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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
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

847/845, the cuthbert comma, is a 13-limit (also 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:

Meanwhile, it can be factorized as 1001/1000 × 2200/2197.


Tempering out this comma in the 13-limit results in the rank-5 cuthbert temperament and enables the cuthbert chords.

See also