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)~~]]. In fact, these temperaments are exactly the set of all 5-[[limit]] temperaments supported by [[7edo~~]].

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…

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Also fractional values of ''n'': [[enipucrop]] (''n'' = 1.5), [[seville]] (''n'' = 2.{{overline|3}}), [[sixix]] (''n'' = 2.5), [[sevond]] (''n'' = 3.5), [[brahmagupta]] (''n'' = 5.25).

Also fractional values of ''n'': [[enipucrop]] (''n'' = 1.5), [[seville]] (''n'' = 2.{{overline|3}}), [[sixix]] (''n'' = 2.5), [[sevond]] (''n'' = 3.5), [[brahmagupta]] (''n'' = 5.25). If we allow non-integer ''n'', the continuum describe the set of all 5-[[limit]] temperaments supported by [[7edo]].

== Absurdity ==

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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)]]. In fact, these temperaments are exactly the set of all 5-[[limit]] temperaments supported by [[7edo]].
+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…
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 |}
-Also fractional values of ''n'': [[enipucrop]] (''n'' = 1.5), [[seville]] (''n'' = 2.{{overline|3}}), [[sixix]] (''n'' = 2.5), [[sevond]] (''n'' = 3.5), [[brahmagupta]] (''n'' = 5.25).
+Also fractional values of ''n'': [[enipucrop]] (''n'' = 1.5), [[seville]] (''n'' = 2.{{overline|3}}), [[sixix]] (''n'' = 2.5), [[sevond]] (''n'' = 3.5), [[brahmagupta]] (''n'' = 5.25).  If we allow non-integer ''n'', the continuum describe the set of all 5-[[limit]] temperaments supported by [[7edo]].
 == Absurdity ==