65edt: Difference between revisions
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== Theory == | == Theory == | ||
65edt is almost identical to [[41edo]], but with the | 65edt is almost identical to [[41edo]], but with the perfect twelfth rather than the [[2/1|octave]] being just. The octave is about 0.305 cents compressed. Like 41edo, 65edt is [[consistent]] to the [[integer limit|16-integer-limit]], and in comparison, it improves the intonation of primes 3, [[11/1|11]], [[13/1|13]], and [[17/1|17]] at the expense of less accurate intonations of 2, [[5/1|5]], [[7/1|7]], and [[19/1|19]], commending itself as a suitable tuning for [[13-limit|13-]] and [[17-limit]]-focused harmonies. | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|65|3|1|intervals=integer}} | {{Harmonics in equal|65|3|1|intervals=integer}} | ||
{{Harmonics in equal|65|3|1|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 65edt (continued)}} | {{Harmonics in equal|65|3|1|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 65edt (continued)}} | ||
=== Subsets and supersets === | |||
Since 65 factors into primes as {{nowrap| 5 × 13 }}, 65edt contains [[5edt]] and [[13edt]] as subset edts. | |||
== Intervals == | == Intervals == | ||
| Line 220: | Line 223: | ||
| 1170.4 | | 1170.4 | ||
| 800.0 | | 800.0 | ||
| [[55/28]], [[63/32]] | | [[49/25]], [[55/28]], [[63/32]] | ||
|- | |- | ||
| 41 | | 41 | ||
| Line 230: | Line 233: | ||
| 1229.0 | | 1229.0 | ||
| 840.0 | | 840.0 | ||
| [[49/24]], [[81/40]] | | [[45/22]], [[49/24]], [[55/27]], [[81/40]] | ||
|- | |- | ||
| 43 | | 43 | ||
| Line 340: | Line 343: | ||
| 1872.7 | | 1872.7 | ||
| 1280.0 | | 1280.0 | ||
| [[ | | [[44/15]] | ||
|- | |- | ||
| 65 | | 65 | ||
| Line 347: | Line 350: | ||
| [[3/1]] | | [[3/1]] | ||
|} | |} | ||
== See also == | |||
* [[24edf]] – relative edf | |||
* [[41edo]] – relative edo | |||
* [[95ed5]] – relative ed5 | |||
* [[106ed6]] – relative ed6 | |||
* [[147ed12]] – relative ed12 | |||
* [[361ed448]] – close to the zeta-optimized tuning for 41edo | |||
[[Category:41edo]] | |||