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= Title1 =
= Title1 =
== Octave stretch or compression ==
== Octave stretch or compression ==
What follows is a comparison of stretched- and compressed-octave EDONAME tunings.
 
; [[ed6|152ed6]]
* Octave size: NNN{{c}}
_ing the octave of 59edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 152ed6 does this.
{{Harmonics in equal|152|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 152ed6}}
{{Harmonics in equal|152|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 152ed6 (continued)}}
 
; [[zpi|294zpi]]
* Step size: 20.399{{c}}, octave size: NNN{{c}}
_ing the octave of 59edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 294zpi does this.
{{Harmonics in cet|20.399|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 294zpi}}
{{Harmonics in cet|20.399|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 294zpi (continued)}}
 
; [[211ed12]]
* Step size: NNN{{c}}, octave size: NNN{{c}}
_ing the octave of 59edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 211ed12 does this.
{{Harmonics in equal|211|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 211ed12}}
{{Harmonics in equal|211|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 211ed12 (continued)}}


; [[zpi|ZPINAME]]  
; [[zpi|ZPINAME]]  
* Step size: NNN{{c}}, octave size: NNN{{c}}
* Step size: 20.342{{c}}, octave size: NNN{{c}}
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning ZPINAME does this.
_ing the octave of 59edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 295zpi does this.
{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in cet|20.342|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 295zpi}}
{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
{{Harmonics in cet|20.342|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 295zpi (continued)}}


; [[EDONOI]]
; 59edo
* Step size: NNN{{c}}, octave size: NNN{{c}}
* Step size: 20.339{{c}}, octave size: 1200.00{{c}}  
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning EDONOI does this.
Pure-octaves 59edo approximates all harmonics up to 16 within NNN{{c}}. So does the tuning [[ed|137ed5]] whose octave is identical within 0.05{{c}}.
{{Harmonics in equal|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|59|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 59edo}}
{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
{{Harmonics in equal|59|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 59edo (continued)}}


; [[WE|ETNAME, SUBGROUP WE tuning]]  
; [[WE|59et, 13-limit WE tuning]]  
* Step size: NNN{{c}}, octave size: NNN{{c}}
* Step size: 20.320{{c}}, octave size: NNN{{c}}
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its SUBGROUP WE tuning and SUBGROUP [[TE]] tuning both do this.
_ing the octave of 59edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
{{Harmonics in cet|20.320|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 59et, 13-limit WE tuning}}
{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
{{Harmonics in cet|20.320|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 59et, 13-limit WE tuning (continued)}}


; EDONAME
; [[WE|59et, 7-limit WE tuning]]
* Step size: NNN{{c}}, octave size: NNN{{c}}  
* Step size: 20.301{{c}}, octave size: NNN{{c}}
Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.
_ing the octave of 59edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this.
{{Harmonics in equal|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}
{{Harmonics in cet|20.301|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, 59et, 7-limit WE tuning}}
{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}}
{{Harmonics in cet|20.301|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 59et, 7-limit WE tuning (continued)}}


; [[WE|ETNAME, SUBGROUP WE tuning]]  
; [[166ed7]]  
* Step size: NNN{{c}}, octave size: NNN{{c}}
* Step size: NNN{{c}}, octave size: NNN{{c}}
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its SUBGROUP WE tuning and SUBGROUP [[TE]] tuning both do this.
_ing the octave of 59edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 166ed7 does this.
{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
{{Harmonics in equal|166|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 166ed7}}
{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
{{Harmonics in equal|166|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 166ed7 (continued)}}


; [[EDONOI]]  
; [[212ed12]]  
* Step size: NNN{{c}}, octave size: NNN{{c}}
* Step size: NNN{{c}}, octave size: NNN{{c}}
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning EDONOI does this.
_ing the octave of 59edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 212ed12 does this.
{{Harmonics in equal|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|212|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 212ed12}}
{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
{{Harmonics in equal|212|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 212ed12 (continued)}}
 
; [[zpi|296zpi]]
* Step size: 20.282{{c}}, octave size: NNN{{c}}
_ing the octave of 59edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 296zpi does this.
{{Harmonics in cet|20.282|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 296zpi}}
{{Harmonics in cet|20.282|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 296zpi (continued)}}


; [[zpi|ZPINAME]]  
; [[153ed6]]  
* Step size: NNN{{c}}, octave size: NNN{{c}}
* Step size: NNN{{c}}, octave size: NNN{{c}}
_ing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning ZPINAME does this.
_ing the octave of 59edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 153ed6 does this.
{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in equal|153|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 153ed6}}
{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
{{Harmonics in equal|153|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 153ed6 (continued)}}


= Title2 =
= Title2 =
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