31/24: Difference between revisions

In 31-limit just intonation, 31/24 is either the tricesimoprimal ultramajor third or tricesimoprimal semidiminished fourth. It is sharp of the Pythagorean major third (81/64) by 248/243, and flat of the perfect fourth (4/3) by 32/31. It can be used as a generator tuning for the sensi temperament, and more accurate interpretations of the extended harmony of the 5-limit sensipent temperament, wherein it is equated to its complement relative to 5/3, that is, 40/31.

Approximation

31/24 is approximated by 7\19, and is extremely close to 24\65 (being just 0.0036 ¢ sharp of it).

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-In [[31-limit]] [[just intonation]], '''31/24''' is either the '''tricesimoprimal ultramajor third''' or '''tricesimoprimal semidiminished fourth'''. It is sharp of the [[81/64|Pythagorean major third (81/64)]] by [[248/243]], and flat of the [[4/3|perfect fourth (4/3)]] by [[32/31]]. It can be used as a [[generator]] tuning for the [[sensi]] temperament, and more accurate interpretations of the extended harmony of the [[5-limit]] [[sensipent]] temperament, where it is equated to its complement relative to [[5/3]], that is, [[40/31]].
+In [[31-limit]] [[just intonation]], '''31/24''' is either the '''tricesimoprimal ultramajor third''' or '''tricesimoprimal semidiminished fourth'''. It is sharp of the [[81/64|Pythagorean major third (81/64)]] by [[248/243]], and flat of the [[4/3|perfect fourth (4/3)]] by [[32/31]]. It can be used as a [[generator]] tuning for the [[sensi]] temperament, and more accurate interpretations of the extended harmony of the [[5-limit]] [[sensipent]] temperament, wherein it is equated to its complement relative to [[5/3]], that is, [[40/31]].
 == Approximation ==