19-comma
| Factorization | 2-30 × 319 |
| Monzo | [-30 19⟩ |
| Size in cents | 137.14502¢ |
| Names | 19-comma, Pythagorean kleisma, Pythagorean inverse double-diminished second |
| Color name | L3w-2, trilawa negative 2nd |
| FJS name | [math]\text{dd}{-2}[/math] |
| Special properties | reduced, reduced harmonic |
| Tenney height (log2 nd) | 60.1143 |
| Weil height (log2 max(n, d)) | 60.2286 |
| Wilson height (sopfr (nd)) | 117 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.25307 bits |
| open this interval in xen-calc | |
The 19-comma, otherwise known as the Pythagorean kleisma (monzo: [-30 19⟩, ratio: 1162261467/1073741824), is an interval of about 137.1 ¢. It is the amount by which nineteen perfect fifths exceed eleven octaves, or (3/2)19/211. If used as an interval in its own right, it is the Pythagorean inverse double-diminished second. Treating it as a comma, tempering out this comma gives rise to graywood, which is supported by edos 19, 38, 57, and 76 in their patent vals.
Terminology
The term Pythagorean kleisma seems to be first used by Flora Canou in 2024, for this is the moskleisma of the Pythagorean diatonic scale, where kleisma (adjective: kleismic) refers to the inverse double-diminished 1-step i.e. |2L - 3s|. It is equated with the 5-limit kleisma of 15625/15552 along with many other intervals in meantone. It can also be reasoned as a fitting name as by tempering out this comma alongside the meantone comma (81/80), we get 19edo, which supports kleismic.