19-comma
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Factorization | 2^{-30} × 3^{19} |
Monzo | [-30 19⟩ |
Size in cents | 137.14502¢ |
Names | 19-comma, Pythagorean kleisma, Pythagorean inverse double-diminished second |
Color name | L^{3}w-2, trilawa negative 2nd |
FJS name | [math]\text{dd}{-2}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 60.1143 |
Weil height (log_{2} 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}/2^{11}. If used as an interval in its own right, it is the Pythagorean inverse double-diminished second.
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.