40/31: Difference between revisions

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{{Infobox Interval

| Name = tricesimoprimal semidiminished fourth, tricesimoprimal supermajor third

| Color name = ~~31o3~~, ~~thiwo 3rd~~

| Color name = 31uy4, thiwuyo 4th

}}

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]], ~~and flat~~ of the [[4/3|~~perfect fourth~~ (4/3)]] by [[31/30]]~~. 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. In this context, it is equated to its complement relative to [[5~~/3~~]], that is, [[31~~/~~24]].~~

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 general, it can serve as an alternative sharp [[major third (interval region~~)~~|supermajor third~~]] ~~to [[9/7]], which is flat of it~~ by [[~~280~~/~~279]~~]~~, for greater flexibility in [[otonal~~]~~] chords containing intervals that do not have a 7 in their denominator~~.

== Approximation ==

40/31 is approximated by [[19edo|7\19]], and is extremely close to [[155edo|57\155]] (being just 0.012{{c}} sharp of it).

40/31 is approximated by [[19edo|7\19]] or [[30edo|11\30]], and is extremely close to [[155edo|57\155]] (being just 0.012{{c}} sharp of it).

== See also ==

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 {{Infobox Interval
 | Name = tricesimoprimal semidiminished fourth, tricesimoprimal supermajor third
-| Color name = 31o3, thiwo 3rd
+| Color name = 31uy4, thiwuyo 4th
 }}
-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]], and flat of the [[4/3|perfect fourth (4/3)]] by [[31/30]]. 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. In this context, it is equated to its complement relative to [[5/3]], that is, [[31/24]].
+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 general, it can serve as an alternative sharp [[major third (interval region)|supermajor third]] to [[9/7]], which is flat of it by [[280/279]], for greater flexibility in [[otonal]] chords containing intervals that do not have a 7 in their denominator.
 == Approximation ==
-/31 is approximated by [[19edo|7\19]], and is extremely close to [[155edo|57\155]] (being just 0.012{{c}} sharp of it).
+/31 is approximated by [[19edo|7\19]] or [[30edo|11\30]], and is extremely close to [[155edo|57\155]] (being just 0.012{{c}} sharp of it).
 == See also ==