1573/1568
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| 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{n\cdot d}[/math]) |
~2.52758 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.