4131/4096: Difference between revisions

m Fix typo
Clarify direction of deviation
 
(12 intermediate revisions by 9 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| JI glyph =
| Ratio = 4131/4096
| Monzo = -12 5 0 0 0 0 1
| Cents = 14.730
| Name = septendecimal comma
| Name = septendecimal comma
| Color name =  
| Color name = L17o1, laso 1sn,<br>Laso comma
| FJS name = P1<sup>17</sup>
| Comma = yes
| Sound =  
}}
}}
'''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]].


The '''septendecimal comma''', '''4131/4096''', is a [[17-limit]] [[comma]] measuring about 14.7 cents. It is the amount by which [[17/16]] deviates from [[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]].  


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.  


The septendecimal comma is significant in [[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 [[Helmholtz-Ellis notation]] (2020 version), 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 ==
== See also ==
* [[Comma]]
* [[Small comma]]


[[Category:17-limit]]
[[Category:Commas named for the intervals they stack]]
[[Category:Comma]]
[[Category:Ratio]]