69edf: Difference between revisions

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== Theory ==

69edf is closely related to [[118edo]], but with the [[3/2|perfect fifth]] rather than the [[~~2/1|~~octave]] being just. The octave is [[stretched and compressed tuning|stretched]] by about 0.445 cents. Like 118edo, 69edf is [[consistent]] to the [[integer limit|12-integer-limit]]. While the 5-limit [[microtemperament|microtempering]] quality of 118edo is sort of compromised here due to the [[prime harmonic|prime]] [[5/1|5]] being sharp by more than a cent, the approximated [[prime harmonic]]s [[7/1|7]], [[11/1|11]], [[17/1|17]], and [[19/1|19]] are much improved, as befits the purpose of no-13 19-limit harmony.

69edf is closely related to [[118edo]], but with the [[3/2|perfect fifth]] rather than the [[octave]] being just. The octave is [[stretched and compressed tuning|stretched]] by about 0.445 cents. Like 118edo, 69edf is [[consistent]] to the [[integer limit|12-integer-limit]]. While the 5-limit [[microtemperament|microtempering]] quality of 118edo is sort of compromised here due to the [[prime harmonic|prime]] [[5/1|5]] being sharp by more than a cent, the approximated [[prime harmonic]]s [[7/1|7]], [[11/1|11]], [[17/1|17]], and [[19/1|19]] are much improved, as befits the purpose of no-13 19-limit harmony.

=== Harmonics ===

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 == Theory ==
-edf is closely related to [[118edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is [[stretched and compressed tuning|stretched]] by about 0.445 cents. Like 118edo, 69edf is [[consistent]] to the [[integer limit|12-integer-limit]]. While the 5-limit [[microtemperament|microtempering]] quality of 118edo is sort of compromised here due to the [[prime harmonic|prime]] [[5/1|5]] being sharp by more than a cent, the approximated [[prime harmonic]]s [[7/1|7]], [[11/1|11]], [[17/1|17]], and [[19/1|19]] are much improved, as befits the purpose of no-13 19-limit harmony.
+edf is closely related to [[118edo]], but with the [[3/2|perfect fifth]] rather than the [[octave]] being just. The octave is [[stretched and compressed tuning|stretched]] by about 0.445 cents. Like 118edo, 69edf is [[consistent]] to the [[integer limit|12-integer-limit]]. While the 5-limit [[microtemperament|microtempering]] quality of 118edo is sort of compromised here due to the [[prime harmonic|prime]] [[5/1|5]] being sharp by more than a cent, the approximated [[prime harmonic]]s [[7/1|7]], [[11/1|11]], [[17/1|17]], and [[19/1|19]] are much improved, as befits the purpose of no-13 19-limit harmony.
 === Harmonics ===