2187/2176

Interval information

Ratio	2187/2176
Subgroup monzo	2.3.17 [-7 7 -1⟩
Size in cents	8.729597¢
Name	septendecimal schisma
Color name	L17u-2, lasu negative 2nd, Lasu comma
FJS name	[math]\text{d}{-2}_{17}[/math]
Special properties	reduced
Tenney height (log2 nd)	22.1822
Weil height (log2 max(n, d))	22.1895
Wilson height (sopfr(nd))	52
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.88062 bits
Comma size	small
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The septendecimal schisma, 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.