4131/4096: Difference between revisions

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'''4131/4096''', the '''septendecimal comma''' or '''Hunt flat 2 comma''', is a [[17-limit]] [[comma]] measuring about 14.7{{cent}}. It is the amount by which [[17/16]] ~~deviates from~~ [[256/243]].

'''4131/4096''', the '''septendecimal comma''' or '''Hunt flat 2 comma''', is a [[17-limit]] [[comma]] measuring about 14.7{{cent}}. It is the amount by which [[17/16]] exceeds [[256/243]].

Besides the relationship above, it is also the difference between [[18/17]] and [[2187/2048]], between [[17/12]] and [[1024/729]], and their respective inverses. Furthermore, it and the septendecimal schisma [[2187/2176]] make a [[Pythagorean comma]].

The septendecimal comma is significant in the [[Functional Just System]] as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as a minor second. In the 2020 version of [[Helmholtz-Ellis notation]], however, that role is taken by [[2187/2176]], so 17/16 is represented as an augmented unison.

== Sagittal notation ==

In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal | ~|( }} and is called the '''17 comma''', or '''17C''' for short, because the simplest interval it notates is 17/1 (equiv. 17/16), as for example in E-F{{nbhsp}}{{sagittal | ~|( }}. The downward version is called '''1/17C''' or '''17C down''' and is represented by {{sagittal| ~!( }}.

== See also ==

* [[Small comma]]

[[Category:Commas named for the intervals they stack]]

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 | Comma = yes
 }}
-'''4131/4096''', the '''septendecimal comma''' or '''Hunt flat 2 comma''', is a [[17-limit]] [[comma]] measuring about 14.7{{cent}}. It is the amount by which [[17/16]] deviates from [[256/243]].
+'''4131/4096''', the '''septendecimal comma''' or '''Hunt flat 2 comma''', is a [[17-limit]] [[comma]] measuring about 14.7{{cent}}. It is the amount by which [[17/16]] exceeds [[256/243]].
 Besides the relationship above, it is also the difference between [[18/17]] and [[2187/2048]], between [[17/12]] and [[1024/729]], and their respective inverses. Furthermore, it and the septendecimal schisma [[2187/2176]] make a [[Pythagorean comma]].
 The septendecimal comma is significant in the [[Functional Just System]] as the 17-limit formal comma which translates a Pythagorean interval to a nearby septendecimal interval. Consequently, 17/16 is represented as a minor second. In the 2020 version of [[Helmholtz-Ellis notation]], however, that role is taken by [[2187/2176]], so 17/16 is represented as an augmented unison.
+== Sagittal notation ==
+In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal | ~|( }} and is called the '''17 comma''', or '''17C''' for short, because the simplest interval it notates is 17/1 (equiv. 17/16), as for example in E-F{{nbhsp}}{{sagittal | ~|( }}. The downward version is called '''1/17C''' or '''17C down''' and is represented by {{sagittal| ~!( }}.
 == See also ==
 * [[Small comma]]
+[[Category:Commas named for the intervals they stack]]