31/24: Difference between revisions

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{{Infobox Interval

~~| Ratio = 31/24~~

| Name = tricesimoprimal ultramajor third, tricesimoprimal subfourth

~~| Monzo = -3 -1 0 0 0 0 0 0 0 0 1~~

| Color name = 31o3, thiwo 3rd

~~| Cents = 443.08057~~

| Name = ~~sensi supermajor~~ third

| Color name =

~~| FJS name = M3<sup>31</sup>~~

| 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]].

~~'''31/24'''~~, ~~the '''sensi~~ supermajor third~~'''~~, ~~can be used as a generator tuning for~~ [[~~Sensipent family#Sensi|sensi temperament~~]], ~~especially~~ for ~~the~~ [[~~5-limit~~]] ~~sensipent temperament~~. It is ~~very~~ close to ~~the 24\~~[[65edo|65]] ~~generator~~.

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).

== See also ==

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

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

~~[[Category:31-limit]]~~

[[Category:Third]]

[[Category:Supermajor third]]

[[Category:Interseptimal]]

[[Category:Fourth]]

[[Category:Subfourth]]

[[Category:Interseptimal intervals]]

[[Category:Naiadic]]

~~{{todo|add color name}}~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 31/24
+| Name = tricesimoprimal ultramajor third, tricesimoprimal subfourth
-| Monzo = -3 -1 0 0 0 0 0 0 0 0 1
+| Color name = 31o3, thiwo 3rd
-| Cents = 443.08057
-| Name = sensi supermajor third
-| Color name =
-| FJS name = M3<sup>31</sup>
 | 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]].
-'''31/24''', the '''sensi supermajor third''', can be used as a generator tuning for [[Sensipent family#Sensi|sensi temperament]], especially for the [[5-limit]] sensipent temperament. It is very close to the 24\[[65edo|65]] generator.
+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 ==
+/24 is approximated by [[19edo|7\19]], and is extremely close to [[65edo|24\65]] (being just 0.0036{{c}} sharp of it).
+== See also ==
+* [[48/31]] – its [[octave complement]]
+* [[36/31]] – its [[fifth complement]]
-[[Category:31-limit]]
 [[Category:Third]]
 [[Category:Supermajor third]]
-[[Category:Interseptimal]]
+[[Category:Fourth]]
+[[Category:Subfourth]]
+[[Category:Interseptimal intervals]]
 [[Category:Naiadic]]
-{{todo|add color name}}