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The '''septendecimal schisma''', '''2187/2176''', is a [[17-limit]] [[comma]] measuring about 8.7 cents. 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. | The '''septendecimal schisma'''<ref>[https://marsbat.space/pdfs/HEJI2legend+series.pdf The Helmholtz-Ellis JI Pitch Notation (HEJI)]</ref>, '''2187/2176''', is a [[17-limit]] [[comma]] measuring about 8.7 cents. 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]]. | 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]]. | ||
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== See also == | == See also == | ||
* [[Comma]] | * [[Comma]] | ||
* Footnotes | |||
<references/> | |||
[[Category:17-limit]] | [[Category:17-limit]] | ||
[[Category:Small comma]] | [[Category:Small comma]] | ||
[[Category:Ratio]] | [[Category:Ratio]] | ||
Revision as of 09:56, 8 November 2020
| Interval information |
The septendecimal schisma[1], 2187/2176, is a 17-limit comma measuring about 8.7 cents. 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 Functional Just System, however, that role is taken by 4131/4096, so 17/16 is represented as a minor second.
See also
- Comma
- Footnotes