1573/1568
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Ratio | 1573/1568 |
Factorization | 2^{-5} × 7^{-2} × 11^{2} × 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 (log_{2} nd) | 21.234 |
Weil height (log_{2} 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
[⟨ | 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.