Xenharmonic Wiki

User:BudjarnLambeth/Sandbox2: Difference between revisions

← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,282 edits
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,282 edits
Line 5: Line 5:
= Title1 =
= Title1 =
== Octave stretch or compression ==
== Octave stretch or compression ==
What follows is a comparison of stretched- and compressed-octave EDONAME tunings.
What follows is a comparison of stretched- and compressed-octave 54edo tunings.


; [[zpi|ZPINAME]]  
; [[ed6|139ed6]]  
* 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.
Stretching the octave of 54edo 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 139ed6 does this. So does the tuning 262zpi whose octave is identical to 139ed6 within 0.2{{c}}.
{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in equal|139|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 139ed6}}
{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
{{Harmonics in equal|139|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 139ed6 (continued)}}


; [[EDONOI]]  
; [[ed7|151ed7]]
* 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.
Stretching the octave of 54edo 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 151ed7 does this.
{{Harmonics in equal|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|151|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 151ed7}}
{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
{{Harmonics in equal|151|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 151ed7 (continued)}}


; [[WE|ETNAME, SUBGROUP WE tuning]]  
; [[ed12|193ed12]]
* 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.
Stretching the octave of 54edo 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 193ed12 does this.
{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
{{Harmonics in equal|193|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 193ed12}}
{{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|193|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 193ed12 (continued)}}


; EDONAME
; [[zpi|263zpi]]
* Step size: NNN{{c}}, octave size: NNN{{c}}  
* Step size: 22.243{{c}}, octave size: NNN{{c}}
Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.
Stretching the octave of 54edo 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 263zpi does this.
{{Harmonics in equal|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}
{{Harmonics in cet|22.243|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 263zpi}}
{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}}
{{Harmonics in cet|22.243|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 263zpi (continued)}}


; [[WE|ETNAME, SUBGROUP WE tuning]]  
; 54edo
* Step size: 22.222{{c}}, octave size: NNN{{c}}
Pure-octaves 54edo approximates all harmonics up to 16 within NNN{{c}}.
{{Harmonics in equal|54|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 54edo}}
{{Harmonics in equal|54|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 54edo (continued)}}
 
; [[WE|54et, 13-limit WE tuning]]
* Step size: 22.198{{c}}, octave size: NNN{{c}}
Compressing the octave of 54edo 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. So does the tuning [[equal tuning|187ed11]] whose octave is identical to 13lim WE within 0.1{{c}}.
{{Harmonics in cet|22.198|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 54et, 13-limit WE tuning}}
{{Harmonics in cet|22.198|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 54et, 13-limit WE tuning (continued)}}
 
; [[zpi|264zpi]]
* Step size: 22.175{{c}}, octave size: NNN{{c}}
Compressing the octave of 54edo 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 264zpi does this. So does the tuning 194ed12 whose octave is identical to 264zpi within 0.01{{c}}.
{{Harmonics in cet|22.175|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 264zpi}}
{{Harmonics in cet|22.175|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 264zpi (continued)}}
 
; [[ed7|152ed7]]  
* 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.
Compressing the octave of 54edo 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 152ed7 does this.
{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
{{Harmonics in equal|152|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 152ed7}}
{{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|152|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 152ed7 (continued)}}


; [[EDONOI]]  
; [[ed6|140ed6]]  
* 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.
Compressing the octave of 54edo 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 140ed6 does this.
{{Harmonics in equal|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|140|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 140ed6}}
{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
{{Harmonics in equal|140|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 140ed6 (continued)}}


; [[zpi|ZPINAME]]  
; [[ed5|126ed5]]  
* 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.
Compressing the octave of 54edo 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 126ed5 does this. So does the tuning [[86edt]] whose octave is identical to 126ed5 within 0.1{{c}}.
{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in equal|126|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 126ed5}}
{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
{{Harmonics in equal|126|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 126ed5 (continued)}}


= Title2 =
= Title2 =
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/Sandbox2"