32/17: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = septendecimal major seventh, septendecimal diminished octave

~~| Ratio = 32/17~~

~~| Monzo = 5 0 0 0 0 0 -1~~

~~| Cents = 1095.04459~~

| Name = ~~small~~ septendecimal major seventh

| Color name = 17u7, su 7th

~~| FJS name = M7<sub>17</sub>~~

| Sound = jid_32_17_pluck_adu_dr220.mp3

}}

In [[17-limit]] [[just intonation]], '''32/17''' is the '''septendecimal major seventh''' or the '''septendecimal diminished octave''', depending on how one views it. It is also the octave-reduced 17th [[subharmonic]]. Its inversion is [[17/16]], the octave-reduced 17th harmonic. Measuring about 1095{{cent}}, it is the [[mediant]] between [[15/8]] and [[17/9]].

~~In [[17-limit]] [[just intonation]], '''~~32/17~~''' is the '''small septendecimal~~ major seventh~~''', as well as the 17th~~ [[~~subharmonic~~]] ~~octave-reduced. Measuring about 1095¢~~, ~~it is~~ the [[~~mediant~~]] ~~between~~ [[15/8]] ~~and~~ [[~~17/9~~]], the ~~"large septendecimal major seventh". Its inversion is~~ [[17/16]], the ~~"large septendecimal semitone"~~.

== Terminology and notation ==

There exists a disagreement in different conceptualization systems on whether 32/17 should be a major seventh or a diminished octave. The major seventh view corresponds to [[Functional Just System]], with the formal comma [[4131/4096]] separating it from [[243/128]], the Pythagorean major seventh. The diminished octave view corresponds to [[Helmholtz-Ellis notation]], with the formal comma [[2187/2176]] separating it from [[4096/2187]], the Pythagorean diminished octave.

~~There exists a disagreement in different notation systems on whether 32/17 should be notated as a major seventh or a diminished octave~~. In [[~~Functional Just System~~]]~~, it~~ is a ~~major seventh, whereas in~~ [[~~Helmholtz-Ellis notation~~]]~~, it is a diminished octave~~.

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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* [[Gallery of just intervals]]

~~[[Category:17-limit]]~~

~~[[Category:Interval ratio]]~~

~~[[Category:Just interval]]~~

[[Category:Seventh]]

[[Category:Major seventh]]

[[Category:Octave]]

[[Category:Diminished octave]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = septendecimal major seventh, septendecimal diminished octave
-| Ratio = 32/17
-| Monzo = 5 0 0 0 0 0 -1
-| Cents = 1095.04459
-| Name = small septendecimal major seventh
 | Color name = 17u7, su 7th
-| FJS name = M7<sub>17</sub>
 | Sound = jid_32_17_pluck_adu_dr220.mp3
 }}
+In [[17-limit]] [[just intonation]], '''32/17''' is the '''septendecimal major seventh''' or the '''septendecimal diminished octave''', depending on how one views it. It is also the octave-reduced 17th [[subharmonic]]. Its inversion is [[17/16]], the octave-reduced 17th harmonic. Measuring about 1095{{cent}}, it is the [[mediant]] between [[15/8]] and [[17/9]].
-In [[17-limit]] [[just intonation]], '''32/17''' is the '''small septendecimal major seventh''', as well as the 17th [[subharmonic]] octave-reduced. Measuring about 1095¢, it is the [[mediant]] between [[15/8]] and [[17/9]], the "large septendecimal major seventh". Its inversion is [[17/16]], the "large septendecimal semitone".
+== Terminology and notation ==
+There exists a disagreement in different conceptualization systems on whether 32/17 should be a major seventh or a diminished octave. The major seventh view corresponds to [[Functional Just System]], with the formal comma [[4131/4096]] separating it from [[243/128]], the Pythagorean major seventh. The diminished octave view corresponds to [[Helmholtz-Ellis notation]], with the formal comma [[2187/2176]] separating it from [[4096/2187]], the Pythagorean diminished octave.
-There exists a disagreement in different notation systems on whether 32/17 should be notated as a major seventh or a diminished octave. In [[Functional Just System]], it is a major seventh, whereas in [[Helmholtz-Ellis notation]], it is a diminished octave.
+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 ==
@@ Line 18: / Line 15: @@
 * [[Gallery of just intervals]]
-[[Category:17-limit]]
-[[Category:Interval ratio]]
-[[Category:Just interval]]
 [[Category:Seventh]]
 [[Category:Major seventh]]
+[[Category:Octave]]
+[[Category:Diminished octave]]