2187/2176
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 (log_{2} 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.