17/9: Difference between revisions

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In [[17-limit]] [[just intonation]], '''17/9''' is the '''large septendecimal major seventh''', measuring about 1101¢. It is the [[mediant]] between [[15/8]] and [[2/1]]. Its inversion is [[18/17]], the "small septendecimal semitone".  
In [[17-limit]] [[just intonation]], '''17/9''' is the '''septendecimal diminished octave''' or the '''septendecimal major seventh''', depending on how one views it. It measures about 1101¢. It is the [[mediant]] between [[15/8]] and [[2/1]]. Its inversion is [[18/17]], the "small septendecimal semitone".  


There exists a disagreement in different notation systems on whether 17/9 should be notated as a major seventh or a diminished octave. In the [[Functional Just System]], it is a diminished octave, whereas in [[Helmholtz-Ellis notation]], it is a major seventh.  
== Terminology ==
There exists a disagreement in different conceptualization systems on whether 17/9 should be a major seventh or a diminished octave. The diminished octave view corresponds to [[Functional Just System]], with the formal comma [[4131/4096]] separating it from [[4096/2187]], the Pythagorean diminished octave. The major seventh view corresponds to [[Helmholtz-Ellis notation]], with the formal comma [[2187/2176]] separating it from [[243/128]], the Pythagorean major seventh.


== See also ==
== See also ==
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[[Category:Seventh]]
[[Category:Seventh]]
[[Category:Major seventh]]
[[Category:Major seventh]]
[[Category:Octave]]
[[Category:Diminished octave]]

Revision as of 09:12, 12 January 2023

Interval information
Ratio 17/9
Subgroup monzo 3.17 [-2 1
Size in cents 1101.045¢
Name large septendecimal major seventh
Color name 17o8, iso octave
FJS name [math]\displaystyle{ \text{d8}^{17} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.25739
Weil norm (log2 max(n, d)) 8.17493
Wilson norm (sopfr(nd)) 23

[sound info]
Open this interval in xen-calc

In 17-limit just intonation, 17/9 is the septendecimal diminished octave or the septendecimal major seventh, depending on how one views it. It measures about 1101¢. It is the mediant between 15/8 and 2/1. Its inversion is 18/17, the "small septendecimal semitone".

Terminology

There exists a disagreement in different conceptualization systems on whether 17/9 should be a major seventh or a diminished octave. The diminished octave view corresponds to Functional Just System, with the formal comma 4131/4096 separating it from 4096/2187, the Pythagorean diminished octave. The major seventh view corresponds to Helmholtz-Ellis notation, with the formal comma 2187/2176 separating it from 243/128, the Pythagorean major seventh.

See also