31/27: Difference between revisions

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

Revision as of 10:30, 28 September 2025

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

This interval is very accurately approximated by 1\5. 5 of them fall short of the octave by 28697814/28629151

@@ Line 3: / Line 3: @@
 | 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]], 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]].
+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 ==
-This interval is very accurately approximated by [[5edo|1\5]].
+This interval is very accurately approximated by [[5edo|1\5]]. 5 of them fall short of the octave by [[28697814/28629151]]
 == See also ==