32/17: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Ratio = 32/17
| Ratio = 32/17
| Monzo = 5 0 0 0 0 0 -1
| Monzo = 5 0 0 0 0 0 -1
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| Sound = jid_32_17_pluck_adu_dr220.mp3
| Sound = jid_32_17_pluck_adu_dr220.mp3
}}
}}
In [[17-limit]] [[just intonation]], '''32/17''' is the '''small septendecimal major seventh''', as well as the 17th [[subharmonic]] octave-reduced. Measuring about 1095{{cent}}, it is the [[mediant]] between [[15/8]] and [[17/9]], the "large septendecimal major seventh". Its inversion is [[17/16]], the "large septendecimal semitone".


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


== See also ==
== See also ==
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[[Category:17-limit]]
[[Category:17-limit]]
[[Category:Interval ratio]]
[[Category:Just interval]]
[[Category:Seventh]]
[[Category:Seventh]]
[[Category:Major seventh]]
[[Category:Major seventh]]
[[Category:Octave-reduced subharmonics]]

Revision as of 12:44, 23 March 2022

Interval information
Ratio 32/17
Subgroup monzo 2.17 [5 -1
Size in cents 1095.045¢
Name small septendecimal major seventh
Color name 17u7, su 7th
FJS name [math]\displaystyle{ \text{M7}_{17} }[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 9.08746
Weil height (log2 max(n, d)) 10
Wilson height (sopfr(nd)) 27

[sound info]
Open this interval in xen-calc

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".

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

See also