31/24: Difference between revisions

| Sound = jid_31_24_pluck_adu_dr220.mp3

In [[31-limit]] [[just intonation]], '''31/24''' is either the '''tricesimoprimal ultramajor third''' or '''tricesimoprimal subfourth'''. 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 ==

31/24 is approximated by [[19edo|7\19]], and is extremely close to [[65edo|24\65]] (being just 0.0036{{c}} sharp of it).

 

* [[48/31]] – its [[octave complement]]

* [[36/31]] – its [[fifth complement]]