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]].


== Gallery of equal divisions ==
== 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 ===
; … of a given cents value
* [[65cET]]
* [[65cET]]
* [[88cET]]
* [[88cET]]
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* [[125cET]]
* [[125cET]]


=== … of a rational interval ===
; … 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]]