847/845

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Interval information
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:

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.

See also