6]] – relative ed6 | * [[80ed6]] – relative ed6 | ||
* [[87ed7]] – relative ed7 | * [[87ed7]] – relative ed7 | ||
* [[107ed11]] – relative ed11 | |||
* [[111ed12]] – relative ed12 | * [[111ed12]] – relative ed12 | ||
* [[138ed22]] – relative ed22 | |||
* [[204ed96]] – close to the zeta-optimized tuning for 31edo | |||
* [[39cET]] | * [[39cET]] | ||
[[Category:31edo]] | |||