22edo: Difference between revisions

Line 1,470:

; [[57ed6]]

* Step size: 54.420{{c}}, octave size: 1197.2{{c}}

Compressing the octave of 22edo by around 3{{c}} results in greatly improved primes 3 and 7, but far worse primes 5 and 11 and a [[JND|just noticeably worse]] 2. The mapping of 13 differs from 22edo but has about the same amount of error. This approximates all harmonics up to 16 within 21.9{{c}}. With its worse 5 and 11, it only really makes sense as a [[2.3.7]] tuning, eg for [[archy]] (2.37 superpyth) temperament. The tuning 57ed6 does this.

Compressing the octave of 22edo by around 3{{c}} results in greatly improved primes 3 and 7, but far worse primes 5 and 11 and a [[JND|just noticeably worse]] 2. The mapping of 13 differs from 22edo but has about the same amount of error. This approximates all harmonics up to 16 within 21.9{{c}}. With its worse 5 and 11, it only really makes sense as a [[2.3.7]] tuning, eg for [[archy]] (2.3.7 superpyth) temperament. The tuning 57ed6 does this.

{{Harmonics in equal|57|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 57ed6}}

{{Harmonics in equal|57|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 57ed6 (continued)}}

@@ Line 1,470: / Line 1,470: @@
 ; [[57ed6]]
 * Step size: 54.420{{c}}, octave size: 1197.2{{c}}
-Compressing the octave of 22edo by around 3{{c}} results in greatly improved primes 3 and 7, but far worse primes 5 and 11 and a [[JND|just noticeably worse]] 2. The mapping of 13 differs from 22edo but has about the same amount of error. This approximates all harmonics up to 16 within 21.9{{c}}. With its worse 5 and 11, it only really makes sense as a [[2.3.7]] tuning, eg for [[archy]] (2.37 superpyth) temperament. The tuning 57ed6 does this.
+Compressing the octave of 22edo by around 3{{c}} results in greatly improved primes 3 and 7, but far worse primes 5 and 11 and a [[JND|just noticeably worse]] 2. The mapping of 13 differs from 22edo but has about the same amount of error. This approximates all harmonics up to 16 within 21.9{{c}}. With its worse 5 and 11, it only really makes sense as a [[2.3.7]] tuning, eg for [[archy]] (2.3.7 superpyth) temperament. The tuning 57ed6 does this.
 {{Harmonics in equal|57|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 57ed6}}
 {{Harmonics in equal|57|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 57ed6 (continued)}}