40/31: Difference between revisions
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Created page with "{{Infobox Interval | Name = tricesimoprimal semidiminished fourth, tricesimoprimal supermajor third | Color name = 31o3, thiwo 3rd }} In 31-limit just intonation, '''40/31''' is either the '''tricesimoprimal semidiminished fourth''' or '''tricesimoprimal supermajor third'''. It is sharp of the Pythagorean major third (81/64) by 2560/2511, and flat of the perfect fourth (4/3) by 31/30. It can be used as a generator tuning for the se..." Tags: Mobile edit Mobile web edit |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = tricesimoprimal semidiminished fourth, tricesimoprimal supermajor third | | Name = tricesimoprimal semidiminished fourth, tricesimoprimal supermajor third | ||
| Color name = | | Color name = 31uy4, thiwuyo 4th | ||
}} | }} | ||
In [[31-limit]] [[just intonation]], '''40/31''' is either the '''tricesimoprimal semidiminished fourth''' or '''tricesimoprimal supermajor third'''. It is sharp of the [[81/64|Pythagorean major third (81/64)]] by [[2560/2511]], and flat of the [[4/3|perfect fourth (4/3)]] by [[31/30]]. It | In [[31-limit]] [[just intonation]], '''40/31''' is either the '''tricesimoprimal semidiminished fourth''' or '''tricesimoprimal supermajor third'''. It is sharp of the [[81/64|Pythagorean major third (81/64)]] by [[2560/2511]], sharp of the [[9/7|septimal major third (9/7)]] by [[280/279]], and flat of the [[4/3|perfect fourth (4/3)]] by [[31/30]]. It is an excellent [[generator]] tuning for the [[clyde]] temperament, and this interval is an interpretation of the generator in the extended harmony of the [[5-limit]] [[sensipent]] temperament. In this context, it is equated to its complement relative to [[5/3]], that is, [[31/24]]. | ||
== Approximation == | == Approximation == | ||
40/31 is approximated by [[19edo|7\19]], and is extremely close to [[155edo|57\155]] (being just 0.012{{c}} sharp of it). | 40/31 is approximated by [[19edo|7\19]] or [[30edo|11\30]], and is extremely close to [[155edo|57\155]] (being just 0.012{{c}} sharp of it). | ||
== See also == | == See also == | ||
Latest revision as of 02:38, 22 August 2025
| Interval information |
tricesimoprimal supermajor third
In 31-limit just intonation, 40/31 is either the tricesimoprimal semidiminished fourth or tricesimoprimal supermajor third. It is sharp of the Pythagorean major third (81/64) by 2560/2511, sharp of the septimal major third (9/7) by 280/279, and flat of the perfect fourth (4/3) by 31/30. It is an excellent generator tuning for the clyde temperament, and this interval is an interpretation of the generator in the extended harmony of the 5-limit sensipent temperament. In this context, it is equated to its complement relative to 5/3, that is, 31/24.
Approximation
40/31 is approximated by 7\19 or 11\30, and is extremely close to 57\155 (being just 0.012 ¢ sharp of it).
See also
- 31/20 – its octave complement