31/24: Difference between revisions

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| Sound = jid_31_24_pluck_adu_dr220.mp3

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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, ~~wherein~~ 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. In this context, it is equated to its complement relative to [[5/3]], that is, [[40/31]].

In general, it can serve as an alternative sharp [[major third (interval region)|supermajor third]] to [[9/7]], which is flat of it by [[217/216]], for greater flexibility in [[otonal]] chords containing intervals that do not have a 7 in their denominator.

== Approximation ==

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 | Sound = jid_31_24_pluck_adu_dr220.mp3
 }}
-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]].
+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. In this context, it is equated to its complement relative to [[5/3]], that is, [[40/31]].
+In general, it can serve as an alternative sharp [[major third (interval region)|supermajor third]] to [[9/7]], which is flat of it by [[217/216]], for greater flexibility in [[otonal]] chords containing intervals that do not have a 7 in their denominator.
 == Approximation ==