19-comma

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.

Interval information

Factorization	2-30 × 319
Monzo	[-30 19⟩
Size in cents	137.145¢
Names	19-comma, Pythagorean kleisma
FJS name	[math]\displaystyle{ \text{dd}{-2} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	60.1143
Weil norm (log2 max(n, d))	60.2286
Wilson norm (sopfr(nd))	117
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Terminology

The term Pythagorean kleisma seems to be first used by Flora Canou in 2024, for this is the kleisma of the Pythagorean diatonic scale, where kleisma 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.

See also

• Large comma