72edo: Difference between revisions
→Intervals: +19/13 and 26/19 |
→Theory: +octave stretch |
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{{Harmonics in equal|72|columns=9}} | {{Harmonics in equal|72|columns=9}} | ||
{{Harmonics in equal|72|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 72edo (continued)}} | {{Harmonics in equal|72|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 72edo (continued)}} | ||
=== Octave stretch === | |||
72edo's approximations of harmonics 3, 5, 7, 11, 13 and 17 can all be improved by slightly [[stretched and compressed tuning|stretching the octave]], using tunings such as [[114edt]] or [[186ed6]]. 114edt is quite hard and might be best for the 13- or 17-limit specifically. 186ed6 is milder and less disruptive, suitable for 11-limit and/or full 19-limit harmonies. | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 72 factors into 2<sup>3</sup> × 3<sup>2</sup>, 72edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36 }}. [[144edo]], which doubles it, provides a possible correction to its approximate harmonic 13. | Since 72 factors into primes as {{nowrap| 2<sup>3</sup> × 3<sup>2</sup> }}, 72edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36 }}. [[144edo]], which doubles it, provides a possible correction to its approximate harmonic 13. | ||
== Intervals == | == Intervals == | ||