User:BudjarnLambeth/Sandbox2: Difference between revisions

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What follows is a comparison of stretched-octave 72edo tunings.

; ~~EDONAME~~

; 72edo

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

* Step size: NNN{{c}}, octave size: 1200.00{{c}}

Pure-octaves ~~EDONAME~~ approximates all harmonics up to 16 within NNN{{c}}.

Pure-octaves 72edo approximates all harmonics up to 16 within NNN{{c}}.

{{Harmonics in equal|72|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}

{{Harmonics in equal|72|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}}

; [[258ed12]]

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

* Step size: NNN{{c}}, octave size: 1200.55{{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 72edo by around NNN{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7, 11 and 13, but an unnoticeably worse prime 2. This approximates all harmonics up to 16 within NNN{{c}}. The tuning EDONOI does this.

{{Harmonics in equal|258|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}

{{Harmonics in equal|258|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

; [[WE|72et, 11-limit WE tuning]]

; [[186ed6]] / [[WE|72et, 11-limit WE tuning]]

* Step size: ~~16.677~~{{c}}, octave size: ~~NNN~~{{c}}

* Step size: NNN{{c}}, octave size: 1200.76{{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 72edo by around NNN{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7, 11 and 13, but an unnoticeably worse prime 2. This approximates all harmonics up to 16 within NNN{{c}}. Its tuning EDONOI does this. 72et's 11-limit WE tuning and 11-limit [[TE]] tuning both do this, their octave differing from 186ed6's by only 0.02{{c}}.

~~{{Harmonics in cet|16.677|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME~~, ~~SUBGROUP WE tuning}}~~

~~{{Harmonics in cet|16.677|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}~~

~~; [[~~186ed6]]

* 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~~.

{{Harmonics in equal|186|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}

{{Harmonics in equal|186|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

; [[zpi|380zpi]]

* Step size: 16.678{{c}}, octave size: ~~NNN~~{{c}}

* Step size: 16.678{{c}}, octave size: 1200.82{{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 72edo by around NNN{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7 and 13, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within NNN{{c}}. The tuning ZPINAME does this.

{{Harmonics in cet|16.678|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}

{{Harmonics in cet|16.678|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}

; [[WE|72et, 13-limit WE tuning]]

* Step size: 16.680{{c}}, octave size: ~~NNN~~{{c}}

* Step size: 16.680{{c}}, octave size: 1200.96{{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 72edo by around NNN{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7 and 13, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within NNN{{c}}. Its SUBGROUP WE tuning and SUBGROUP [[TE]] tuning both do this.

{{Harmonics in cet|16.680|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}

{{Harmonics in cet|16.680|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}

; [[~~144edt~~]]

; [[114edt]]

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

* Step size: NNN{{c}}, octave size: 1201.93{{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 72edo by around NNN{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7 and 13, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within NNN{{c}}. The tuning EDONOI does this.

{{Harmonics in equal|144|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}

{{Harmonics in equal|~~144~~|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

{{Harmonics in equal|114|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

@@ Line 11: / Line 11: @@
 What follows is a comparison of stretched-octave 72edo tunings.
-; EDONAME
+; 72edo
-* Step size: NNN{{c}}, octave size: NNN{{c}}
+* Step size: NNN{{c}}, octave size: 1200.00{{c}}
-Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.
+Pure-octaves 72edo approximates all harmonics up to 16 within NNN{{c}}.
 {{Harmonics in equal|72|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}
 {{Harmonics in equal|72|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}}
 ; [[258ed12]]
-* Step size: NNN{{c}}, octave size: NNN{{c}}
+* Step size: NNN{{c}}, octave size: 1200.55{{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 72edo by around NNN{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7, 11 and 13, but an unnoticeably worse prime 2. This approximates all harmonics up to 16 within NNN{{c}}. The tuning EDONOI does this.
 {{Harmonics in equal|258|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
 {{Harmonics in equal|258|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
-; [[WE|72et, 11-limit WE tuning]]
+; [[186ed6]] / [[WE|72et, 11-limit WE tuning]]
-* Step size: 16.677{{c}}, octave size: NNN{{c}}
+* Step size: NNN{{c}}, octave size: 1200.76{{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 72edo by around NNN{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7, 11 and 13, but an unnoticeably worse prime 2. This approximates all harmonics up to 16 within NNN{{c}}. Its tuning EDONOI does this. 72et's 11-limit WE tuning and 11-limit [[TE]] tuning both do this, their octave differing from 186ed6's by only 0.02{{c}}.
-{{Harmonics in cet|16.677|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
-{{Harmonics in cet|16.677|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
-; [[186ed6]]
-* 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.
 {{Harmonics in equal|186|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
 {{Harmonics in equal|186|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
 ; [[zpi|380zpi]]
-* Step size: 16.678{{c}}, octave size: NNN{{c}}
+* Step size: 16.678{{c}}, octave size: 1200.82{{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 72edo by around NNN{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7 and 13, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within NNN{{c}}. The tuning ZPINAME does this.
 {{Harmonics in cet|16.678|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
 {{Harmonics in cet|16.678|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
 ; [[WE|72et, 13-limit WE tuning]]
-* Step size: 16.680{{c}}, octave size: NNN{{c}}
+* Step size: 16.680{{c}}, octave size: 1200.96{{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 72edo by around NNN{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7 and 13, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within NNN{{c}}. Its SUBGROUP WE tuning and SUBGROUP [[TE]] tuning both do this.
 {{Harmonics in cet|16.680|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
 {{Harmonics in cet|16.680|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
-; [[144edt]]
+; [[114edt]]
-* Step size: NNN{{c}}, octave size: NNN{{c}}
+* Step size: NNN{{c}}, octave size: 1201.93{{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 72edo by around NNN{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7 and 13, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within NNN{{c}}. The tuning EDONOI does this.
 {{Harmonics in equal|144|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
-{{Harmonics in equal|144|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
+{{Harmonics in equal|114|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}