Equal-step tuning: Difference between revisions
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For the mathematically inclined, this kind of diagram is closely related to [[The_Riemann_Zeta_Function_and_Tuning|the Riemann zeta function]]. | For the mathematically inclined, this kind of diagram is closely related to [[The_Riemann_Zeta_Function_and_Tuning|the Riemann zeta function]]. | ||
== | == Catalog of equal-step tunings == | ||
=== Equal divisions === | |||
* [[Ed16/15]] (… of the classic diatonic semitone) | * [[Ed16/15]] (… of the classic diatonic semitone) | ||
** 8 – [[Delta scale]] (8ed16/15) | ** 8 – [[Delta scale]] (8ed16/15) | ||
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* [[Ed13]] (… of the 13th harmonic) | * [[Ed13]] (… of the 13th harmonic) | ||
== Equal multiplications == | === Equal multiplications === | ||
An equal multiplication of a rational interval can also be called an [[AS|ambitonal sequence (AS)]]. For example, the 25/24 equal-step tuning could also be written AS25/24. An equal multiplication of an irrational interval can also be called an [[APS|arithmetic pitch sequence (APS)]]. For example, the 65cET could also be written APS65c. The union of both is equivalent to the unity division of a target interval. For example, 25/24 is 1ed25/24, and 65cET is 1ed65¢. | An equal multiplication of a rational interval can also be called an [[AS|ambitonal sequence (AS)]]. For example, the 25/24 equal-step tuning could also be written AS25/24. An equal multiplication of an irrational interval can also be called an [[APS|arithmetic pitch sequence (APS)]]. For example, the 65cET could also be written APS65c. The union of both is equivalent to the unity division of a target interval. For example, 25/24 is 1ed25/24, and 65cET is 1ed65¢. | ||
; … of a given cents value | |||
* [[65cET]] | * [[65cET]] | ||
* [[88cET]] | * [[88cET]] | ||
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* [[125cET]] | * [[125cET]] | ||
; … of a rational interval | |||
* [[8/7 equal-step tuning]] – multiples of [[8/7]] | * [[8/7 equal-step tuning]] – multiples of [[8/7]] | ||
* [[9/8 equal-step tuning]] – multiples of [[9/8]] | * [[9/8 equal-step tuning]] – multiples of [[9/8]] | ||