16/13: Difference between revisions

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'''16/13'''
{{Infobox Interval
|4 0 0 0 0 -1>
| Icon =
| Ratio = 16/13
| Monzo = 4 0 0 0 0 -1
| Cents = 359.47234
| Name = neutral tridecimal third
| Color name =
| Sound = jid_16_13_pluck_adu_dr220.mp3
}}


359.47234 cents
In [[13-limit]] [[just intonation]], '''16/13''' is a tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion of [[13/8]], the 13th harmonic. It differs from [[5/4]] by [[65/64]], about 26.8¢. It differs from the undecimal neutral third [[11/9]] by [[144/143]], about 12¢. A [[List_of_root-3rd-P5_triads_in_JI|root-3rd-P5 triad]] featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, [[39/32]], which measures about 342.5¢. The interval between these two intervals is 512/507, about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th overtone of the [[harmonic series]].


[[File:jid_16_13_pluck_adu_dr220.mp3]] [[:File:jid_16_13_pluck_adu_dr220.mp3|sound sample]]
See: [[Gallery of Just Intervals]]    


In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], 16/13 is a tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion of [[13/8|13/8]], the 13th harmonic. It differs from [[5/4|5/4]] by [[65/64|65/64]], about 26.8¢. It differs from the undecimal neutral third [[11/9|11/9]] by [[144/143|144/143]], about 12¢. A [[List_of_root-3rd-P5_triads_in_JI|root-3rd-P5 triad]] featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, [[39/32|39/32]], which measures about 342.5¢. The interval between these two intervals is 512/507, about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th overtone of the [[OverToneSeries|harmonic series]].
[[Category:13-limit]]
 
[[Category:Interval]]
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:13-limit]]
[[Category:Just interval]]
[[Category:interval]]
[[Category:Neutral third]]
[[Category:just_interval]]
[[Category:Ratio]]
[[Category:neutral_3rd]]
[[Category:Third]]
[[Category:ratio]]
[[Category:Tridecimal]]
[[Category:third]]
[[Category:tridecimal]]

Revision as of 14:06, 7 June 2020

Interval information
Ratio 16/13
Subgroup monzo 2.13 [4 -1⟩
Size in cents 359.4723¢
Name neutral tridecimal third
FJS name [math]\displaystyle{ \text{M3}_{13} }[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 7.70044
Weil height (log2 max(n, d)) 8
Wilson height (sopfr(nd)) 21

[sound info]
Open this interval in xen-calc

In 13-limit just intonation, 16/13 is a tridecimal (13-based) neutral third measuring about 359.5¢. It is the inversion of 13/8, the 13th harmonic. It differs from 5/4 by 65/64, about 26.8¢. It differs from the undecimal neutral third 11/9 by 144/143, about 12¢. A root-3rd-P5 triad featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, 39/32, which measures about 342.5¢. The interval between these two intervals is 512/507, about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th overtone of the harmonic series.

See: Gallery of Just Intervals

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