22edo: Difference between revisions

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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 1,476:

; [[35edt]]

* Step size: 54.342{{c}}, octave size: 1195.5{{c}}

Compressing the octave of 22edo by around 4.5{{c}} results in greatly improved primes 3, 7 and 13, but far worse primes 5 and 11 and a ~~[[JND|just noticeably~~ worse]] 2. This approximates all harmonics up to 16 within 21.4{{c}}. The tunings 35edt and [[equal tuning|62ed7]] both do this. This extends 57ed6's 2.3.7 tuning into a 2.3.7.13 [[subgroup]] tuning.

Compressing the octave of 22edo by around 4.5{{c}} results in greatly improved primes 3, 7 and 13, but far worse primes 5 and 11 and a moderately worse 2. This approximates all harmonics up to 16 within 21.4{{c}}. The tunings 35edt and [[equal tuning|62ed7]] both do this. This extends 57ed6's 2.3.7 tuning into a 2.3.7.13 [[subgroup]] tuning.

{{Harmonics in equal|35|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 35edt}}

{{Harmonics in equal|35|3|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 35edt (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)}}
@@ Line 1,476: / Line 1,476: @@
 ; [[35edt]]
 * Step size: 54.342{{c}}, octave size: 1195.5{{c}}
-Compressing the octave of 22edo by around 4.5{{c}} results in greatly improved primes 3, 7 and 13, but far worse primes 5 and 11 and a [[JND|just noticeably worse]] 2. This approximates all harmonics up to 16 within 21.4{{c}}. The tunings 35edt and [[equal tuning|62ed7]] both do this. This extends 57ed6's 2.3.7 tuning into a 2.3.7.13 [[subgroup]] tuning.
+Compressing the octave of 22edo by around 4.5{{c}} results in greatly improved primes 3, 7 and 13, but far worse primes 5 and 11 and a moderately worse 2. This approximates all harmonics up to 16 within 21.4{{c}}. The tunings 35edt and [[equal tuning|62ed7]] both do this. This extends 57ed6's 2.3.7 tuning into a 2.3.7.13 [[subgroup]] tuning.
 {{Harmonics in equal|35|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 35edt}}
 {{Harmonics in equal|35|3|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 35edt (continued)}}