Syntonic–chromatic equivalence continuum: Difference between revisions
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The '''syntonic-chromatic equivalence continuum''' is a continuum of temperaments which equate a number of [[81/80|syntonic commas (81/80)]] with the [[2187/2048|apotome (2187/2048)]]. | The '''syntonic-chromatic equivalence continuum''' is a continuum of temperaments which equate a number of [[81/80|syntonic commas (81/80)]] with the [[2187/2048|apotome (2187/2048)]]. | ||
All temperaments in the continuum satisfy (81/80)<sup>''n''</sup> ~ 2187/2048. Varying ''n'' results in different temperaments such as [[whitewood]], [[mavila]], [[dicot]], [[porcupine]], [[tetracot]], [[amity]], [[gravity]], and [[absurdity]]. It converges to [[meantone]] as ''n'' approaches infinity. The just value of ''n'' is 5.2861… | All temperaments in the continuum satisfy (81/80)<sup>''n''</sup> ~ 2187/2048. Varying ''n'' results in different temperaments such as [[whitewood]], [[mavila]], [[dicot]], [[porcupine]], [[tetracot]], [[amity]], [[gravity]], and [[absurdity]]. It converges to [[meantone]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 5-[[limit]] temperaments supported by [[7edo]]. The just value of ''n'' is 5.2861… | ||
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Also fractional values of ''n'': [[ | Also fractional values of ''n'': | ||
* [[Enipucrop]] (''n'' = 1.5) | |||
* [[Seville]] (''n'' = 7/3 = 2.{{overline|3}}) | |||
* [[Sixix]] (''n'' = 2.5) | |||
* [[Sevond]] (''n'' = 3.5) | |||
* [[Brahmagupta]] (''n'' = 21/4 = 5.25) | |||
* [[Raider]] (''n'' = 37/7 = 5.{{overline|285714}}) | |||
== Absurdity == | == Absurdity == | ||