2187/2176: Difference between revisions

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{{Infobox Interval

~~| JI glyph =~~

~~| Ratio = 2187/2176~~

~~| Monzo = -7 7 0 0 0 0 -1~~

~~| Cents = 8.72960~~

| Name = septendecimal schisma

| Color name =

| Color name = L17u-2, lasu negative 2nd,<br>Lasu comma

~~| FJS name = d~~-2<~~sub>17</sub~~>

| Comma = yes

| ~~Sound~~ =

}}

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 [[small comma|small]] [[17-limit]] [[comma]] measuring about 8.7{{cent}}.

~~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~~]].

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.

~~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~~.

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]].

~~== See also ==~~

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.

* [[~~Comma~~]]

~~[[Category:17-limit]]~~

== References ==

~~[[Category:Comma]]~~

[[Category:~~Ratio~~]]

[[Category:Commas named for their regular temperament properties]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph =
-| Ratio = 2187/2176
-| Monzo = -7 7 0 0 0 0 -1
-| Cents = 8.72960
 | Name = septendecimal schisma
-| Color name =
+| Color name = L17u-2, lasu negative 2nd,<br>Lasu comma
-| FJS name = d-2<sub>17</sub>
+| Comma = yes
-| Sound =
 }}
-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 [[small comma|small]] [[17-limit]] [[comma]] measuring about 8.7{{cent}}.
-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]].
+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.
-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.
+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]].
-== See also ==
+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.
-* [[Comma]]
-[[Category:17-limit]]
+== References ==
-[[Category:Comma]]
+<references/>
-[[Category:Ratio]]
+[[Category:Commas named for their regular temperament properties]]