20480/19683: Difference between revisions

Interval information
Ratio	20480/19683
Factorization	212 × 3-9 × 5
Monzo	[12 -9 1⟩
Size in cents	68.71871¢
Names	retroptolemaic minor second,; superpyth comma
Color name	sayo 2nd, sy2, Sayo comma
FJS name	[math]\displaystyle{ \text{m2}^{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	28.5866
Weil norm (log2 max(n, d))	28.6439
Wilson norm (sopfr(nd))	56
	Open this interval in xen-calc

Revision as of 05:04, 25 February 2024

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.

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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 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]].
 [[Category:Second]]
 [[Category:Semitone]]