4131/4096: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 4131/4096
| Monzo = -12 5 0 0 0 0 1
| Cents = 14.73041
| Name = septendecimal comma
| Name = septendecimal comma
| Color name =
| Comma = yes
| FJS name = P1<sup>17</sup>
| 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]] 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]] deviates from [[256/243]].  
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== See also ==
== See also ==
* [[Small comma]]
* [[Small comma]]
[[Category:17-limit]]
[[Category:Small commas]]
{{todo|add color name}}

Revision as of 15:45, 25 October 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
Comma size small
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