Syntonic–diatonic equivalence continuum: Difference between revisions
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== University == | == University == | ||
: ''For extensions, see [[Gamelismic clan #Gidorah]] and [[Mint temperaments #Penta]].'' | : ''For extensions, see [[Gamelismic clan #Gidorah]] and [[Mint temperaments #Penta]].'' | ||
Named by [[John Moriarty]], university is the {{nowrap| 5 & 6b }} temperament, and tempers out [[144/125]], the triptolemaic diminished third. It corresponds to {{nowrap| ''n'' {{=}} −3/2 }} and {{nowrap| ''m'' {{=}} 3/5 }}. In this temperament, two instances of [[6/5]] make a [[5/4]], and three make a [[3/2]]. Equating 6/5 with [[8/7]] (which makes sense since it is already very flat in the most accurate tunings of this temperament) leads to [[Gamelismic clan #Gidorah|gidorah]], and 6/5 with [[7/6]] leads to [[Mint temperaments #Penta|penta]]. | Named by [[John Moriarty]], university is the {{nowrap| 5 & 6b }} temperament, and tempers out [[144/125]], the triptolemaic diminished third. It corresponds to {{nowrap| ''n'' {{=}} −3/2 }} and {{nowrap| ''m'' {{=}} 3/5 }}. In this temperament, two instances of [[6/5]] make a [[5/4]], and three make a [[3/2]]. Equating 6/5 with [[8/7]] (which makes sense since it is already very flat in the most accurate tunings of this temperament) leads to [[Gamelismic clan #Gidorah|gidorah]], and 6/5 with [[7/6]] leads to [[Mint temperaments #Penta|penta]]. | ||
University widens the classical major and minor chords to [[Extraclassical tonality|tendo and arto chords.]] | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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[[Badness]] (Sintel): 2.39 | [[Badness]] (Sintel): 2.39 | ||
=== Music === | |||
The purely 5-limit university mapping, using the 21cc [[val]], was in mind when writing this song. | |||
; [[John Moriarty]] | |||
* [https://soundcloud.com/john-lank1/uni ''Uni''] (2013) – University[6] in approximately 21edo | |||
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[http://x31eq.com/cgi-bin/rt.cgi?ets=5_56&limit=5 The temperament finder - 5-limit 5 & 56] | [http://x31eq.com/cgi-bin/rt.cgi?ets=5_56&limit=5 The temperament finder - 5-limit 5 & 56] | ||
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== Hemiseven (5-limit) == | == Hemiseven (5-limit) == | ||
: ''For extensions, see [[Gamelismic clan #Hemiseven]].'' | : ''For extensions, see [[Gamelismic clan #Hemiseven]].'' | ||