31/24: Difference between revisions
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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, | 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 == | == Approximation == | ||
Revision as of 12:17, 18 March 2025
| Interval information |
tricesimoprimal semidiminished fourth
[sound info]
In 31-limit just intonation, 31/24 is either the tricesimoprimal ultramajor third or tricesimoprimal semidiminished fourth. 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