20/17: Difference between revisions

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'''20/17'''
{{Infobox Interval
|2 0 1 0 0 0 -1>
| Name = diatismic minor third
| Sound = jid_20_17_pluck_adu_dr220.mp3
| Color name = 17uy2, suyo 2nd
}}


281.3583 cents
In [[17-limit]] [[just intonation]], '''20/17''' is the '''diatismic minor third''', measuring about 281.4{{cent}}. It falls short of the [[32/27|Pythagorean minor third (32/27)]] by a [[136/135|diatisma (136/135)]], hence the name. It is the [[mediant]] of [[7/6]] and [[13/11]], as it is (7 + 13)/(6 + 11). It is found in the [[harmonic series]] between the 17th and 20th [[harmonic]]s.


[[File:jid_20_17_pluck_adu_dr220.mp3]] [[:File:jid_20_17_pluck_adu_dr220.mp3|sound sample]]
== See also ==
* [[17/10]] – its [[octave complement]]
* [[51/40]] – its [[fifth complement]]
* [[17/15]] – its [[fourth complement]]
* [[17edo|4\17]] (282.353 cents)
* [[Gallery of just intervals]]


In [[17-limit|17-limit]] [[Just_intonation|Just Intonation]], 20/17 is the "septendecimal minor third", measuring about 281.4¢. It is the [[mediant|mediant]] between [[7/6|7/6]] and [[13/11|13/11]], as it is (7+13)/(6+11). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 20th harmonics.
[[Category:Third]]
 
[[Category:Minor third]]
See:
[[Category:Diatismic]]
 
<ul><li>[[17edo|4\17]] (282.353 cents)</li><li>[[17/10|17/10]] the octave complement</li><li>[[Gallery_of_Just_Intervals|Gallery of Just Intervals]]</li></ul>      [[Category:just_interval]]
[[Category:minor_third]]
[[Category:septendecimal]]

Latest revision as of 13:47, 1 June 2024

Interval information
Ratio 20/17
Factorization 22 × 5 × 17-1
Monzo [2 0 1 0 0 0 -1⟩
Size in cents 281.3583¢
Name diatismic minor third
Color name 17uy2, suyo 2nd
FJS name [math]\displaystyle{ \text{A2}^{5}_{17} }[/math]
Special properties reduced
Tenney height (log2 nd) 8.40939
Weil height (log2 max(n, d)) 8.64386
Wilson height (sopfr(nd)) 26

[sound info]
Open this interval in xen-calc

In 17-limit just intonation, 20/17 is the diatismic minor third, measuring about 281.4 ¢. It falls short of the Pythagorean minor third (32/27) by a diatisma (136/135), hence the name. It is the mediant of 7/6 and 13/11, as it is (7 + 13)/(6 + 11). It is found in the harmonic series between the 17th and 20th harmonics.

See also

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