40/31 - Revision history

Lériendil at 02:38, 22 August 2025

2025-08-22T02:38:37Z

← Older revision		Revision as of 02:38, 22 August 2025
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	\| Color name = 31uy4, thiwuyo 4th		\| 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]], 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]].		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 ==

Xenllium at 13:01, 27 April 2025

2025-04-27T13:01:45Z

← Older revision		Revision as of 13:01, 27 April 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = tricesimoprimal semidiminished fourth, tricesimoprimal supermajor third		\| Name = tricesimoprimal semidiminished fourth, tricesimoprimal supermajor third
	\| Color name = ~~31o3~~, ~~thiwo 3rd~~		\| 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 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, [[31~~/~~24]].~~		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]].

	~~In general, it can serve as an alternative sharp [[major third (interval region~~)~~\|supermajor third~~]] ~~to [[9/7]], which is flat of it~~ by [[~~280~~/~~279]~~]~~, for greater flexibility in [[otonal~~]~~] chords containing intervals that do not have a 7 in their denominator~~.

	== 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 ==

Xenllium: 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..."

2025-04-27T12:47:38Z

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..."

New page

{{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 [[81/64|Pythagorean major third (81/64)]] by [[2560/2511]], and flat of the [[4/3|perfect fourth (4/3)]] by [[31/30]]. 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, [[31/24]].

In general, it can serve as an alternative sharp [[major third (interval region)|supermajor third]] to [[9/7]], which is flat of it by [[280/279]], for greater flexibility in [[otonal]] chords containing intervals that do not have a 7 in their denominator.

== 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).

== See also ==
* [[31/20]] – its [[octave complement]]

[[Category:Fourth]]
[[Category:Subfourth]]
[[Category:Third]]
[[Category:Supermajor third]]
[[Category:Interseptimal intervals]]
[[Category:Naiadic]]