20480/19683: Difference between revisions

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{{Infobox Interval|Name=superpyth comma|Color name=sayo 2nd, ~~sayo~~ comma}}

{{Infobox Interval

| Name = retroptolemaic minor second, superpyth comma

| Color name = sayo 2nd, sy2, Sayo comma

}}

'''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.

~~20480/19683~~, the superpyth comma, is the difference between 5/4 and an [[~~Octave~~ reduction|octave-reduced]] stack of nine 3/2s, as well as 25/24 minus a [[schisma]] (32805/32768). Tempering it out by itself defines the 5-limit version of [[superpyth]] ~~temperament~~. Notable [[~~EDO|EDOs~~]] that temper it out include [[~~17edo~~|17]], [[~~22edo~~|22]], and [[~~27edo~~|27]].

== 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]]

@@ Line 1: / Line 1: @@
-{{Infobox Interval|Name=superpyth comma|Color name=sayo 2nd, sayo comma}}
+{{Infobox Interval
+| Name = retroptolemaic minor second, superpyth comma
+| Color name = sayo 2nd, sy2, Sayo comma
+}}
+'''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.
-/19683, the superpyth comma, is the difference between 5/4 and an [[Octave reduction|octave-reduced]] stack of nine 3/2s, as well as 25/24 minus a [[schisma]] (32805/32768). Tempering it out by itself defines the 5-limit version of [[superpyth]] temperament. Notable [[EDO|EDOs]] that temper it out include [[17edo|17]], [[22edo|22]], and [[27edo|27]].
+== 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]]