2187/2176: Difference between revisions
Created page with "{{Infobox Interval | JI glyph = | Ratio = 2187/2176 | Monzo = -7 7 0 0 0 0 -1 | Cents = 8.7296 | Name = septendecimal schisma | Color name = | FJS name = d-2<sub>17</sub> |..." |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septendecimal schisma | | Name = septendecimal schisma | ||
| Color name = | | Color name = L17u-2, lasu negative 2nd,<br>Lasu comma | ||
| Comma = yes | |||
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}} | }} | ||
The '''septendecimal schisma''', '''2187/2176''', is a [[17-limit]] [[comma]] measuring about 8.7 | The '''septendecimal schisma'''<ref>[https://marsbat.space/pdfs/HEJI2legend+series.pdf The Helmholtz-Ellis JI Pitch Notation (HEJI)]</ref>, '''2187/2176''', is a [[small comma|small]] [[17-limit]] [[comma]] measuring about 8.7{{cent}}. | ||
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]], 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. | |||
== References == | |||
<references/> | |||
[[Category: | |||
[[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.