2187/2176: Difference between revisions
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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 [[17/1|17th harmonic]] and a stack of seven [[3/2]] perfect fifths. | 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 [[17/1|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]]. | Besides the relationship above, it is also the difference between [[18/17]] and [[256/243]], between [[24/17]] and [[1024/729]], between [[81/64]] and [[34/27]], 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. | 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. | ||
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== References == | == References == | ||
<references/> | <references/> | ||
[[Category:Commas named for their regular temperament properties]] | |||
Latest revision as of 00:48, 13 March 2026
| Interval information |
Lasu comma
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, between 81/64 and 34/27, 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.