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 and notation ==

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.

In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded [[circle-of-fifths notation]] is to prepare a [[Pythagorean comma]] accidental so that the interval can be notated in either category.

== See also ==

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[[Category:Seventh]]

[[Category:Major seventh]]

[[Category:Octave]]

[[Category:Diminished octave]]

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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 and notation ==
+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.
+In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded [[circle-of-fifths notation]] is to prepare a [[Pythagorean comma]] accidental so that the interval can be notated in either category.
 == See also ==
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 [[Category:Seventh]]
 [[Category:Major seventh]]
+[[Category:Octave]]
+[[Category:Diminished octave]]