# 1573/1568

 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 $\text{M}{-2}^{11,11,13}_{7,7}$ 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, $\sqrt{nd}$) ~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

 [⟨ 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.