User:BudjarnLambeth/Sandbox2: Difference between revisions

Line 16:

; [[ed7|179ed7]]

* Octave size: ~~NNN~~{{c}}

* Octave size: 1204.50{{c}}

Stretching the octave of 64edo 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 179ed7 does this. So does the tuning 326zpi whose octave is identical within 0.3{{c}}.

Stretching the octave of 64edo by around 4.5{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 16 within 8.99{{c}}. The tuning 179ed7 does this. So does the tuning 326zpi whose octave is identical within 0.3{{c}}.

{{Harmonics in equal|179|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 179ed7}}

{{Harmonics in equal|179|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 179ed7 (continued)}}

; [[ed6|165ed6]]

* Octave size: ~~NNN~~{{c}}

* Octave size: 1203.18{{c}}

Stretching the octave of 64edo 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 165ed6 does this.

Stretching the octave of 64edo by around 3{{c}} results in improved primes 3, 5, 7, 11, 13 and 17, but a worse prime 2. This approximates all harmonics up to 16 within 9.25{{c}}. The tuning 165ed6 does this.

{{Harmonics in equal|165|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~EDONOI~~}}

{{Harmonics in equal|165|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 165ed6}}

{{Harmonics in equal|165|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 165ed6 (continued)}}

; [[ed12|229ed12]]

* Octave size: ~~NNN~~{{c}}

* Octave size: 1202.29{{c}}

Stretching the octave of 64edo 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 229ed12 does this. So does the tuning [[equal tuning|221ed11]] whose octave is identical within 0.1{{c}}.

Stretching the octave of 64edo by around 2{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 9.17{{c}}. The tuning 229ed12 does this. So does the tuning [[equal tuning|221ed11]] whose octave is identical within 0.1{{c}}.

{{Harmonics in equal|229|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 229ed12}}

{{Harmonics in equal|229|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 229ed12 (continued)}}

; [[zpi|327zpi]]

* Step size: 18.767{{c}}, octave size: ~~NNN~~{{c}}

* Step size: 18.767{{c}}, octave size: 1201.09{{c}}

Stretching the octave of 64edo 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 327zpi does this.

Stretching the octave of 64edo by around 1{{c}} results in improved primes 3 and 11, but worse primes 2, 5, 7 and 13. This approximates all harmonics up to 16 within 9.23{{c}}. The tuning 327zpi does this.

{{Harmonics in cet|18.767|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 327zpi}}

{{Harmonics in cet|18.767|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 327zpi (continued)}}

; [[WE|64et, 11-limit WE tuning]]

* Step size: 18.755{{c}}, octave size: ~~NNN~~{{c}}

* Step size: 18.755{{c}}, octave size: 1200.32{{c}}

Stretching the octave of 64edo by around ~~NNN{{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.

Stretching the octave of 64edo by around a third of a cent results in slightly improved primes 3 and 11, but slightly worse primes 2, 5, 7 and 13. This approximates all harmonics up to 16 within 8.50{{c}}. Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this.

{{Harmonics in cet|18.755|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 64et, 11-limit WE tuning}}

{{Harmonics in cet|18.755|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 64et, 11-limit WE tuning (continued)}}

Line 47:

; 64edo

* Step size: 18.750{{c}}, octave size: 1200.00{{c}}

Pure-octaves 64edo approximates all harmonics up to 16 within ~~NNN~~{{c}}. The octave of 64edo's 13-limit [[WE]] tuning differs by only 0.13{{c}} from pure.

Pure-octaves 64edo approximates all harmonics up to 16 within 8.21{{c}}. The octave of 64edo's 13-limit [[WE]] tuning differs by only 0.13{{c}} from pure.

{{Harmonics in equal|64|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 64edo}}

{{Harmonics in equal|64|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 64edo (continued)}}

; [[zpi|328zpi]]

* Step size: 18.721{{c}}, octave size: ~~NNN~~{{c}}

* Step size: 18.721{{c}}, octave size: 1198.14{{c}}

Compressing the octave of 64edo 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 328zpi does this.

Compressing the octave of 64edo by just under 2{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 8.02{{c}}. The tuning 328zpi does this.

{{Harmonics in cet|18.721|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 328zpi}}

{{Harmonics in cet|18.721|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 328zpi (continued)}}

; [[ed7|180ed7]]

* Octave size: ~~NNN~~{{c}}

* Octave size: 1197.80{{c}}

Compressing the octave of 64edo 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 180ed7 does this.

Compressing the octave of 64edo by just over 2{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 9.34{{c}}. The tuning 180ed7 does this.

{{Harmonics in equal|180|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 180ed7}}

{{Harmonics in equal|180|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 180ed7 (continued)}}

; [[ed12|230ed12]]

* Octave size: ~~NNN~~{{c}}

* Octave size: 1197.07{{c}}

Compressing the octave of 64edo 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 230ed12 does this.

Compressing the octave of 64edo by around 3{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 8.80{{c}}. The tuning 230ed12 does this.

{{Harmonics in equal|230|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 230ed12}}

{{Harmonics in equal|230|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 230ed12 (continued)}}

Line 72:

* Step size: Octave size: NNN{{c}}

Compressing the octave of 64edo 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 149ed5 does this.

{{Harmonics in equal|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 149ed5}}

{{Harmonics in equal|149|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 149ed5}}

{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 149ed5 (continued)}}

{{Harmonics in equal|149|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 149ed5 (continued)}}

= Title2 =

@@ Line 16: / Line 16: @@
 ; [[ed7|179ed7]]
-* Octave size: NNN{{c}}
+* Octave size: 1204.50{{c}}
-Stretching the octave of 64edo 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 179ed7 does this. So does the tuning 326zpi whose octave is identical within 0.3{{c}}.
+Stretching the octave of 64edo by around 4.5{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 16 within 8.99{{c}}. The tuning 179ed7 does this. So does the tuning 326zpi whose octave is identical within 0.3{{c}}.
 {{Harmonics in equal|179|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 179ed7}}
 {{Harmonics in equal|179|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 179ed7 (continued)}}
 ; [[ed6|165ed6]]
-* Octave size: NNN{{c}}
+* Octave size: 1203.18{{c}}
-Stretching the octave of 64edo 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 165ed6 does this.
+Stretching the octave of 64edo by around 3{{c}} results in improved primes 3, 5, 7, 11, 13 and 17, but a worse prime 2. This approximates all harmonics up to 16 within 9.25{{c}}. The tuning 165ed6 does this.
-{{Harmonics in equal|165|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in equal|165|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 165ed6}}
 {{Harmonics in equal|165|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 165ed6 (continued)}}
 ; [[ed12|229ed12]]
-* Octave size: NNN{{c}}
+* Octave size: 1202.29{{c}}
-Stretching the octave of 64edo 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 229ed12 does this. So does the tuning [[equal tuning|221ed11]] whose octave is identical within 0.1{{c}}.
+Stretching the octave of 64edo by around 2{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 9.17{{c}}. The tuning 229ed12 does this. So does the tuning [[equal tuning|221ed11]] whose octave is identical within 0.1{{c}}.
 {{Harmonics in equal|229|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 229ed12}}
 {{Harmonics in equal|229|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 229ed12 (continued)}}
 ; [[zpi|327zpi]]
-* Step size: 18.767{{c}}, octave size: NNN{{c}}
+* Step size: 18.767{{c}}, octave size: 1201.09{{c}}
-Stretching the octave of 64edo 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 327zpi does this.
+Stretching the octave of 64edo by around 1{{c}} results in improved primes 3 and 11, but worse primes 2, 5, 7 and 13. This approximates all harmonics up to 16 within 9.23{{c}}. The tuning 327zpi does this.
 {{Harmonics in cet|18.767|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 327zpi}}
 {{Harmonics in cet|18.767|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 327zpi (continued)}}
 ; [[WE|64et, 11-limit WE tuning]]
-* Step size: 18.755{{c}}, octave size: NNN{{c}}
+* Step size: 18.755{{c}}, octave size: 1200.32{{c}}
-Stretching the octave of 64edo by around NNN{{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.
+Stretching the octave of 64edo by around a third of a cent results in slightly improved primes 3 and 11, but slightly worse primes 2, 5, 7 and 13. This approximates all harmonics up to 16 within 8.50{{c}}. Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this.
 {{Harmonics in cet|18.755|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 64et, 11-limit WE tuning}}
 {{Harmonics in cet|18.755|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 64et, 11-limit WE tuning (continued)}}
@@ Line 47: / Line 47: @@
 ; 64edo
 * Step size: 18.750{{c}}, octave size: 1200.00{{c}}
-Pure-octaves 64edo approximates all harmonics up to 16 within NNN{{c}}. The octave of 64edo's 13-limit [[WE]] tuning differs by only 0.13{{c}} from pure.
+Pure-octaves 64edo approximates all harmonics up to 16 within 8.21{{c}}. The octave of 64edo's 13-limit [[WE]] tuning differs by only 0.13{{c}} from pure.
 {{Harmonics in equal|64|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 64edo}}
 {{Harmonics in equal|64|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 64edo (continued)}}
 ; [[zpi|328zpi]]
-* Step size: 18.721{{c}}, octave size: NNN{{c}}
+* Step size: 18.721{{c}}, octave size: 1198.14{{c}}
-Compressing the octave of 64edo 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 328zpi does this.
+Compressing the octave of 64edo by just under 2{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 8.02{{c}}. The tuning 328zpi does this.
 {{Harmonics in cet|18.721|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 328zpi}}
 {{Harmonics in cet|18.721|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 328zpi (continued)}}
 ; [[ed7|180ed7]]
-* Octave size: NNN{{c}}
+* Octave size: 1197.80{{c}}
-Compressing the octave of 64edo 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 180ed7 does this.
+Compressing the octave of 64edo by just over 2{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 9.34{{c}}. The tuning 180ed7 does this.
 {{Harmonics in equal|180|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 180ed7}}
 {{Harmonics in equal|180|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 180ed7 (continued)}}
 ; [[ed12|230ed12]]
-* Octave size: NNN{{c}}
+* Octave size: 1197.07{{c}}
-Compressing the octave of 64edo 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 230ed12 does this.
+Compressing the octave of 64edo by around 3{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 8.80{{c}}. The tuning 230ed12 does this.
 {{Harmonics in equal|230|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 230ed12}}
 {{Harmonics in equal|230|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 230ed12 (continued)}}
@@ Line 72: / Line 72: @@
 * Step size: Octave size: NNN{{c}}
 Compressing the octave of 64edo 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 149ed5 does this.
-{{Harmonics in equal|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 149ed5}}
+{{Harmonics in equal|149|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 149ed5}}
-{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 149ed5 (continued)}}
+{{Harmonics in equal|149|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 149ed5 (continued)}}
 = Title2 =