26/17: Difference between revisions

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'''26/17'''
{{Infobox Interval
|1 0 0 0 0 1 -1>
| JI glyph =
| Ratio = 26/17
| Monzo = 1 0 0 0 0 1 -1
| Cents = 735.57225
| Name = septendecimal super-fifth
| Color name =
| FJS name =
| Sound = jid_26_17_pluck_adu_dr220.mp3
}}


735.5723 cents
In [[17-limit]] [[Just Intonation]], '''26/17''' is the ''septendecimal super-fifth''. It differs from a [[3/2]] perfect fifth by the [[comma]] [[52/51]], about 33.6¢. Although this difference is considerable, 26/17 may be used as a wide perfect fifth, thus allowing septendecimal versions of [[List of root-3rd-P5 triads in JI|root-3rd-P5]] chords – in particular, 17:20:26, 17:21:26, 17:22:26.


[[File:jid_26_17_pluck_adu_dr220.mp3]] [[:File:jid_26_17_pluck_adu_dr220.mp3|sound sample]]
26/17 is the [[mediant]] of 3/2 and [[23/15]]. Its [[octave complement]] is [[17/13]], the septendecimal sub-fourth.


In [[17-limit|17-limit]] [[Just_intonation|Just Intonation]], 26/17 is the "septendecimal super-fifth," measuring about 735.6¢. It differs from a [[3/2|3/2]] perfect fifth by the [[Comma|comma]] 52/51, about 33.6¢. Although this difference is considerable, 26/17 may be used as a wide perfect fifth, thus allowing septendecimal versions of [[List_of_root-3rd-P5_triads_in_JI|root-3rd-P5]] chords -- in particular, 17:20:26, 17:21:26, 17:22:26.
See: [[Gallery of Just Intervals]]
 
26/17 is the [[mediant|mediant]] between 3/2 and 23/15. Its inversion is [[17/13|17/13]], the "septendecimal sub-fourth".
 
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]


[[Category:Interseptimal]]
[[Category:Interseptimal]]
[[Category:17-limit]]
[[Category:Just interval]]

Revision as of 17:50, 8 November 2020

Interval information
Ratio 26/17
Subgroup monzo 2.13.17 [1 1 -1⟩
Size in cents 735.5723¢
Name septendecimal super-fifth
FJS name [math]\displaystyle{ \text{P5}^{13}_{17} }[/math]
Special properties reduced
Tenney height (log2 nd) 8.7879
Weil height (log2 max(n, d)) 9.40088
Wilson height (sopfr(nd)) 32

[sound info]
Open this interval in xen-calc

In 17-limit Just Intonation, 26/17 is the septendecimal super-fifth. It differs from a 3/2 perfect fifth by the comma 52/51, about 33.6¢. Although this difference is considerable, 26/17 may be used as a wide perfect fifth, thus allowing septendecimal versions of root-3rd-P5 chords – in particular, 17:20:26, 17:21:26, 17:22:26.

26/17 is the mediant of 3/2 and 23/15. Its octave complement is 17/13, the septendecimal sub-fourth.

See: Gallery of Just Intervals

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