13/8: Difference between revisions

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13/8 is a neutral sixth measuring about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3/2|3/2]] and [[7/4|7/4]], separated from each by the [[superparticular|superparticular]] ratios [[13/12|13/12]] and [[14/13|14/13]], respectively. It differs from the [[11-limit|11-limit]] neutral sixth [[18/11|18/11]] by [[144/143|144/143]], about 12.1¢.
'''13/8''' is the '''tridecimal neutral sixth''' measuring about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit]] [[Just intonation]], 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3/2]] and [[7/4]], separated from each by the [[superparticular]] ratios [[13/12]] and [[14/13]], respectively. It differs from the [[11-limit]] neutral sixth [[18/11]] by [[144/143]], about 12.1¢.


See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]     [[Category:13-limit]]
== See also ==
[[Category:interval]]
* [[Gallery of just intervals]]
[[Category:just_interval]]
* [[16/13]] its octave complement
[[Category:listen]]
 
[[Category:neutral_sixth]]
[[Category:13-limit]]
[[Category:ratio]]
[[Category:Interval ratio]]
[[Category:sixth]]
[[Category:Just interval]]
[[Category:tridecimal]]
[[Category:Listen]]
[[Category:untwelve]]
[[Category:Neutral sixth]]
[[Category:Sixth]]
[[Category:Tridecimal]]
[[Category:Untwelve]]
[[Category:Overtone]]

Revision as of 15:11, 12 July 2020

Interval information
Ratio 13/8
Subgroup monzo 2.13 [-3 1⟩
Size in cents 840.5277¢
Name tridecimal neutral sixth
Color name 3o6, tho 6th
FJS name [math]\displaystyle{ \text{m6}^{13} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 6.70044
Weil height (log2 max(n, d)) 7.40088
Wilson height (sopfr(nd)) 19

[sound info]
Open this interval in xen-calc

13/8 is the tridecimal neutral sixth measuring about 840.5¢, falling between the categories of minor sixth and major sixth. In 13-limit Just intonation, 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of 3/2 and 7/4, separated from each by the superparticular ratios 13/12 and 14/13, respectively. It differs from the 11-limit neutral sixth 18/11 by 144/143, about 12.1¢.

See also

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