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]] | '''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]]. | 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]]. | ||
Latest revision as of 20:10, 29 July 2025
| Interval information |
Laso comma
reduced harmonic
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 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 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 . The downward version is called 1/17C or 17C down and is represented by .