FloraC: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 69edf is closely related to 118edo, but with the perfect fifth rather than the octave being just. The octave is stretched by about 0.445 cents. Like 118edo, 69edf is consistent to the 12-integer-limit. While the 5-limit microtempering quality of 118edo is sort of compromised here due to the prime 5 being s..."

2025-04-15T11:24:34Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 69edf is closely related to 118edo, but with the perfect fifth rather than the octave being just. The octave is stretched by about 0.445 cents. Like 118edo, 69edf is consistent to the 12-integer-limit. While the 5-limit microtempering quality of 118edo is sort of compromised here due to the prime 5 being s..."

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{{Infobox ET}}
{{ED intro}}

== 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.

=== Harmonics ===
{{Harmonics in equal|69|3|2|intervals=integer|columns=11}}
{{Harmonics in equal|69|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 69edf (continued)}}

=== Subsets and supersets ===
Since 69 factors into primes as {{nowrap| 3 × 23 }}, 69edf contains [[3edf]] and [[23edf]] as subset edfs.

== See also ==
* [[118edo]] – relative edo
* [[187edt]] – relative edt

69edf - Revision history