31/24: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = tricesimoprimal ultramajor third, tricesimoprimal subfourth | ||
| Color name = 31o3, thiwo 3rd | |||
| Sound = jid_31_24_pluck_adu_dr220.mp3 | | 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). | |||
== See also == | |||
* [[48/31]] – its [[octave complement]] | |||
* [[36/31]] – its [[fifth complement]] | |||
[[Category:Third]] | [[Category:Third]] | ||
[[Category:Supermajor third]] | [[Category:Supermajor third]] | ||
[[Category:Interseptimal]] | [[Category:Fourth]] | ||
[[Category:Subfourth]] | |||
[[Category:Interseptimal intervals]] | |||
[[Category:Naiadic]] | [[Category:Naiadic]] | ||
Latest revision as of 12:48, 27 April 2025
| Interval information |
tricesimoprimal subfourth
[sound info]
In 31-limit just intonation, 31/24 is either the tricesimoprimal ultramajor third or tricesimoprimal subfourth. It is sharp of the Pythagorean major third (81/64) by 248/243, and flat of the 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 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 7\19, and is extremely close to 24\65 (being just 0.0036 ¢ sharp of it).
See also
- 48/31 – its octave complement
- 36/31 – its fifth complement