847/845

Interval information

Ratio	847/845
Factorization	5-1 × 7 × 112 × 13-2
Monzo	[0 0 -1 1 2 -2⟩
Size in cents	4.092754¢
Name	cuthbert comma
Color name	3uu1oozg1, thuthulolozogu unison
FJS name	[math]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~1.35416 bits
Comma size	small
S-expression	S11 / S13
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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

Meanwhile, it can be factorized as 1001/1000 × 2200/2197 or 441/440 × 10648/10647.

Temperaments

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

See also

• Small comma