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 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]]. | ||
== 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:Second]] | [[Category:Second]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||