4131/4096

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Interval information
Ratio 4131/4096
Subgroup monzo 2.3.17 [-12 5 1
Size in cents 14.730414¢
Name septendecimal comma
Color name L17o1, laso 1sn,
Laso comma
FJS name [math]\text{P1}^{17}[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 n⋅d) 24.0123
Weil height (max(n, d)) 4131
Benedetti height (n⋅d) 16920576
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~3.2013 bits
Comma size small
open this interval in xen-calc

4131/4096, the septendecimal comma or Hunt flat 2 comma, is a 17-limit comma measuring about 14.7 ¢. It is the amount by which 17/16 deviates from 256/243.

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 the 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 a 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