4131/4096: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| JI glyph =
| Ratio = 4131/4096
| Ratio = 4131/4096
| Monzo = -12 5 0 0 0 0 1
| Monzo = -12 5 0 0 0 0 1
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| Sound =  
| Sound =  
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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]].  
The '''septendecimal comma''' or '''Hunt flat 2 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 [[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.  
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 [[Helmholtz-Ellis notation]] (2020 version), however, that role is taken by 2187/2176, so 17/16 is represented as an augmented unison.  


== See also ==
== See also ==
* [[Comma]]
* [[Small comma]]


[[Category:17-limit]]
[[Category:17-limit]]
[[Category:Small commas]]
[[Category:Small commas]]
[[Category:Ratio]]
 
{{todo|add color name}}

Revision as of 21:27, 12 April 2022

Interval information
Ratio 4131/4096
Subgroup monzo 2.3.17 [-12 5 1
Size in cents 14.73041¢
Name septendecimal comma
FJS name [math]\displaystyle{ \text{P1}^{17} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 24.0123
Weil norm (log2 max(n, d)) 24.0246
Wilson norm (sopfr(nd)) 56
Open this interval in xen-calc

4131/4096, the septendecimal comma or Hunt flat 2 comma, is a 17-limit comma measuring about 14.7 ¢. 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.

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 Helmholtz-Ellis notation (2020 version), however, that role is taken by 2187/2176, so 17/16 is represented as an augmented unison.

See also