20480/19683
(Redirected from Superpyth comma)
Jump to navigation
Jump to search
| 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.
