1573/1568

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Interval information
Ratio 1573/1568
Factorization 2-5 × 7-2 × 112 × 13
Monzo [-5 0 0 -2 2 1
Size in cents 5.5117336¢
Name lambeth comma
Color name 3o1oorr-2, thobiloru negative 2nd
FJS name [math]\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]\sqrt{nd}[/math])
~1.47855 bits
Comma size small
open this interval in xen-calc

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 sequence17c, 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