2187/2176
Interval information |
Lasu comma
(Shannon, [math]\sqrt{nd}[/math])
The septendecimal schisma[1], 2187/2176, is a small 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, which means it is the difference between 17th harmonic and a stack of seven 3/2 perfect fifths.
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.