User:BudjarnLambeth/Sandbox2: Difference between revisions

Line 25:

; [[zpi|127zpi]]

* Step size: 38.737{{c}}, octave size: 1200.8{{c}}

Stretching the octave of 31edo by slightly less than 1{{c}} results in slightly improved primes 3~~, 7~~ and 11, but slightly worse primes 2, 5 and 13. This approximates all harmonics up to 16 within 14.2{{c}}. The tuning 127zpi does this.

Stretching the octave of 31edo by slightly less than 1{{c}} 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 14.2{{c}}. The tuning 127zpi does this.

{{Harmonics in cet|38.737|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 127zpi}}

{{Harmonics in cet|38.737|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 127zpi (continued)}}

Line 31:

; [[WE|31et, 11-limit WE tuning]]

* Step size: 38.748{{c}}, octave size: 1201.2{{c}}

Stretching the octave of 31edo by slightly more than 1{{c}} results in moderately improved primes 3~~, 7~~ and 11, but moderately worse primes 2, 5 and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]].

Stretching the octave of 31edo by slightly more than 1{{c}} results in moderately improved primes 3 and 11, but moderately worse primes 2, 5, 7 and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]].

{{Harmonics in cet|38.748|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 31et, 11-limit WE tuning}}

{{Harmonics in cet|38.748|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 31et, 11-limit WE tuning (continued)}}

Line 37:

; [[80ed6]]

* Step size: 38.774{{c}}, octave size: 1202.0{{c}}

Stretching the octave of 31edo by ~~slightly more than 1~~{{c}} results in moderately improved primes 3~~, 7~~ and 11, but moderately worse primes 2, 5 and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]]~~... Slightly more than this - a stretch of 2.239{{c}} - is the absolute maximum amount of octave stretch 31edo can tolerate before the mapping of the 13th harmonic changes~~.

Stretching the octave of 31edo by about 2{{c}} results in moderately improved primes 3 and 11, but moderately worse primes 2, 5, 7 and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]].

{{Harmonics in equal|80|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 80ed6}}

{{Harmonics in equal|80|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 80ed6 (continued)}

{{Harmonics in equal|80|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 80ed6 (continued)}}

; [[18edf]]

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

Stretching the octave of 31edo by slightly more than 1{{c}} results in moderately improved primes 3 and 11, but moderately worse primes 2, 5, 7and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]]... Slightly more than this - a stretch of 2.239{{c}} - is the absolute maximum amount of octave stretch 31edo can tolerate before the mapping of the 13th harmonic changes.

{{Harmonics in equal|18|3|2|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 18edf}}

{{Harmonics in equal|18|3|2|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 18edf (continued)}}

; [[49edt]]

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

Stretching the octave of 31edo by slightly more than 1{{c}} results in moderately improved primes 3 and 11, but moderately worse primes 2, 5, 7and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]]... Slightly more than this - a stretch of 2.239{{c}} - is the absolute maximum amount of octave stretch 31edo can tolerate before the mapping of the 13th harmonic changes.

{{Harmonics in equal|49|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 49edt}}

{{Harmonics in equal|49|3|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 49edt (continued)}}

@@ Line 25: / Line 25: @@
 ; [[zpi|127zpi]]
 * Step size: 38.737{{c}}, octave size: 1200.8{{c}}
-Stretching the octave of 31edo by slightly less than 1{{c}} results in slightly improved primes 3, 7 and 11, but slightly worse primes 2, 5 and 13. This approximates all harmonics up to 16 within 14.2{{c}}. The tuning 127zpi does this.
+Stretching the octave of 31edo by slightly less than 1{{c}} 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 14.2{{c}}. The tuning 127zpi does this.
 {{Harmonics in cet|38.737|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 127zpi}}
 {{Harmonics in cet|38.737|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 127zpi (continued)}}
@@ Line 31: / Line 31: @@
 ; [[WE|31et, 11-limit WE tuning]]
 * Step size: 38.748{{c}}, octave size: 1201.2{{c}}
-Stretching the octave of 31edo by slightly more than 1{{c}} results in moderately improved primes 3, 7 and 11, but moderately worse primes 2, 5 and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]].
+Stretching the octave of 31edo by slightly more than 1{{c}} results in moderately improved primes 3 and 11, but moderately worse primes 2, 5, 7 and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]].
 {{Harmonics in cet|38.748|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 31et, 11-limit WE tuning}}
 {{Harmonics in cet|38.748|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 31et, 11-limit WE tuning (continued)}}
@@ Line 37: / Line 37: @@
 ; [[80ed6]]
 * Step size: 38.774{{c}}, octave size: 1202.0{{c}}
-Stretching the octave of 31edo by slightly more than 1{{c}} results in moderately improved primes 3, 7 and 11, but moderately worse primes 2, 5 and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]]... Slightly more than this - a stretch of 2.239{{c}} - is the absolute maximum amount of octave stretch 31edo can tolerate before the mapping of the 13th harmonic changes.
+Stretching the octave of 31edo by about 2{{c}} results in moderately improved primes 3 and 11, but moderately worse primes 2, 5, 7 and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]].
 {{Harmonics in equal|80|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 80ed6}}
-{{Harmonics in equal|80|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 80ed6 (continued)}
+{{Harmonics in equal|80|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 80ed6 (continued)}}
+; [[18edf]]
+* Step size: nnn{{c}}, octave size: nnn{{c}}
+Stretching the octave of 31edo by slightly more than 1{{c}} results in moderately improved primes 3 and 11, but moderately worse primes 2, 5, 7and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]]... Slightly more than this - a stretch of 2.239{{c}} - is the absolute maximum amount of octave stretch 31edo can tolerate before the mapping of the 13th harmonic changes.
+{{Harmonics in equal|18|3|2|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 18edf}}
+{{Harmonics in equal|18|3|2|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 18edf (continued)}}
+; [[49edt]]
+* Step size: nnn{{c}}, octave size: nnn{{c}}
+Stretching the octave of 31edo by slightly more than 1{{c}} results in moderately improved primes 3 and 11, but moderately worse primes 2, 5, 7and 13. This approximates all harmonics up to 16 within 15.5{{c}} Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this, so does the tuning [[111ed12]]... Slightly more than this - a stretch of 2.239{{c}} - is the absolute maximum amount of octave stretch 31edo can tolerate before the mapping of the 13th harmonic changes.
+{{Harmonics in equal|49|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 49edt}}
+{{Harmonics in equal|49|3|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 49edt (continued)}}