20480/19683

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Interval information
Ratio 20480/19683
Factorization 212 × 3-9 × 5
Monzo [12 -9 1
Size in cents 68.718706¢
Names retroptolemaic minor second,
superpyth comma
Color name sayo 2nd, sy2, Sayo comma
FJS name [math]\text{m2}^{5}[/math]
Special properties reduced
Tenney height (log2 nd) 28.5866
Weil height (log2 max(n, d)) 28.6439
Wilson height (sopfr (nd)) 56
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.35763 bits
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.

Comma pump example

The progression returns to the original chord in 22edo, but modulates downward by 20480/19683 in JI.

Superpyth comma pump in JI and 22edo.