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
Color name
3uu1oozg1, thuthulolozogu unison
FJS name
[math]\text{P1}^{7,11,11}_{5,13,13}[/math]
Special properties
reduced
Tenney height (log2 nd)
19.449
Weil height (log2 max(n, d))
19.4524
Wilson height (sopfr(nd))
60
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~1.35416 bits
Comma size
small
S-expression
S11 / S13
open this interval in xen-calc
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
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 the following superparticular pairs:
- 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 chords.