2187/2176: Difference between revisions

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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{{cent}}~~. It is most intuitively described as the difference betwen the stack of 7 [[3/2]] perfect fifths and [[17/1|17th harmonic]]~~.

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.

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]].

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.

~~== See also ==~~

* [[Comma]]

== References ==

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-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{{cent}}. It is most intuitively described as the difference betwen the stack of 7 [[3/2]] perfect fifths and [[17/1|17th harmonic]].
+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.
+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]].
 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.
-== See also ==
-* [[Comma]]
 == References ==
 <references/>