2187/2176

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Interval information
Ratio 2187/2176
Subgroup monzo 2.3.17 [-7 7 -1
Size in cents 8.7295966¢
Name septendecimal schisma
FJS name [math]\text{d}{-2}_{17}[/math]
Special properties reduced
Tenney height (log2 n⋅d) 22.1822
Weil height (max(n, d)) 2187
Benedetti height (n⋅d) 4758912
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.71278 bits
Comma size small
open this interval in xen-calc

The septendecimal schisma[1], 2187/2176, is a 17-limit comma measuring about 8.7 ¢. Although several times in size, it shares similarities with the schisma – while the schisma is the amount by which 16/15 deviates from 2187/2048, the septendecimal schisma is the amount by which 17/16 deviates from 2187/2048.

Besides the relationship above, it is also the difference between 18/17 and 256/243, between 24/17 and 1024/729, and their respective inverses. Furthermore, it and the septendecimal comma 4131/4096 make a Pythagorean comma.

The septendecimal schisma is significant in Helmholtz-Ellis notation (2020 version) as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as an augmented unison. In the Functional Just System, however, that role is taken by 4131/4096, so 17/16 is represented as a minor second.

See also

References