847/845: Difference between revisions

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Created page with "{{Infobox Interval | Icon = | Ratio = 847/845 | Monzo = 0 0 -1 1 2 -2 | Cents = 4.09275 | Name = cuthbert comma | Color name = | Sound = }} '''847/845''', the '''cuthbert co..."
 
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[[Category:13-limit]]
[[Category:13-limit]]
[[Category:Small comma]]
[[Category:Small commas]]
[[Category:Ratio]]
[[Category:Ratio]]
[[Category:Cuthbert]]
[[Category:Cuthbert]]

Revision as of 21:59, 20 March 2022

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
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
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 cents. 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