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]] | ||
Revision as of 13:55, 23 March 2024
| Interval information |
superpyth comma
20480/19683, the retroptolemaic minor second, is a 5-limit interval measuring about 68.7 ¢. It is equal to the Pythagorean minor second (256/243) flattened by a 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-reduced stack of nine 3/2's, as well as 25/24 minus a schisma (32805/32768). Tempering it out by itself defines the 5-limit version of superpyth temperament. Notable edos that temper it out include 17, 22, and 27.
Comma pump example
The progression returns to the original chord in 22edo, but modulates downward by 20480/19683 in JI.
