User:BudjarnLambeth/Sandbox2: Difference between revisions

Line 7:

; 18edo

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

* Step size: 66.667{{c}}, octave size: 1200.0{{c}}

Pure-octaves 18edo approximates all harmonics up to 16 within ~~NNN~~{{c}}.

Pure-octaves 18edo approximates all harmonics up to 15 within 31.4{{c}}.

{{Harmonics in equal|18|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18edo}}

{{Harmonics in equal|18|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18edo (continued)}}

Line 14:

; [[WE|18et, 13-limit WE tuning]]

* Step size: 66.291{{c}}, octave size: 1193.2{{c}}

Compressing the octave of 18edo by around 7{{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 18edo by around 7{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 15 within 25.3{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.

{{Harmonics in cet|66.291|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18et, 13-limit WE tuning}}

{{Harmonics in cet|66.291|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18et, 13-limit WE tuning (continued)}}

Line 20:

; [[zpi|61zpi]]

* Step size: 66.228{{c}}, octave size: 1192.1{{c}}

Compressing the octave of 18edo by around 8{{c}} results in improved primes ~~NNN~~, but worse primes ~~NNN~~. This approximates all harmonics up to 16 within ~~NNN~~{{c}}. The tuning 61zpi does this.

Compressing the octave of 18edo by around 8{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 15 within 28.9{{c}}. The tuning 61zpi does this.

{{Harmonics in cet| 66.228 |intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 61zpi}}

{{Harmonics in cet| 66.228 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 61zpi (continued)}}

; [[65ed12]]

* ~~Step size: NNN{{c}}, octave~~ size: 1191.3{{c}}

* Octave size: 1191.3{{c}}

Compressing the octave of 18edo by around 9{{c}} results in improved primes ~~NNN~~, but worse primes ~~NNN~~. This approximates all harmonics up to 16 within ~~NNN~~{{c}}. The tuning 65ed12 does this.

Compressing the octave of 18edo by around 9{{c}} results in improved primes 3, 5, 7 and 13, but a worse primes 2. This approximates all harmonics up to 15 within 31.4{{c}}. The tuning 65ed12 does this.

{{Harmonics in equal|65|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 65ed12}}

{{Harmonics in equal|65|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 65ed12 (continued)}}

~~; [[WE|18et, 7-limit WE tuning]]~~

* Step size: 66.148{{c}}, octave size: 1190.7{{c}}

Compressing the octave of 18edo by around 9.5{{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.

~~{{Harmonics in cet| 66.148 |intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18et, 7-limit WE tuning}}~~

~~{{Harmonics in cet| 66.148 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18et, 7-limit WE tuning (continued)}}~~

; [[47ed6]]

* Step size: NNN{{c}}, octave size: 1188.0{{c}}

Compressing the octave of 18edo by around 12{{c}} results in improved primes ~~NNN~~, but worse primes ~~NNN~~. This approximates all harmonics up to 16 within ~~NNN~~{{c}}. The tuning 47ed6 does this.

Compressing the octave of 18edo by around 12{{c}} results in improved primes 3, 7, 11 and 13, but worse primes 2 and 5. This approximates all harmonics up to 15 within 29.9{{c}}. The tuning 47ed6 does this.

{{Harmonics in equal|47|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 47ed6}}

{{Harmonics in equal|47|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 47ed6 (continued)}}

@@ Line 7: / Line 7: @@
 ; 18edo
-* Step size: NNN{{c}}, octave size: NNN{{c}}
+* Step size: 66.667{{c}}, octave size: 1200.0{{c}}
-Pure-octaves 18edo approximates all harmonics up to 16 within NNN{{c}}.
+Pure-octaves 18edo approximates all harmonics up to 15 within 31.4{{c}}.
 {{Harmonics in equal|18|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18edo}}
 {{Harmonics in equal|18|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18edo (continued)}}
@@ Line 14: / Line 14: @@
 ; [[WE|18et, 13-limit WE tuning]]
 * Step size: 66.291{{c}}, octave size: 1193.2{{c}}
-Compressing the octave of 18edo by around 7{{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 18edo by around 7{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 15 within 25.3{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
 {{Harmonics in cet|66.291|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18et, 13-limit WE tuning}}
 {{Harmonics in cet|66.291|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18et, 13-limit WE tuning (continued)}}
@@ Line 20: / Line 20: @@
 ; [[zpi|61zpi]]
 * Step size: 66.228{{c}}, octave size: 1192.1{{c}}
-Compressing the octave of 18edo by around 8{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 61zpi does this.
+Compressing the octave of 18edo by around 8{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 15 within 28.9{{c}}. The tuning 61zpi does this.
 {{Harmonics in cet| 66.228 |intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 61zpi}}
 {{Harmonics in cet| 66.228 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 61zpi (continued)}}
 ; [[65ed12]]
-* Step size: NNN{{c}}, octave size: 1191.3{{c}}
+* Octave size: 1191.3{{c}}
-Compressing the octave of 18edo by around 9{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 65ed12 does this.
+Compressing the octave of 18edo by around 9{{c}} results in improved primes 3, 5, 7 and 13, but a worse primes 2. This approximates all harmonics up to 15 within 31.4{{c}}. The tuning 65ed12 does this.
 {{Harmonics in equal|65|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 65ed12}}
 {{Harmonics in equal|65|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 65ed12 (continued)}}
-; [[WE|18et, 7-limit WE tuning]]
-* Step size: 66.148{{c}}, octave size: 1190.7{{c}}
-Compressing the octave of 18edo by around 9.5{{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.
-{{Harmonics in cet| 66.148 |intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18et, 7-limit WE tuning}}
-{{Harmonics in cet| 66.148 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18et, 7-limit WE tuning (continued)}}
 ; [[47ed6]]
 * Step size: NNN{{c}}, octave size: 1188.0{{c}}
-Compressing the octave of 18edo by around 12{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 47ed6 does this.
+Compressing the octave of 18edo by around 12{{c}} results in improved primes 3, 7, 11 and 13, but worse primes 2 and 5. This approximates all harmonics up to 15 within 29.9{{c}}. The tuning 47ed6 does this.
 {{Harmonics in equal|47|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 47ed6}}
 {{Harmonics in equal|47|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 47ed6 (continued)}}