32/17: Difference between revisions

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'''32/17'''

{{Infobox Interval

~~|5 0 0 0 0 0~~ -~~1>~~

| Name = septendecimal major seventh, septendecimal diminished octave

| Color name = 17u7, su 7th

| 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]].

~~1095~~.~~0446 cents~~

== 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.

[[~~File:jid_32_17_pluck_adu_dr220.mp3~~]] [[~~:File:jid_32_17_pluck_adu_dr220.mp3|sound sample~~]]

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.

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

== See also ==

* [[17/16]] – its [[octave complement]]

* [[Gallery of just intervals]]

~~See~~: [[~~Gallery_of_Just_Intervals|Gallery of Just Intervals~~]]

[[Category:Seventh]]

[[Category:Major seventh]]

[[Category:Octave]]

[[Category:Diminished octave]]

@@ Line 1: / Line 1: @@
-'''32/17'''
+{{Infobox Interval
-|5 0 0 0 0 0 -1&gt;
+| Name = septendecimal major seventh, septendecimal diminished octave
+| Color name = 17u7, su 7th
+| 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]].
-.0446 cents
+== 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.
-[[File:jid_32_17_pluck_adu_dr220.mp3]] [[:File:jid_32_17_pluck_adu_dr220.mp3|sound sample]]
+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.
-In [[17-limit|17-limit]] [[Just_intonation|Just Intonation]], 32/17 is the "small septendecimal major seventh," as well as the 17th [[subharmonic|subharmonic]] octave-reduced. Measuring about 1095¢, it is the [[mediant|mediant]] between [[15/8|15/8]] and [[17/9|17/9]], the "large septendecimal major seventh". Its inversion is [[17/16|17/16]], the "large septendecimal semitone".
+== See also ==
+* [[17/16]] – its [[octave complement]]
+* [[Gallery of just intervals]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
+[[Category:Seventh]]
+[[Category:Major seventh]]
+[[Category:Octave]]
+[[Category:Diminished octave]]