59edo: Difference between revisions

Line 122:

; [[zpi|295zpi]]

* Step size: 20.342{{c}}, octave size: 1200.18{{c}}

Stretching the octave of 59edo by around a fifth of a cent results in slightly improved primes 11 and 13, but slightly worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 9.97{{c}}. The tuning 294zpi does this. 294zpi shares error equally between the two mappings of harmonic 3, so it is the best [[dual fifth]] option for 59edo.

Stretching the octave of 59edo by around a fifth of a cent results in slightly improved primes 11 and 13, but slightly worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 9.97{{c}}. The tuning 294zpi does this. 294zpi shares error equally between the two mappings of harmonic 3, so it is the best [[dual-fifth]] option for 59edo.

{{Harmonics in cet|20.342|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 295zpi}}

{{Harmonics in cet|20.342|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 295zpi (continued)}}

Line 144:

{{Harmonics in cet|20.301|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 59et, 7-limit WE tuning (continued)}}

; [[166ed7]]

; [[ed7|166ed7]]

* Octave size: 1197.35{{c}}

Compressing the octave of 59edo by around 2.5{{c}} results in improved primes 3, 7 and 13, but worse primes 2, 5 and 11. This approximates all harmonics up to 16 within 9.71{{c}}. The tuning 166ed7 does this.

Line 150:

{{Harmonics in equal|166|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 166ed7 (continued)}}

; [[212ed12]]

; [[ed12|212ed12]]

* Octave size: 1197.24{{c}}

Compressing the octave of 59edo by around 3{{c}} results in improved primes 3, 7 and 13, but worse primes 2, 5 and 11. This approximates all harmonics up to 16 within 9.26{{c}}. The tuning 212ed12 does this.

@@ Line 122: / Line 122: @@
 ; [[zpi|295zpi]]
 * Step size: 20.342{{c}}, octave size: 1200.18{{c}}
-Stretching the octave of 59edo by around a fifth of a cent results in slightly improved primes 11 and 13, but slightly worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 9.97{{c}}. The tuning 294zpi does this. 294zpi shares error equally between the two mappings of harmonic 3, so it is the best [[dual fifth]] option for 59edo.
+Stretching the octave of 59edo by around a fifth of a cent results in slightly improved primes 11 and 13, but slightly worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 9.97{{c}}. The tuning 294zpi does this. 294zpi shares error equally between the two mappings of harmonic 3, so it is the best [[dual-fifth]] option for 59edo.
 {{Harmonics in cet|20.342|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 295zpi}}
 {{Harmonics in cet|20.342|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 295zpi (continued)}}
@@ Line 144: / Line 144: @@
 {{Harmonics in cet|20.301|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 59et, 7-limit WE tuning (continued)}}
-; [[166ed7]]
+; [[ed7|166ed7]]
 * Octave size: 1197.35{{c}}
 Compressing the octave of 59edo by around 2.5{{c}} results in improved primes 3, 7 and 13, but worse primes 2, 5 and 11. This approximates all harmonics up to 16 within 9.71{{c}}. The tuning 166ed7 does this.
@@ Line 150: / Line 150: @@
 {{Harmonics in equal|166|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 166ed7 (continued)}}
-; [[212ed12]]
+; [[ed12|212ed12]]
 * Octave size: 1197.24{{c}}
 Compressing the octave of 59edo by around 3{{c}} results in improved primes 3, 7 and 13, but worse primes 2, 5 and 11. This approximates all harmonics up to 16 within 9.26{{c}}. The tuning 212ed12 does this.