31/16: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| JI glyph =
| Name = tricesimoprimal ultramajor seventh, tricesimoprimal semidiminished octave, octave-reduced 31st harmonic
| Ratio = 31/16
| Color name = 31o7, thiwo 7th
| Monzo = -4 0 0 0 0 0 0 0 0 0 1
| Cents = 1145.03557
| Name = octave-reduced 31st harmonic
| Color name =  
| FJS name =
| Sound = jid_31_16_pluck_adu_dr220.mp3
| Sound = jid_31_16_pluck_adu_dr220.mp3
}}
}}


'''31/16''' = 2<sup>−4</sup> ⋅ 31, the octave-reduced 31st harmonic.
In [[31-limit]] [[just intonation]], '''31/16''' is either the '''tricesimoprimal ultramajor seventh''' or '''tricesimoprimal semidiminished octave''', which is also the [[octave reduction|octave-reduced]] [[31/1|31st]] [[harmonic]]. It is sharp of the [[243/128|Pythagorean major seventh (243/128)]] by [[248/243]], and flat of the octave by [[32/31]].  


[[Category:Interval]]
== Approximation ==
31/16 is very well approximated by [[22edo]], with 21\22 being 0.4 [[Cent|¢]] sharp of 31/16.


[[Category:todo:expand]]
== See also ==
* [[32/31]] – its [[octave complement]]
* [[48/31]] – its [[twelfth complement]]
 
[[Category:Seventh]]
[[Category:Supermajor seventh]]
[[Category:Octave]]
[[Category:Suboctave]]

Latest revision as of 20:49, 24 September 2024

Interval information
Ratio 31/16
Subgroup monzo 2.31 [-4 1
Size in cents 1145.036¢
Names tricesimoprimal ultramajor seventh,
tricesimoprimal semidiminished octave,
octave-reduced 31st harmonic
Color name 31o7, thiwo 7th
FJS name [math]\displaystyle{ \text{M7}^{31} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 8.9542
Weil height (log2 max(n, d)) 9.90839
Wilson height (sopfr(nd)) 39

[sound info]
Open this interval in xen-calc

In 31-limit just intonation, 31/16 is either the tricesimoprimal ultramajor seventh or tricesimoprimal semidiminished octave, which is also the octave-reduced 31st harmonic. It is sharp of the Pythagorean major seventh (243/128) by 248/243, and flat of the octave by 32/31.

Approximation

31/16 is very well approximated by 22edo, with 21\22 being 0.4 ¢ sharp of 31/16.

See also