60edo: Difference between revisions
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== Scales == | == Scales == | ||
* [[5- to 10-tone scales in 60edo]] | * [[5- to 10-tone scales in 60edo]] | ||
== Nearby equal-step tunings == | |||
There are a few other useful [[equal-step tuning]]s which occur close to 60edo in step size: | |||
; 168ed7, 207ed11 | |||
The tunings [[168ed7]] and [[207ed11]] are almost identical. Each is [[60edo]] but with slightly ''[[Octave stretch|stretched]]'' octaves. | |||
Each causes relatively large improvement to [[5/1]], [[7/1]] and [[11/1]] at the cost of moderate worsening of [[2/1]] and [[3/1]]. | |||
Each also causes the [[val]]s to flip for [[11/1]] and [[13/1]]. | |||
{{Harmonics in equal|207|11|1|intervals=prime|columns=11|collapsed=1}} | |||
{{Harmonics in equal|168|7|1|intervals=prime|columns=11|collapsed=1}} | |||
; 301zpi | |||
The tuning [[301zpi]], the 301st [[zeta peak index]], is [[60edo]] but with slightly ''[[Octave stretch|stretched]]'' octaves. | |||
It causes relatively large improvement to [[3/1]], [[5/1]], [[7/1]], [[11/1]] and [[17/1]] at the cost of relatively small worsening of [[2/1]] and relatively large worsening of [[3/1]]. | |||
It also causes the [[val]] for [[11/1]] to flip from 208 steps to 207 steps. | |||
301zpi is both [[consistent]] and [[distinctly consistent]] up to the 10-[[integer-limit]], which is unusually high for a two digit edo or three digit zpi. | |||
{{Harmonics in equal|1|38083|37645| 20.0266469020418 |intervals=prime|columns=11|title= Approximation of prime harmonics in 301zpi|collapsed=1}} | |||
; 60edo | |||
{{Harmonics in equal|60|2|1|intervals=prime|columns=11|collapsed=1}} | |||
; 255ed19 | |||
The tuning [[255ed19]] is [[60edo]] but with slightly ''[[Octave shrinking|compressed]]'' octaves. | |||
It causes a relatively large improvement to [[11/1]], at the cost of relatively small worsening of every smaller prime. | |||
It also causes the [[val]] for [[7/1]] to flip from 168 steps to 169. | |||
{{Harmonics in equal|255|19|1|intervals=prime|columns=11|collapsed=1}} | |||
; 208ed11 | |||
The tuning [[208ed11]] is [[60edo]] but with slightly ''[[Octave shrinking|compressed]]'' octaves. | |||
It causes a relatively large improvement to [[7/1]] and [[11/1]], at the cost of moderate worsening of [[2/1]], [[3/1]] and [[5/1]]. | |||
It also causes the [[val]]s to flip for [[5/1]], [[7/1]] and [[17/1]]. | |||
These characteristics are ideal for [[catnip]] temperament, so 208ed11 can be thought of as a 60edo clone tailor-made for catnip. | |||
{{Harmonics in equal|208|11|1|intervals=prime|columns=11|collapsed=1}} | |||
== Instruments == | == Instruments == | ||