40/31: Difference between revisions

In 31-limit just intonation, 40/31 is either the tricesimoprimal semidiminished fourth or tricesimoprimal supermajor third. It is sharp of the Pythagorean major third (81/64) by 2560/2511, sharp of the septimal major third (9/7) by 280/279, and flat of the perfect fourth (4/3) by 31/30. It is an excellent generator tuning for the clyde temperament, and this interval is an interpretation of the generator in the extended harmony of the 5-limit sensipent temperament. In this context, it is equated to its complement relative to 5/3, that is, 31/24.

Approximation

40/31 is approximated by 7\19 or 11\30, and is extremely close to 57\155 (being just 0.012 ¢ sharp of it).

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-In [[31-limit]] [[just intonation]], '''40/31''' is either the '''tricesimoprimal semidiminished fourth''' or '''tricesimoprimal supermajor third'''. It is sharp of the [[81/64|Pythagorean major third (81/64)]] by [[2560/2511]], sharp of the [[9/7|septimal major third (9/7)]] by [[280/279]], and flat of the [[4/3|perfect fourth (4/3)]] by [[31/30]].
+In [[31-limit]] [[just intonation]], '''40/31''' is either the '''tricesimoprimal semidiminished fourth''' or '''tricesimoprimal supermajor third'''. It is sharp of the [[81/64|Pythagorean major third (81/64)]] by [[2560/2511]], sharp of the [[9/7|septimal major third (9/7)]] by [[280/279]], and flat of the [[4/3|perfect fourth (4/3)]] by [[31/30]]. It is an excellent [[generator]] tuning for the [[clyde]] temperament, and this interval is an interpretation of the generator in the extended harmony of the [[5-limit]] [[sensipent]] temperament. In this context, it is equated to its complement relative to [[5/3]], that is, [[31/24]].
 == Approximation ==