20480/19683

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]\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
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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.

Superpyth comma pump in JI and 22edo.