User:BudjarnLambeth/Sandbox2: Difference between revisions

Line 8:

; [[35edf]]

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

* Step size: NNN{{c}}, octave size: 1203.35{{c}}

~~_ing~~ the octave of 60edo 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 35edf does this.

Stretching the octave of 60edo by a little over 3{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 35edf does this.

{{Harmonics in equal|35|3|2|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 35edf}}

{{Harmonics in equal|35|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 35edf (continued)}}

; [[139ed5]]

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

* Step size: NNN{{c}}, octave size: 1202.73{{c}}

~~_ing~~ the octave of 60edo 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 139ed5 does this.

Stretching the octave of 60edo by a little under{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 139ed5 does this.

{{Harmonics in equal|139|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 139ed5}}

{{Harmonics in equal|139|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 139ed5 (continued)}}

Line 21:

; [[zpi|301zpi]]

* Step size: 20.027{{c}}, octave size: NNN{{c}}

~~_ing~~ the octave of 60edo 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 301zpi does this.

Stretching the octave of 60edo by around 1.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 301zpi does this.

{{Harmonics in cet|20.027|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 301zpi}}

{{Harmonics in cet| 20.027 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 301zpi (continued)}}

; [[95edt]]

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

* Step size: NNN{{c}}, octave size: 1201.23{{c}}

~~_ing~~ the octave of 60edo 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 95edt does this.

Stretching the octave of 60edo by just over a cent results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 95edt does this.

{{Harmonics in equal|95|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 95edt}}

{{Harmonics in equal|95|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 95edt (continued)}}

; [[WE|60et, 13-limit WE tuning]] / [[155ed6]]

* Step size: 20.013{{c}}, octave size: ~~NNN~~{{c}}

* Step size: 20.013{{c}}, octave size: 1200.78{{c}}

~~_ing~~ the octave of 60edo 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 155ed6 whose octaves differ by only 0.02{{c}}.

Stretching the octave of 60edo by just under a cent 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 155ed6 whose octaves differ by only 0.02{{c}}.

{{Harmonics in cet|20.013|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 60et, 13-limit WE tuning}}

{{Harmonics in cet|20.013|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 60et, 13-limit WE tuning (continued)}}

; [[215ed12]]

* Step size: NNN{{c}}, octave size: 1200.55{{c}}

Stretching the octave of 215ed12 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 215ed12 does this.

{{Harmonics in equal|215|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 215ed12}}

{{Harmonics in equal|215|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 215ed12 (continued)}}

; 60edo

Line 42:

Line 48:

{{Harmonics in equal|60|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 60edo}}

{{Harmonics in equal|60|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 60edo (continued)}}

~~; [[215ed12]]~~

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

~~_ing the octave of 215ed12 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 215ed12 does this.~~

~~{{Harmonics in equal|215|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 215ed12}}~~

~~{{Harmonics in equal|215|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 215ed12 (continued)}}~~

; [[zpi|302zpi]]

* Step size: 19.962{{c}}, octave size: ~~NNN~~{{c}}

* Step size: 19.962{{c}}, octave size: 1197.72{{c}}

~~_ing~~ the octave of 60edo 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 202zpi does this.

Compressing the octave of 60edo by around 2{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 202zpi does this.

{{Harmonics in cet|19.962|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 302zpi}}

{{Harmonics in cet|19.962|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 302zpi (continued)}}

; [[208ed11]]

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

* Step size: NNN{{c}}, octave size: 1197.50{{c}}

~~_ing~~ the octave of 60edo 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 208ed11 does this.

Compressing the octave of 60edo 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 208ed11 does this.

{{Harmonics in equal|208|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 208ed11}}

{{Harmonics in equal|208|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 208ed11 (continued)}}

; [[zpi|303zpi]]

* Step size: 19.913{{c}}, octave size: ~~NNN~~{{c}}

* Step size: 19.913{{c}}, octave size: 1194.78{{c}}

~~_ing~~ the octave of 60edo 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 303zpi does this.

Compressing the octave of 60edo by around 5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 303zpi does this.

{{Harmonics in cet|19.913|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 303zpi}}

{{Harmonics in cet|19.913|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 303zpi (continued)}}

@@ Line 8: / Line 8: @@
 ; [[35edf]]
-* Step size: NNN{{c}}, octave size: NNN{{c}}
+* Step size: NNN{{c}}, octave size: 1203.35{{c}}
-_ing the octave of 60edo 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 35edf does this.
+Stretching the octave of 60edo by a little over 3{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 35edf does this.
 {{Harmonics in equal|35|3|2|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 35edf}}
 {{Harmonics in equal|35|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 35edf (continued)}}
 ; [[139ed5]]
-* Step size: NNN{{c}}, octave size: NNN{{c}}
+* Step size: NNN{{c}}, octave size: 1202.73{{c}}
-_ing the octave of 60edo 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 139ed5 does this.
+Stretching the octave of 60edo by a little under{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 139ed5 does this.
 {{Harmonics in equal|139|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 139ed5}}
 {{Harmonics in equal|139|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 139ed5 (continued)}}
@@ Line 21: / Line 21: @@
 ; [[zpi|301zpi]]
 * Step size: 20.027{{c}}, octave size: NNN{{c}}
-_ing the octave of 60edo 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 301zpi does this.
+Stretching the octave of 60edo by around 1.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 301zpi does this.
 {{Harmonics in cet|20.027|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 301zpi}}
 {{Harmonics in cet| 20.027 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 301zpi (continued)}}
 ; [[95edt]]
-* Step size: NNN{{c}}, octave size: NNN{{c}}
+* Step size: NNN{{c}}, octave size: 1201.23{{c}}
-_ing the octave of 60edo 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 95edt does this.
+Stretching the octave of 60edo by just over a cent results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 95edt does this.
 {{Harmonics in equal|95|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 95edt}}
 {{Harmonics in equal|95|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 95edt (continued)}}
 ; [[WE|60et, 13-limit WE tuning]] / [[155ed6]]
-* Step size: 20.013{{c}}, octave size: NNN{{c}}
+* Step size: 20.013{{c}}, octave size: 1200.78{{c}}
-_ing the octave of 60edo 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 155ed6 whose octaves differ by only 0.02{{c}}.
+Stretching the octave of 60edo by just under a cent 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 155ed6 whose octaves differ by only 0.02{{c}}.
 {{Harmonics in cet|20.013|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 60et, 13-limit WE tuning}}
 {{Harmonics in cet|20.013|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 60et, 13-limit WE tuning (continued)}}
+; [[215ed12]]
+* Step size: NNN{{c}}, octave size: 1200.55{{c}}
+Stretching the octave of 215ed12 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 215ed12 does this.
+{{Harmonics in equal|215|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 215ed12}}
+{{Harmonics in equal|215|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 215ed12 (continued)}}
 ; 60edo
@@ Line 42: / Line 48: @@
 {{Harmonics in equal|60|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 60edo}}
 {{Harmonics in equal|60|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 60edo (continued)}}
-; [[215ed12]]
-* Step size: NNN{{c}}, octave size: NNN{{c}}
-_ing the octave of 215ed12 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 215ed12 does this.
-{{Harmonics in equal|215|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 215ed12}}
-{{Harmonics in equal|215|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 215ed12 (continued)}}
 ; [[zpi|302zpi]]
-* Step size: 19.962{{c}}, octave size: NNN{{c}}
+* Step size: 19.962{{c}}, octave size: 1197.72{{c}}
-_ing the octave of 60edo 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 202zpi does this.
+Compressing the octave of 60edo by around 2{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 202zpi does this.
 {{Harmonics in cet|19.962|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 302zpi}}
 {{Harmonics in cet|19.962|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 302zpi (continued)}}
 ; [[208ed11]]
-* Step size: NNN{{c}}, octave size: NNN{{c}}
+* Step size: NNN{{c}}, octave size: 1197.50{{c}}
-_ing the octave of 60edo 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 208ed11 does this.
+Compressing the octave of 60edo 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 208ed11 does this.
 {{Harmonics in equal|208|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 208ed11}}
 {{Harmonics in equal|208|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 208ed11 (continued)}}
 ; [[zpi|303zpi]]
-* Step size: 19.913{{c}}, octave size: NNN{{c}}
+* Step size: 19.913{{c}}, octave size: 1194.78{{c}}
-_ing the octave of 60edo 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 303zpi does this.
+Compressing the octave of 60edo by around 5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 303zpi does this.
 {{Harmonics in cet|19.913|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 303zpi}}
 {{Harmonics in cet|19.913|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 303zpi (continued)}}