38edo: Difference between revisions

Line 380:

; [[WE|38et, 13-limit WE tuning]]

* Step size: 31.599{{c}}, octave size: 1200.77{{c}}

Stretching the octave of 38edo by around 1{{c}} results in improved primes 3, 5 and 11, but worse primes 2, 7 and 13. This approximates all harmonics up to 16 within 14.9{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.

Stretching the octave of 38edo by around 1{{c}} results in improved primes 3, 5, 11, 17 and 19, but worse primes 2, 7 and 13. This approximates all harmonics up to 16 within 14.9{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.

{{Harmonics in cet|31.599|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 38et, 13-limit WE tuning}}

{{Harmonics in cet|31.599|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 38et, 13-limit WE tuning (continued)}}

Line 386:

; [[ed5|88ed5]]

* Step size: 31.663{{c}}, octave size: 1203.18{{c}}

Stretching the octave of 38edo by around 3{{c}} results in improved primes 3, 5, 11 ~~and~~ 13, but worse primes 2 and 7. This approximates all harmonics up to 16 within 12.7{{c}}. The tuning 88ed5 does this.

Stretching the octave of 38edo by around 3{{c}} results in improved primes 3, 5, 11, 13, 17 and 19 but worse primes 2 and 7. This approximates all harmonics up to 16 within 12.7{{c}}. The tuning 88ed5 does this.

{{Harmonics in equal|88|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 88ed5}}

{{Harmonics in equal|88|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 88ed5 (continued)}}

Line 392:

; [[zpi|166zpi]]

* Step size: 31.671{{c}}, octave size: 1203.48{{c}}

Stretching the octave of 38edo by around 3.5{{c}} results in improved primes 3, 5, 11 and 13, but worse primes 2 and 7. This approximates all harmonics up to 16 within 14.0{{c}}. The tuning 166zpi does this.

Stretching the octave of 38edo by around 3.5{{c}} results in improved primes 3, 5, 11, 13, 17 and 19, but worse primes 2 and 7. This approximates all harmonics up to 16 within 14.0{{c}}. The tuning 166zpi does this.

{{Harmonics in cet|31.671|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 166zpi}}

{{Harmonics in cet|31.671|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 166zpi (continued)}}

@@ Line 380: / Line 380: @@
 ; [[WE|38et, 13-limit WE tuning]]
 * Step size: 31.599{{c}}, octave size: 1200.77{{c}}
-Stretching the octave of 38edo by around 1{{c}} results in improved primes 3, 5 and 11, but worse primes 2, 7 and 13. This approximates all harmonics up to 16 within 14.9{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
+Stretching the octave of 38edo by around 1{{c}} results in improved primes 3, 5, 11, 17 and 19, but worse primes 2, 7 and 13. This approximates all harmonics up to 16 within 14.9{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
 {{Harmonics in cet|31.599|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 38et, 13-limit WE tuning}}
 {{Harmonics in cet|31.599|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 38et, 13-limit WE tuning (continued)}}
@@ Line 386: / Line 386: @@
 ; [[ed5|88ed5]]
 * Step size: 31.663{{c}}, octave size: 1203.18{{c}}
-Stretching the octave of 38edo by around 3{{c}} results in improved primes 3, 5, 11 and 13, but worse primes 2 and 7. This approximates all harmonics up to 16 within 12.7{{c}}. The tuning 88ed5 does this.
+Stretching the octave of 38edo by around 3{{c}} results in improved primes 3, 5, 11, 13, 17 and 19 but worse primes 2 and 7. This approximates all harmonics up to 16 within 12.7{{c}}. The tuning 88ed5 does this.
 {{Harmonics in equal|88|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 88ed5}}
 {{Harmonics in equal|88|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 88ed5 (continued)}}
@@ Line 392: / Line 392: @@
 ; [[zpi|166zpi]]
 * Step size: 31.671{{c}}, octave size: 1203.48{{c}}
-Stretching the octave of 38edo by around 3.5{{c}} results in improved primes 3, 5, 11 and 13, but worse primes 2 and 7. This approximates all harmonics up to 16 within 14.0{{c}}. The tuning 166zpi does this.
+Stretching the octave of 38edo by around 3.5{{c}} results in improved primes 3, 5, 11, 13, 17 and 19, but worse primes 2 and 7. This approximates all harmonics up to 16 within 14.0{{c}}. The tuning 166zpi does this.
 {{Harmonics in cet|31.671|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 166zpi}}
 {{Harmonics in cet|31.671|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 166zpi (continued)}}