20480/19683: Difference between revisions

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This interval has a simple name in Pythagorean-commatic naming
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{{Infobox Interval
{{Infobox Interval
| Name = retroptolemaic minor second, superpyth comma
| Name = retroptolemaic minor second, superpyth comma
| Color name = sayo 2nd, sayo comma
| Color name = sayo 2nd, sy2, Sayo comma
}}
}}
'''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 the 5-limit version of [[superpyth]] temperament. Notable [[edo]]s that temper it out include [[17edo|17]], [[22edo|22]], and [[27edo|27]].

Revision as of 22:57, 21 October 2023

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

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.