20480/19683

Interval information

Ratio

20480/19683

Factorization

2¹² × 3^-9 × 5

[12 -9 1⟩

Size in cents

68.71871¢

Names

retroptolemaic minor second,
superpyth comma

sayo 2nd, sy2, Sayo comma

[math]\displaystyle{ \text{m2}^{5} }[/math]

Special properties

28.5866

Weil height (log₂ max(n, d))

28.6439

56

Harmonic entropy
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])

~4.35763 bits

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. 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

5-limit JI

22edo

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