User:BudjarnLambeth/Sandbox2: Difference between revisions

Line 12:

; [[zpi|288zpi]]

* Step size: 20.736{{c}}, octave size: ~~NNN~~{{c}}

* Step size: 20.736{{c}}, octave size: 1202.69{{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 58edo by around 2.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 288zpi does this.

{{Harmonics in cet|20.736|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~ZPINAME~~}}

{{Harmonics in cet|20.736|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 288zpi}}

{{Harmonics in cet|20.736|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~ZPINAME~~ (continued)}}

{{Harmonics in cet|20.736|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 288zpi (continued)}}

; 58edo

* Step size: 20.690{{c}}, octave size: ~~NNN~~{{c}}

* Step size: 20.690{{c}}, octave size: 1200.00{{c}}

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

Pure-octaves 58edo approximates all harmonics up to 16 within NNN{{c}}.

{{Harmonics in equal|58|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~EDONAME~~}}

{{Harmonics in equal|58|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 58edo}}

{{Harmonics in equal|58|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~EDONAME~~ (continued)}}

{{Harmonics in equal|58|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 58edo (continued)}}

; [[150ed6]]

* Step size: ~~NNN~~{{c}}, octave size: 1199.42{{c}}

* Step size: 20.680{{c}}, octave size: 1199.42{{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 58edo by around half a cent results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 150ed6 does this.

{{Harmonics in equal|150|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~EDONOI~~}}

{{Harmonics in equal|150|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 150ed6}}

{{Harmonics in equal|150|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~EDONOI~~ (continued)}}

{{Harmonics in equal|150|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 150ed6 (continued)}}

; [[92edt]]

* Step size: ~~NNN~~{{c}}, octave size: 1199.06{{c}}

* Step size: 20.673{{c}}, octave size: 1199.06{{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 58edo by around 1{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 92edt does this.

{{Harmonics in equal|92|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~EDONOI~~}}

{{Harmonics in equal|92|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 92edt}}

{{Harmonics in equal|92|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~EDONOI~~ (continued)}}

{{Harmonics in equal|92|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 92edt (continued)}}

; [[zpi|289zpi]] / [[WE|58et, 7-limit WE tuning]]

* Step size: 20.666{{c}}, octave size: 1198.63{{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 7-limit WE tuning and 7-limit [[TE]] tuning both do this. The tuning 289zpi also does this, ~~it's~~ octave differing from 7-limit WE by only 0.06{{c}}.

Compressing the octave of 58edo by just under 1.5{{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. The tuning 289zpi also does this, its octave differing from 7-limit WE by only 0.06{{c}}.

{{Harmonics in cet|20.666|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~ZPINAME~~}}

{{Harmonics in cet|20.666|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 289zpi}}

{{Harmonics in cet|20.666|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~ZPINAME~~ (continued)}}

{{Harmonics in cet|20.666|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 289zpi (continued)}}

; [[WE|58et, 13-limit WE tuning]]

* Step size: 20.663{{c}}, octave size: 1198.45{{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 13-limit WE tuning and 13-limit [[TE]] tuning both do this.

Compressing the octave of 58edo by just over 1.5{{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|20.663|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~ETNAME~~, 13-limit WE tuning}}

{{Harmonics in cet|20.663|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 58et, 13-limit WE tuning}}

{{Harmonics in cet|20.663|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~ETNAME~~, 13-limit WE tuning (continued)}}

{{Harmonics in cet|20.663|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 58et, 13-limit WE tuning (continued)}}

@@ Line 12: / Line 12: @@
 ; [[zpi|288zpi]]
-* Step size: 20.736{{c}}, octave size: NNN{{c}}
+* Step size: 20.736{{c}}, octave size: 1202.69{{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 58edo by around 2.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 288zpi does this.
-{{Harmonics in cet|20.736|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
+{{Harmonics in cet|20.736|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 288zpi}}
-{{Harmonics in cet|20.736|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
+{{Harmonics in cet|20.736|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 288zpi (continued)}}
 ; 58edo
-* Step size: 20.690{{c}}, octave size: NNN{{c}}
+* Step size: 20.690{{c}}, octave size: 1200.00{{c}}
-Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.
+Pure-octaves 58edo approximates all harmonics up to 16 within NNN{{c}}.
-{{Harmonics in equal|58|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}
+{{Harmonics in equal|58|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 58edo}}
-{{Harmonics in equal|58|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}}
+{{Harmonics in equal|58|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 58edo (continued)}}
 ; [[150ed6]]
-* Step size: NNN{{c}}, octave size: 1199.42{{c}}
+* Step size: 20.680{{c}}, octave size: 1199.42{{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 58edo by around half a cent results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 150ed6 does this.
-{{Harmonics in equal|150|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in equal|150|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 150ed6}}
-{{Harmonics in equal|150|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
+{{Harmonics in equal|150|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 150ed6 (continued)}}
 ; [[92edt]]
-* Step size: NNN{{c}}, octave size: 1199.06{{c}}
+* Step size: 20.673{{c}}, octave size: 1199.06{{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 58edo by around 1{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 92edt does this.
-{{Harmonics in equal|92|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in equal|92|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 92edt}}
-{{Harmonics in equal|92|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
+{{Harmonics in equal|92|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 92edt (continued)}}
 ; [[zpi|289zpi]] / [[WE|58et, 7-limit WE tuning]]
 * Step size: 20.666{{c}}, octave size: 1198.63{{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 7-limit WE tuning and 7-limit [[TE]] tuning both do this. The tuning 289zpi also does this, it's octave differing from 7-limit WE by only 0.06{{c}}.
+Compressing the octave of 58edo by just under 1.5{{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. The tuning 289zpi also does this, its octave differing from 7-limit WE by only 0.06{{c}}.
-{{Harmonics in cet|20.666|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
+{{Harmonics in cet|20.666|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 289zpi}}
-{{Harmonics in cet|20.666|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
+{{Harmonics in cet|20.666|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 289zpi (continued)}}
 ; [[WE|58et, 13-limit WE tuning]]
 * Step size: 20.663{{c}}, octave size: 1198.45{{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 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
+Compressing the octave of 58edo by just over 1.5{{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|20.663|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, 13-limit WE tuning}}
+{{Harmonics in cet|20.663|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 58et, 13-limit WE tuning}}
-{{Harmonics in cet|20.663|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, 13-limit WE tuning (continued)}}
+{{Harmonics in cet|20.663|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 58et, 13-limit WE tuning (continued)}}