1573/1568

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
Color name	3o1oorr-2, thobiloru negative 2nd
FJS name	[math]\displaystyle{ \text{M}{-2}^{11,11,13}_{7,7} }[/math]
Special properties	reduced
Tenney height (log2 nd)	21.234
Weil height (log2 max(n, d))	21.2386
Wilson height (sopfr(nd))	59
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.47855 bits
Comma size	small
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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.

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, ~5/4, ~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