Keemic temperaments: Difference between revisions
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This is a collection of [[rank-2 temperament|linear]] [[regular temperament|temperaments]] that [[tempering out|temper out]] the [[keema]] ({{monzo|legend=1| -5 -3 3 1 }}, [[ratio]]: 875/864), with [[S-expression]] S5/S6. Its fundamental equivalence entails that [[6/5]] is sharpened so that it stacks three times to reach [[7/4]], and the interval between 6/5 and [[5/4]] is compressed so that [[7/6]]–6/5–5/4–[[9/7]] are set equidistant from each other. As the canonical extension of rank-3 [[keemic]] to the [[11-limit]] tempers out the commas [[100/99]] and [[385/384]] (whereby ([[6/5]])<sup>2</sup> is identified with [[16/11]]), this provides a clean way to extend the various keemic temperaments to the 11-limit as well. | This is a collection of [[rank-2 temperament|linear]] [[regular temperament|temperaments]] that [[tempering out|temper out]] the [[keema]] ({{monzo|legend=1| -5 -3 3 1 }}, [[ratio]]: 875/864), with [[S-expression]] S5/S6. Its fundamental equivalence entails that [[6/5]] is sharpened so that it stacks three times to reach [[7/4]], and the interval between 6/5 and [[5/4]] is compressed so that [[7/6]]–6/5–5/4–[[9/7]] are set equidistant from each other. As the canonical extension of rank-3 [[keemic]] to the [[11-limit]] tempers out the commas [[100/99]] and [[385/384]] (whereby ([[6/5]])<sup>2</sup> is identified with [[16/11]]), this provides a clean way to extend the various keemic temperaments to the 11-limit as well. | ||
Full [[7-limit]] keemic temperaments discussed elsewhere are: | Full [[7-limit]] keemic temperaments discussed elsewhere are: | ||
* [[Flattone]] (+81/80) → [[Meantone family #Flattone|Meantone family]] | |||
* [[Porcupine]] (+64/63) → [[Porcupine family #Septimal porcupine|Porcupine family]] | |||
* [[Monkey]] (+5120/5103) → [[Tetracot family #Monkey|Tetracot family]] | |||
* [[Magic]] (+225/224) → [[Magic family #Septimal magic|Magic family]] | |||
* [[Keemun]] (+49/48) → [[Kleismic family #Keemun|Kleismic family]] | * [[Keemun]] (+49/48) → [[Kleismic family #Keemun|Kleismic family]] | ||
* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]] | * ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]] | ||
* [[ | * [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic|Gamelismic clan]] | ||
* ''[[Sycamore]]'' (+686/675) → [[Sycamore family #Septimal sycamore|Sycamore family]] | * ''[[Sycamore]]'' (+686/675) → [[Sycamore family #Septimal sycamore|Sycamore family]] | ||
* ''[[Undeka]]'' (+3200/3087) → [[11th-octave temperaments #Undeka|11th-octave temperaments]] | * ''[[Undeka]]'' (+3200/3087) → [[11th-octave temperaments #Undeka|11th-octave temperaments]] | ||
Discussed below are quasitemp, chromo, barbad, hyperkleismic, and sevond. | Discussed below are quasitemp, chromo, barbad, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]]. | ||
== Quasitemp == | == Quasitemp == | ||