31/27: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = tricesimoprimal ultramajor second, tricesimoprimal inframinor third
| Name = (lesser) tricesimoprimal ultramajor second, (lesser) tricesimoprimal inframinor third
| Color name = 31o2, thiwo 2nd
}}
}}
In [[31-limit]] [[just intonation]], '''31/27''' is either the '''tricesimoprimal ultramajor second''' or '''tricesimoprimal inframinor third'''. It is sharp of the [[9/8|Pythagorean major second (9/8)]] by [[248/243]], and flat of the [[32/27|minor third (32/27)]] by [[32/31]].  
In [[31-limit]] [[just intonation]], '''31/27''' is either the '''tricesimoprimal ultramajor second''' or '''tricesimoprimal inframinor third'''. It is sharp of the [[9/8|Pythagorean major second (9/8)]] by [[248/243]], sharp of the [[8/7|septimal major second (8/7)]] by [[217/216]], and flat of the [[32/27|minor third (32/27)]] by [[32/31]]. It differs from the [[23/20|vicesimotertial inframinor third]] by [[621/620]]


== Approximation ==
== Approximation ==
This interval is very accurately approximated by [[5edo|1\5]].  
This interval is very accurately approximated by [[5edo|1\5]]. Five intervals of 31/27 fall short of the octave by [[28697814/28629151]].


== See also ==
== See also ==
* [[54/31]] – its [[octave complement]]
* [[54/31]] – its [[octave complement]]
* [[36/31]] – its [[fourth complement]]


[[Category:Second]]
[[Category:Second]]

Latest revision as of 04:33, 31 January 2026

Interval information
Ratio 31/27
Subgroup monzo 3.31 [-3 1
Size in cents 239.1706¢
Names (lesser) tricesimoprimal ultramajor second,
(lesser) tricesimoprimal inframinor third
Color name 31o2, thiwo 2nd
FJS name [math]\displaystyle{ \text{M2}^{31} }[/math]
Special properties reduced
Tenney norm (log2 nd) 9.70908
Weil norm (log2 max(n, d)) 9.90839
Wilson norm (sopfr(nd)) 40
Open this interval in xen-calc

In 31-limit just intonation, 31/27 is either the tricesimoprimal ultramajor second or tricesimoprimal inframinor third. It is sharp of the Pythagorean major second (9/8) by 248/243, sharp of the septimal major second (8/7) by 217/216, and flat of the minor third (32/27) by 32/31. It differs from the vicesimotertial inframinor third by 621/620

Approximation

This interval is very accurately approximated by 1\5. Five intervals of 31/27 fall short of the octave by 28697814/28629151.

See also