72edo: Difference between revisions

Line 1,541:

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

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

Stretching the octave of 72edo by around 1.25{{c}} results in a [[JND|just-noticeably]] better primes 13 and unnoticeably 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)}}

; [[42edf]]

* Step size: 16.713{{c}}, octave size: 1203.35{{c}}

Stretching the octave of 72edo by around 3{{c}} results in better primes 13, 19 and 23, but worse primes 2, 3, 5, 7, 11 and 17. This approximates all harmonics up to 16 within 8.14{{c}}. The tuning 42edf does this.

{{Harmonics in equal|42|3|2|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 42edf}}

{{Harmonics in equal|42|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 42edf (continued)}}

== Scales ==

@@ Line 1,541: / Line 1,541: @@
 ; [[114edt]] / [[ed5|167ed5]]
 * Step size: 16.684{{c}}, octave size: 1201.23{{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}}.
+Stretching the octave of 72edo by around 1.25{{c}} results in a [[JND|just-noticeably]] better primes 13 and unnoticeably 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)}}
+; [[42edf]]
+* Step size: 16.713{{c}}, octave size: 1203.35{{c}}
+Stretching the octave of 72edo by around 3{{c}} results in better primes 13, 19 and 23, but worse primes 2, 3, 5, 7, 11 and 17. This approximates all harmonics up to 16 within 8.14{{c}}. The tuning 42edf does this.
+{{Harmonics in equal|42|3|2|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 42edf}}
+{{Harmonics in equal|42|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 42edf (continued)}}
 == Scales ==