Equal-step tuning: Difference between revisions
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'''As there are infinite intervals, there are infinite equal scales.''' Barring technicalities, there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings [[ET_surveys|sequentially]] or [[Polymicrotonality|simultaneously]]. | '''As there are infinite intervals, there are infinite equal scales.''' Barring technicalities, there are large quantities of perceivably different equal scales. Seeing such a diverse menagerie at their disposal, some composers choose to combine multiple equal tunings [[ET_surveys|sequentially]] or [[Polymicrotonality|simultaneously]]. | ||
==Simultaneous equal divisions== | == Simultaneous equal divisions == | ||
What do 12ED2, 19ED3, and 28ED5 all have in common? They're all approximately the same scale. This happens because 12ED2 is an accurate temperament (for its size) that contains relatively close approximations of 3/1 and 5/1. In contrast, 11ED2 does not correspond closely to any equal division of 3/1 or 5/1. | What do 12ED2, 19ED3, and 28ED5 all have in common? They're all approximately the same scale. This happens because 12ED2 is an accurate temperament (for its size) that contains relatively close approximations of 3/1 and 5/1. In contrast, 11ED2 does not correspond closely to any equal division of 3/1 or 5/1. | ||
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== Gallery of equal divisions == | == Gallery of equal divisions == | ||
=== [[EdVI through edX|…of sixths through tenths]] === | ===[[EdVI through edX|…of sixths through tenths]]=== | ||
* [[EdVI|'''…of sixths (e. g. 5/3 and 11/7)''']] | * [[EdVI|'''…of sixths (e. g. 5/3 and 11/7)''']] | ||
* [[EdVII|'''…of sevenths (e. g. 9/5)''']] | * [[EdVII|'''…of sevenths (e. g. 9/5)''']] | ||
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* [[Ed13|'''...of the 13th Natural (13/1)''']] | * [[Ed13|'''...of the 13th Natural (13/1)''']] | ||
=== [[EdV|...of fifths (e. g. 3/2 and 13/9)]] === | ===[[EdV|...of fifths (e. g. 3/2 and 13/9)]]=== | ||
* [[EDF|'''...of the Perfect Fifth (3/2)''']] | * [[EDF|'''...of the Perfect Fifth (3/2)''']] | ||
** most famously Carlos Alpha, Beta and Gamma, but lots of others, too | ** most famously Carlos Alpha, Beta and Gamma, but lots of others, too | ||
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** 8 - [[8ed10/7|Eighth root of 10 over 7]] | ** 8 - [[8ed10/7|Eighth root of 10 over 7]] | ||
=== [[EdIV|...of fourths (e. g. 4/3 and 15/11)]] === | ===[[EdIV|...of fourths (e. g. 4/3 and 15/11)]]=== | ||
* '''...of the Perfect Fourth (4/3)''' | * '''...of the Perfect Fourth (4/3)''' | ||
** 3 - [[Cube_Root_of_P4|Cube root of 4/3]] | ** 3 - [[Cube_Root_of_P4|Cube root of 4/3]] | ||
** 5 - [[ | ** 5 - [[Quintilipyth]] scale | ||
** 6 - [[ | ** 6 - [[Sextilipyth]] scale | ||
** 9 - [[Noleta]] scale | ** 9 - [[Noleta]] scale | ||
* '''...of the Septimal Narrow Tritone (7/5)''' | * '''...of the Septimal Narrow Tritone (7/5)''' | ||
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** [[33/32s equal temperament]] - multiples of [[33/32]] | ** [[33/32s equal temperament]] - multiples of [[33/32]] | ||
** [[36/35s equal temperament]] - multiples of [[36/35]] | ** [[36/35s equal temperament]] - multiples of [[36/35]] | ||
* '''...of sixth tones''' | |||
** [[49/48s equal temperament]] - multiples of [[49/48]] | |||
** [[50/49s equal temperament]] - multiples of [[50/49]] | |||
* '''...of various commas''' | |||
** [[64/63s equal temperament]] - multiples of [[64/63]] | |||
** [[81/80s equal temperament]] - multiples of [[81/80]] | |||
== See also == | == See also == | ||
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* [[AS|AS (ambitonal sequence)]] | * [[AS|AS (ambitonal sequence)]] | ||
* [[EPD|EPD (equal pitch division)]] | * [[EPD|EPD (equal pitch division)]] | ||
* [[The Riemann Zeta Function and Tuning]] | * [[The Riemann Zeta Function and Tuning]] | ||
[[Category:Equal-step tuning| ]] <!-- main article --> | |||
[[Category:Tuning]] | [[Category:Tuning]] | ||
[[Category:Temperament]] | [[Category:Temperament]] | ||