1573/1568

1573/1568, the lambeth comma, is a 13-limit (or 2.7.11.13 subgroup) small comma measuring about 5.5 cents. It is the amount by which a stack of two 14/11's falls short of 13/8.

Interval information

Ratio	1573/1568
Factorization	2-5 × 7-2 × 112 × 13
Monzo	[-5 0 0 -2 2 1⟩
Size in cents	5.511734¢
Name	lambeth comma
FJS name	[math]\displaystyle{ \text{M}{-2}^{11,11,13}_{7,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	21.234
Weil norm (log2 max(n, d))	21.2386
Wilson norm (sopfr(nd))	59
Comma size	small
Open this interval in xen-calc

Temperaments

Tempering it out leads to a form of the lambeth temperament, and enables lambeth chords, the essentially tempered chords in the 13-odd-limit.

Subgroup: 2.3.5.7.11.13

Mapping:
[⟨1 0 0 0 0 5],
⟨0 1 0 0 0 0],
⟨0 0 1 0 0 0],
⟨0 0 0 1 0 2],
⟨0 0 0 0 1 -2]]

Mapping generators: ~2, ~3, ~5, ~7, ~11

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9550, ~5/4 = 386.3137, ~7/4 = 969.7592, ~11/8 = 549.9007, ~13/8 = 839.7169

Optimal ET sequence: 17c, 22f, 26, 29, 31, 43, 46, 60e, 63, 68, 72, 103, 111, 140, 183, 212, 243e, 315ef, 323, 395f, 426e, 638eef

Etymology

The lambeth comma was named by Flora Canou in January 2022, referring to the London Borough of Lambeth, where she dwelled at the time.

See also

• Small comma