User:BudjarnLambeth/Sandbox2: Difference between revisions

Line 9:

; 32edo

* Step size: 37.500{{c}}, octave size: 1200.0{{c}}

Pure-octaves 32edo approximates all harmonics up to 16 within ~~NNN~~{{c}}.

Pure-octaves 32edo approximates all harmonics up to 16 within 15.5{{c}}.

{{Harmonics in equal|32|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 32edo}}

{{Harmonics in equal|32|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 32edo (continued)}}

Line 15:

; [[WE|32et, 13-limit WE tuning]]

* Step size: 37.481{{c}}, octave size: 1199.4{{c}}

Compressing the octave of 32edo by around half 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-~~linut~~ [[TE]] tuning both do this.

Compressing the octave of 32edo by around half a cent results in improved primes 3, 7 and 11, but worse primes 5 and 13. This approximates all harmonics up to 16 within 18.3{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.

{{Harmonics in cet|37.481|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 32et, 13-limit WE tuning}}

{{Harmonics in cet|37.481|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}

Line 21:

; [[WE|32et, 11-limit WE tuning]]

* Step size: 37.453{{c}}, octave size: 1198.5{{c}}

Compressing the octave of 32edo by around 1.5{{c}} results in improved primes ~~NNN~~, but worse primes ~~NNN~~. This approximates all harmonics up to 16 within ~~NNN~~{{c}}. Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this.

Compressing the octave of 32edo by around 1.5{{c}} results in improved primes 3, 7 and 11, but worse primes 2, 5 and 13. This approximates all harmonics up to 16 within 16.4{{c}}. Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this.

{{Harmonics in cet|37.453|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 32et, 11-limit WE tuning}}

{{Harmonics in cet|37.453|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 32et, 11-limit WE tuning (continued)}}

; [[90ed7]]

; [[ed7|90ed7]]

* Step size: 37.431{{c}}, octave size: 1197.8{{c}}

Compressing the octave of 32edo by around 2{{c}} results in improved primes ~~NNN~~, but worse primes ~~NNN~~. This approximates all harmonics up to 16 within ~~NNN~~{{c}}. If one wishes to use both of 32edo's mappings of the 5th harmonic simultaneously, this tuning is suited to that due to evenly sharing the error between them. The tuning 90ed7 does this.

Compressing the octave of 32edo by around 2{{c}} results in improved primes 3, 7, 11 and 13, but worse primes 2 and 5. This approximates all harmonics up to 16 within 18.6{{c}}. If one wishes to use both of 32edo's mappings of the 5th harmonic simultaneously, this tuning is suited to that due to evenly sharing the error between them. The tuning 90ed7 does this.

{{Harmonics in equal|90|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 90ed7}}

{{Harmonics in equal|90|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 90ed7 (continued)}}

Line 33:

; [[zpi|133zpi]]

* Step size: 37.418{{c}}, octave size: 1197.375{{c}}

Compressing the octave of 32edo 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 133zpi does this.

Compressing the octave of 32edo by around NNN{{c}} results in improved primes 3, 7, 11 and 13, but worse primes 2 and 5. This approximates all harmonics up to 16 within 17.4{{c}}. The tuning 133zpi does this.

{{Harmonics in cet|37.418|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 133zpi}}

{{Harmonics in cet|37.418|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 133zpi (continued)}}

Line 42:

; [[51edt]]

* Step size: 37.293{{c}}, octave size: 1193.4{{c}}

Compressing the octave of 32edo by around 6.5{{c}} results in improved primes ~~NNN~~, but worse primes ~~NNN~~. This approximates all harmonics up to 16 within ~~NNN~~{{c}}. The tuning 51edt does this.

Compressing the octave of 32edo by around 6.5{{c}} results in improved primes 3, 5 and 13, but worse primes 2 and 7. This approximates all harmonics up to 16 within 18.2{{c}}. The tuning 51edt does this.

{{Harmonics in equal|51|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 51edt}}

{{Harmonics in equal|51|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 51edt (continued)}}

~~; [[zpi|134zpi]]~~

* Step size: 37.176{{c}}, octave size: 1189.6{{c}}

~~Compressing the octave of 134zpi by around 10.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 134zpi does this.~~

~~{{Harmonics in cet|37.176|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 134zpi}}~~

~~{{Harmonics in cet|37.176|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 134zpi (continued)}}~~

~~; [[75ed5]]~~

* Step size: 37.151{{c}}, octave size: 1188.8{{c}}

~~Compressing the octave of 32edo by around 11{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 75ed5 does this.~~

~~{{Harmonics in equal|75|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 75ed5}}~~

~~{{Harmonics in equal|75|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 75ed5 (continued)}}~~

~~; [[WE|ETNAME, SUBGROUP WE tuning]]~~

* 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.

~~{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}~~

~~{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}~~

~~; [[EDONOI]]~~

* 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|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}~~

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

~~; [[zpi|ZPINAME]]~~

* 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.~~

~~{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}~~

~~{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}~~

= Title2 =

@@ Line 9: / Line 9: @@
 ; 32edo
 * Step size: 37.500{{c}}, octave size: 1200.0{{c}}
-Pure-octaves 32edo approximates all harmonics up to 16 within NNN{{c}}.
+Pure-octaves 32edo approximates all harmonics up to 16 within 15.5{{c}}.
 {{Harmonics in equal|32|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 32edo}}
 {{Harmonics in equal|32|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 32edo (continued)}}
@@ Line 15: / Line 15: @@
 ; [[WE|32et, 13-limit WE tuning]]
 * Step size: 37.481{{c}}, octave size: 1199.4{{c}}
-Compressing the octave of 32edo by around half 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-linut [[TE]] tuning both do this.
+Compressing the octave of 32edo by around half a cent results in improved primes 3, 7 and 11, but worse primes 5 and 13. This approximates all harmonics up to 16 within 18.3{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
 {{Harmonics in cet|37.481|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 32et, 13-limit WE tuning}}
 {{Harmonics in cet|37.481|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
@@ Line 21: / Line 21: @@
 ; [[WE|32et, 11-limit WE tuning]]
 * Step size: 37.453{{c}}, octave size: 1198.5{{c}}
-Compressing the octave of 32edo by around 1.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this.
+Compressing the octave of 32edo by around 1.5{{c}} results in improved primes 3, 7 and 11, but worse primes 2, 5 and 13. This approximates all harmonics up to 16 within 16.4{{c}}. Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this.
 {{Harmonics in cet|37.453|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 32et, 11-limit WE tuning}}
 {{Harmonics in cet|37.453|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 32et, 11-limit WE tuning (continued)}}
-; [[90ed7]]
+; [[ed7|90ed7]]
 * Step size: 37.431{{c}}, octave size: 1197.8{{c}}
-Compressing the octave of 32edo by around 2{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. If one wishes to use both of 32edo's mappings of the 5th harmonic simultaneously, this tuning is suited to that due to evenly sharing the error between them. The tuning 90ed7 does this.
+Compressing the octave of 32edo by around 2{{c}} results in improved primes 3, 7, 11 and 13, but worse primes 2 and 5. This approximates all harmonics up to 16 within 18.6{{c}}. If one wishes to use both of 32edo's mappings of the 5th harmonic simultaneously, this tuning is suited to that due to evenly sharing the error between them. The tuning 90ed7 does this.
 {{Harmonics in equal|90|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 90ed7}}
 {{Harmonics in equal|90|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 90ed7 (continued)}}
@@ Line 33: / Line 33: @@
 ; [[zpi|133zpi]]
 * Step size: 37.418{{c}}, octave size: 1197.375{{c}}
-Compressing the octave of 32edo 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 133zpi does this.
+Compressing the octave of 32edo by around NNN{{c}} results in improved primes 3, 7, 11 and 13, but worse primes 2 and 5. This approximates all harmonics up to 16 within 17.4{{c}}. The tuning 133zpi does this.
 {{Harmonics in cet|37.418|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 133zpi}}
 {{Harmonics in cet|37.418|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 133zpi (continued)}}
@@ Line 42: / Line 42: @@
 ; [[51edt]]
 * Step size: 37.293{{c}}, octave size: 1193.4{{c}}
-Compressing the octave of 32edo by around 6.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 51edt does this.
+Compressing the octave of 32edo by around 6.5{{c}} results in improved primes 3, 5 and 13, but worse primes 2 and 7. This approximates all harmonics up to 16 within 18.2{{c}}. The tuning 51edt does this.
 {{Harmonics in equal|51|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 51edt}}
 {{Harmonics in equal|51|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 51edt (continued)}}
-; [[zpi|134zpi]]
-* Step size: 37.176{{c}}, octave size: 1189.6{{c}}
-Compressing the octave of 134zpi by around 10.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 134zpi does this.
-{{Harmonics in cet|37.176|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 134zpi}}
-{{Harmonics in cet|37.176|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 134zpi (continued)}}
-; [[75ed5]]
-* Step size: 37.151{{c}}, octave size: 1188.8{{c}}
-Compressing the octave of 32edo by around 11{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 75ed5 does this.
-{{Harmonics in equal|75|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 75ed5}}
-{{Harmonics in equal|75|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 75ed5 (continued)}}
-; [[WE|ETNAME, SUBGROUP WE tuning]]
-* 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.
-{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
-{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
-; [[EDONOI]]
-* 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|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
-{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
-; [[zpi|ZPINAME]]
-* 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.
-{{Harmonics in cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
-{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
 = Title2 =