20480/19683: Difference between revisions
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Sectioning. Linking. - 17edo in favor of 49edo. + category |
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| Color name = sayo 2nd, sy2, Sayo comma | | Color name = sayo 2nd, sy2, Sayo comma | ||
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'''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. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[ | '''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 == | == Comma pump example == | ||
[[File:Akselai superpyth comma pump (JI).wav|thumb|5-limit JI]] | [[File:Akselai superpyth comma pump (JI).wav|thumb|5-limit JI]] | ||
[[File:Akselai superpyth comma pump (22edo).wav|thumb|22edo]] | [[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. | 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.]] | [[File:Superpyth comma pump.png|thumb|Superpyth comma pump in JI and 22edo.]] | ||
[[Category:Superpyth]] | |||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
Latest revision as of 06:21, 1 May 2026
| Interval information |
superpyth comma
20480/19683, the retroptolemaic minor second, is a 5-limit interval measuring about 68.7 ¢. It gets its name from being equal to being one syntonic comma (81/80) flatter than the 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 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 22, 27, and 49.
Comma pump example
The progression returns to the original chord in 22edo, but modulates downward by 20480/19683 in JI.
