31/24: Difference between revisions

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'''31/24'''

{{Infobox Interval

| Name = tricesimoprimal ultramajor third, tricesimoprimal subfourth

| Color name = 31o3, thiwo 3rd

| 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]].

~~= 2<span style="font-size: 80%; vertical-align: super;">-3<~~/~~span> * 3<span style="font-size: 80%; vertical-align: super;">-1<~~/~~span> * 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.

~~443~~.~~0806 cents~~

== 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).

[[~~File:jid_31_24_pluck_adu_dr220.mp3~~]] [[~~:File:jid_31_24_pluck_adu_dr220.mp3|sound sample~~]]

== See also ==

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

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

~~The sensi supermajor~~ third~~, 31/24, 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.~~

[[Category:Third]]

[[Category:Supermajor third]]

[[Category:Fourth]]

[[Category:Subfourth]]

[[Category:Interseptimal intervals]]

[[Category:Naiadic]]

@@ Line 1: / Line 1: @@
-'''31/24'''
+{{Infobox Interval
+| Name = tricesimoprimal ultramajor third, tricesimoprimal subfourth
+| Color name = 31o3, thiwo 3rd
+| 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]].
-= 2<span style="font-size: 80%; vertical-align: super;">-3</span> * 3<span style="font-size: 80%; vertical-align: super;">-1</span> * 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.
-.0806 cents
+== Approximation ==
+/24 is approximated by [[19edo|7\19]], and is extremely close to [[65edo|24\65]] (being just 0.0036{{c}} sharp of it).
-[[File:jid_31_24_pluck_adu_dr220.mp3]] [[:File:jid_31_24_pluck_adu_dr220.mp3|sound sample]]
+== See also ==
+* [[48/31]] – its [[octave complement]]
+* [[36/31]] – its [[fifth complement]]
-The sensi supermajor third, 31/24, 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.
+[[Category:Third]]
+[[Category:Supermajor third]]
+[[Category:Fourth]]
+[[Category:Subfourth]]
+[[Category:Interseptimal intervals]]
+[[Category:Naiadic]]