20480/19683: Difference between revisions

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'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It is equal to the [[256/243|Pythagorean ~~minor second~~ (256/243)]] ~~flattened by a~~ [[81/~~80|~~syntonic comma ~~(81/80)]]~~. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[~~Octave~~ reduction|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[~~Schisma~~|schisma (32805/32768)]]. Tempering it out by itself defines [[~~Archytas_clan~~#Superpyth|~~the~~ 5-limit version of superpyth temperament]]. Notable [[edo]]s that temper it out include [[~~17edo~~|17]], [[~~22edo~~|22]], and [[~~27edo~~|27]].

'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It gets its name from being equal to being one [[81/80|syntonic comma (81/80)]] flatter than the [[256/243|Pythagorean limma (256/243)]], in contrast to [[16/15]] which is a syntonic comma ''sharper'' than a Pythagorean limma.

== Temperaments ==

When treated as a [[comma]] to be [[tempering out|tempered out]], it is the '''superpyth comma''', and is the difference between [[5/4]] and an [[octave reduction|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[schisma|schisma (32805/32768)]]. Tempering it out by itself defines the [[syntonic–diatonic equivalence continuum #Superpyth (5-limit)|5-limit version of superpyth temperament]]. Notable [[edo]]s that temper it out include [[22edo|22]], [[27edo|27]], and [[49edo|49]].

== Comma pump example ==

[[File:Akselai superpyth comma pump (JI).wav|thumb|5-limit JI]]

[[File:Akselai superpyth comma pump (22edo).wav|thumb|22edo]]

The progression returns to the original chord in 22edo, but modulates downward by 20480/19683 in JI.

[[File:Superpyth comma pump.png|thumb|Superpyth comma pump in JI and 22edo.]]

[[Category:Superpyth]]

[[Category:Second]]

[[Category:Semitone]]

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-'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It is equal to the [[256/243|Pythagorean minor second (256/243)]] flattened by a [[81/80|syntonic comma (81/80)]]. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[Octave reduction|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[Schisma|schisma (32805/32768)]]. Tempering it out by itself defines [[Archytas_clan#Superpyth|the 5-limit version of superpyth temperament]]. Notable [[edo]]s that temper it out include [[17edo|17]], [[22edo|22]], and [[27edo|27]].
+'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It gets its name from being equal to being one [[81/80|syntonic comma (81/80)]] flatter than the [[256/243|Pythagorean limma (256/243)]], in contrast to [[16/15]] which is a syntonic comma ''sharper'' than a Pythagorean limma.
+== Temperaments ==
+When treated as a [[comma]] to be [[tempering out|tempered out]], it is the '''superpyth comma''', and is the difference between [[5/4]] and an [[octave reduction|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[schisma|schisma (32805/32768)]]. Tempering it out by itself defines the [[syntonic–diatonic equivalence continuum #Superpyth (5-limit)|5-limit version of superpyth temperament]]. Notable [[edo]]s that temper it out include [[22edo|22]], [[27edo|27]], and [[49edo|49]].
 == Comma pump example ==
 [[File:Akselai superpyth comma pump (JI).wav|thumb|5-limit JI]]
 [[File:Akselai superpyth comma pump (22edo).wav|thumb|22edo]]
 The progression returns to the original chord in 22edo, but modulates downward by 20480/19683 in JI.
 [[File:Superpyth comma pump.png|thumb|Superpyth comma pump in JI and 22edo.]]
+[[Category:Superpyth]]
 [[Category:Second]]
 [[Category:Semitone]]