20480/19683

Revision as of 14:40, 19 October 2023 by FloraC (talk | contribs) (This interval has a simple name in Pythagorean-commatic naming)

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.

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, 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