4131/4096

The septendecimal comma, 4131/4096, is a 17-limit comma measuring about 14.7 cents. It is the amount by which 17/16 deviates from 256/243.

Interval information

Ratio	4131/4096
Subgroup monzo	2.3.17 [-12 5 1⟩
Size in cents	14.73041¢
Name	septendecimal comma
FJS name	[math]\displaystyle{ \text{P1}^{17} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	24.0123
Weil norm (log2 max(n, d))	24.0246
Wilson norm (sopfr(nd))	56
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Besides the relationship above, it is also the difference between 18/17 and 2187/2048, between 17/12 and 1024/729, and their respective inverses. Furthermore, it and the septendecimal schisma 2187/2176 make a Pythagorean comma.

The septendecimal comma is significant in Functional Just System as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as an minor second. In Helmholtz-Ellis notation (2020 version), however, that role is taken by 2187/2176, so 17/16 is represented as an augmented unison.

See also

• Comma