User:BudjarnLambeth/Sandbox2: Difference between revisions

Line 11:

; 22edo

* Step size: 54.545{{c}}, octave size: 1200.0{{c}}

Pure-octaves 22edo approximates all harmonics up to 16 within ~~NNN~~{{c}}. The optimal 13-limit [[WE]] tuning has octaves only 0.01{{c}} different from pure-octaves 22edo, and the 13-limit [[TE]] tuning has octaves only 0.08{{c}} different, so by those metrics pure-octaves 22edo might be considered already optimal.

Pure-octaves 22edo approximates all harmonics up to 16 within 22.3{{c}}. The optimal 13-limit [[WE]] tuning has octaves only 0.01{{c}} different from pure-octaves 22edo, and the 13-limit [[TE]] tuning has octaves only 0.08{{c}} different, so by those metrics pure-octaves 22edo might be considered already optimal.

{{Harmonics in equal|22|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 22edo}}

{{Harmonics in equal|22|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 22edo (continued)}}

Line 18:

* Step size: 54.494{{c}}, octave size: NNN{{c}}

Compressing the octave of 22edo by around half a cent results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this.

{{Harmonics in cet|~~100~~|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ~~ETNAME~~, ~~SUBGROUP~~ WE tuning}}

{{Harmonics in cet|54.494|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 22et, 11-limit WE tuning}}

{{Harmonics in cet|~~100~~|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in ~~ETNAME~~, ~~SUBGROUP~~ WE tuning (continued)}}

{{Harmonics in cet|54.494|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 22et, 11-limit WE tuning (continued)}}

; [[zpi|80zpi]]

@@ Line 11: / Line 11: @@
 ; 22edo
 * Step size: 54.545{{c}}, octave size: 1200.0{{c}}
-Pure-octaves 22edo approximates all harmonics up to 16 within NNN{{c}}. The optimal 13-limit [[WE]] tuning has octaves only 0.01{{c}} different from pure-octaves 22edo, and the 13-limit [[TE]] tuning has octaves only 0.08{{c}} different, so by those metrics pure-octaves 22edo might be considered already optimal.
+Pure-octaves 22edo approximates all harmonics up to 16 within 22.3{{c}}. The optimal 13-limit [[WE]] tuning has octaves only 0.01{{c}} different from pure-octaves 22edo, and the 13-limit [[TE]] tuning has octaves only 0.08{{c}} different, so by those metrics pure-octaves 22edo might be considered already optimal.
 {{Harmonics in equal|22|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 22edo}}
 {{Harmonics in equal|22|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 22edo (continued)}}
@@ Line 18: / Line 18: @@
 * Step size: 54.494{{c}}, octave size: NNN{{c}}
 Compressing the octave of 22edo by around half a cent results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this.
-{{Harmonics in cet|100|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
+{{Harmonics in cet|54.494|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 22et, 11-limit WE tuning}}
-{{Harmonics in cet|100|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
+{{Harmonics in cet|54.494|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 22et, 11-limit WE tuning (continued)}}
 ; [[zpi|80zpi]]