847/845
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| Ratio | 847/845 |
| Factorization | 5-1 × 7 × 112 × 13-2 |
| Monzo | [0 0 -1 1 2 -2⟩ |
| Size in cents | 4.0927538¢ |
| Name | cuthbert comma |
| FJS name | [math]\text{P1}^{7,11,11}_{5,13,13}[/math] |
| Special properties | reduced |
| Tenney height (log2 n⋅d) | 19.449 |
| Weil height (max(n, d)) | 847 |
| Benedetti height (n⋅d) | 715715 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.47145 bits |
| Comma size | small |
| S-expression | S11 / S13 |
| open this interval in xen-calc | |
847/845, the cuthbert comma, is a 13-limit (also 5.7.11.13 subgroup) comma measuring about 4.09 ¢. It is the difference between 7/5 and a stack of two 13/11's. In terms of commas, it is the difference between:
- 66/65 and 78/77
- 121/120 and 169/168
- 352/351 and 2080/2079
- 385/384 and 4225/4224
- 441/440 and 10648/10647
Meanwhile, it can be factorized as 1001/1000 × 2200/2197.
Temperaments
Tempering out this comma in the 13-limit results in the rank-5 cuthbert temperament and enables the cuthbert triad.