User:BudjarnLambeth/Sandbox2: Difference between revisions

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= Title1 =

{{Harmonics in equal|40|10|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}

{{Harmonics in equal|7|3|2|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}

{{Harmonics in equal|19|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}

{{Harmonics in equal|31|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}

= Title2 =

== Octave stretch or compression ==

What follows is a comparison of stretched- and compressed-octave 12edo tunings.

; [[40ed10]]

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

Compressing 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 40ed10 does this.

{{Harmonics in equal|40|10|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 40ed10}}

{{Harmonics in equal|40|10|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 40ed10 (continued)}}

; [[WE|12et, 7-limit WE tuning]]

* Step size: 99.664{{c}}, octave size: NNN{{c}}

Compressing 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.

{{Harmonics in cet|99.664|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 7-limit WE tuning}}

{{Harmonics in cet|99.664|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 7-limit WE tuning (continued)}}

; [[zpi|34zpi]]

* Step size: 99.807{{c}}, octave size: NNN{{c}}

Compressing the octave of 12edo 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 34zpi does this.

{{Harmonics in cet|99.807|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 34zpi}}

{{Harmonics in cet|99.807|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 34zpi (continued)}}

; [[WE|12et, 5-limit WE tuning]]

* Step size: 99.868{{c}}, octave size: NNN{{c}}

Compressing 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 5-limit WE tuning and 5-limit [[TE]] tuning both do this.

{{Harmonics in cet|99.868|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 5-limit WE tuning}}

{{Harmonics in cet|99.868|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 5-limit WE tuning (continued)}}

; [[WE|12et, 2.3.5.17.19 WE tuning]]

* Step size: 99.930{{c}}, octave size: NNN{{c}}

Compressing the octave of 12edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The 2.3.5.17.19 WE tuning and 2.3.5.17.19 [[TE]] tuning both do this.

{{Harmonics in cet|99.930|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 2.3.5.17.19 WE tuning}}

{{Harmonics in cet|99.930|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 2.3.5.17.19 WE tuning (continued)}}

; 12edo

* Step size: 100.000{{c}}, octave size: 1200.0{{c}}

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

{{Harmonics in equal|12|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in EDONAME}}

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

; [[31ed6]]

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

Stretching the octave of 12edo 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 31ed6 does this.

{{Harmonics in equal|31|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 31ed6}}

{{Harmonics in equal|31|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 31ed6 (continued)}}

; [[19edt]]

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

Stretching the octave of 12edo 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 19edt does this.

{{Harmonics in equal|19|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 19edt}}

{{Harmonics in equal|19|3|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 19edt (continued)}}

; [[7edf]]

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

Stretching the octave of 12edo 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 7edf does this.

{{Harmonics in equal|7|3|2|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 7edf}}

{{Harmonics in equal|7|3|2|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7edf (continued)}}

@@ Line 1: / Line 1: @@
+= Title1 =
 {{Harmonics in equal|40|10|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}
 {{Harmonics in equal|7|3|2|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}
 {{Harmonics in equal|19|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}
 {{Harmonics in equal|31|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}
+= Title2 =
+== Octave stretch or compression ==
+What follows is a comparison of stretched- and compressed-octave 12edo tunings.
+; [[40ed10]]
+* Step size: NNN{{c}}, octave size: NNN{{c}}
+Compressing 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 40ed10 does this.
+{{Harmonics in equal|40|10|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 40ed10}}
+{{Harmonics in equal|40|10|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 40ed10 (continued)}}
+; [[WE|12et, 7-limit WE tuning]]
+* Step size: 99.664{{c}}, octave size: NNN{{c}}
+Compressing 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.
+{{Harmonics in cet|99.664|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 7-limit WE tuning}}
+{{Harmonics in cet|99.664|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 7-limit WE tuning (continued)}}
+; [[zpi|34zpi]]
+* Step size: 99.807{{c}}, octave size: NNN{{c}}
+Compressing the octave of 12edo 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 34zpi does this.
+{{Harmonics in cet|99.807|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 34zpi}}
+{{Harmonics in cet|99.807|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 34zpi (continued)}}
+; [[WE|12et, 5-limit WE tuning]]
+* Step size: 99.868{{c}}, octave size: NNN{{c}}
+Compressing 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 5-limit WE tuning and 5-limit [[TE]] tuning both do this.
+{{Harmonics in cet|99.868|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 5-limit WE tuning}}
+{{Harmonics in cet|99.868|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 5-limit WE tuning (continued)}}
+; [[WE|12et, 2.3.5.17.19 WE tuning]]
+* Step size: 99.930{{c}}, octave size: NNN{{c}}
+Compressing the octave of 12edo by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The 2.3.5.17.19 WE tuning and 2.3.5.17.19 [[TE]] tuning both do this.
+{{Harmonics in cet|99.930|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 2.3.5.17.19 WE tuning}}
+{{Harmonics in cet|99.930|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 12et, 2.3.5.17.19 WE tuning (continued)}}
+; 12edo
+* Step size: 100.000{{c}}, octave size: 1200.0{{c}}
+Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.
+{{Harmonics in equal|12|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in EDONAME}}
+{{Harmonics in equal|12|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in EDONAME (continued)}}
+; [[31ed6]]
+* Step size: NNN{{c}}, octave size: NNN{{c}}
+Stretching the octave of 12edo 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 31ed6 does this.
+{{Harmonics in equal|31|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 31ed6}}
+{{Harmonics in equal|31|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 31ed6 (continued)}}
+; [[19edt]]
+* Step size: NNN{{c}}, octave size: NNN{{c}}
+Stretching the octave of 12edo 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 19edt does this.
+{{Harmonics in equal|19|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 19edt}}
+{{Harmonics in equal|19|3|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 19edt (continued)}}
+; [[7edf]]
+* Step size: NNN{{c}}, octave size: NNN{{c}}
+Stretching the octave of 12edo 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 7edf does this.
+{{Harmonics in equal|7|3|2|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 7edf}}
+{{Harmonics in equal|7|3|2|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7edf (continued)}}