72edo: Difference between revisions

Line 1,529:

; [[zpi|380zpi]]

* Step size: 16.678{{c}}, octave size: 1200.82{{c}}

Stretching the octave of 72edo by around 0.8{{c}} results in [[JND|~~unnoticeably~~]] better primes 3, 5, 7 ~~and 13~~, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 4.18{{c}}. The tuning 380zpi does this.

Stretching the octave of 72edo by around 0.8{{c}} results in a [[JND|just-noticeably]] better primes 13 and unnoticeable better primes 3, 5, and 7, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 4.18{{c}}. The tuning 380zpi does this.

{{Harmonics in cet|16.678|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 380zpi}}

{{Harmonics in cet|16.678|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 380zpi (continued)}}

Line 1,535:

; [[WE|72et, 13-limit WE tuning]]

* Step size: 16.680{{c}}, octave size: 1200.96{{c}}

Stretching the octave of 72edo by around 1{{c}} results in [[JND|~~unnoticeably~~]] better primes 3, 5, 7 ~~and 13~~, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 3.84{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.

Stretching the octave of 72edo by around 1{{c}} results in a [[JND|just-noticeably]] better primes 13 and unnoticeable better primes 3, 5, and 7, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 3.84{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.

{{Harmonics in cet|16.680|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 72et, 13-limit WE tuning}}

{{Harmonics in cet|16.680|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 72et, 13-limit WE tuning (continued)}}

Line 1,541:

; [[114edt]] / [[167ed5]]

* Step size: 16.684{{c}}, octave size: 1201.23{{c}}

Stretching the octave of 72edo by around 1.25{{c}} results in [[JND|~~unnoticeably~~]] better primes 3, 5, 7 ~~and 13~~, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 4.94{{c}}. The tuning 144edt does this. The tuning 167ed5 does this also, its octave differing from 114edt by only 0.05{{c}}.

Stretching the octave of 72edo by around 1.25{{c}} results in a [[JND|just-noticeably]] better primes 13 and unnoticeable better primes 3, 5, and 7, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 4.94{{c}}. The tuning 144edt does this. The tuning 167ed5 does this also, its octave differing from 114edt by only 0.05{{c}}.

{{Harmonics in equal|114|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 114edt}}

{{Harmonics in equal|114|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 114edt (continued)}}

@@ Line 1,529: / Line 1,529: @@
 ; [[zpi|380zpi]]
 * Step size: 16.678{{c}}, octave size: 1200.82{{c}}
-Stretching the octave of 72edo by around 0.8{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7 and 13, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 4.18{{c}}. The tuning 380zpi does this.
+Stretching the octave of 72edo by around 0.8{{c}} results in a [[JND|just-noticeably]] better primes 13 and unnoticeable better primes 3, 5, and 7, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 4.18{{c}}. The tuning 380zpi does this.
 {{Harmonics in cet|16.678|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 380zpi}}
 {{Harmonics in cet|16.678|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 380zpi (continued)}}
@@ Line 1,535: / Line 1,535: @@
 ; [[WE|72et, 13-limit WE tuning]]
 * Step size: 16.680{{c}}, octave size: 1200.96{{c}}
-Stretching the octave of 72edo by around 1{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7 and 13, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 3.84{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
+Stretching the octave of 72edo by around 1{{c}} results in a [[JND|just-noticeably]] better primes 13 and unnoticeable better primes 3, 5, and 7, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 3.84{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
 {{Harmonics in cet|16.680|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 72et, 13-limit WE tuning}}
 {{Harmonics in cet|16.680|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 72et, 13-limit WE tuning (continued)}}
@@ Line 1,541: / Line 1,541: @@
 ; [[114edt]] / [[167ed5]]
 * Step size: 16.684{{c}}, octave size: 1201.23{{c}}
-Stretching the octave of 72edo by around 1.25{{c}} results in [[JND|unnoticeably]] better primes 3, 5, 7 and 13, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 4.94{{c}}. The tuning 144edt does this. The tuning 167ed5 does this also, its octave differing from 114edt by only 0.05{{c}}.
+Stretching the octave of 72edo by around 1.25{{c}} results in a [[JND|just-noticeably]] better primes 13 and unnoticeable better primes 3, 5, and 7, but unnoticeably worse primes 2 and 11. This approximates all harmonics up to 16 within 4.94{{c}}. The tuning 144edt does this. The tuning 167ed5 does this also, its octave differing from 114edt by only 0.05{{c}}.
 {{Harmonics in equal|114|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 114edt}}
 {{Harmonics in equal|114|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 114edt (continued)}}