20480/19683: Difference between revisions

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| 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 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. 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 ==

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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. 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 ==