31/24 - Revision history

Xenllium at 12:48, 27 April 2025

2025-04-27T12:48:33Z

← Older revision		Revision as of 12:48, 27 April 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~(greater)~~ tricesimoprimal ultramajor third, ~~(greater)~~ tricesimoprimal ~~semidiminished fourth~~		\| Name = tricesimoprimal ultramajor third, tricesimoprimal subfourth
	\| Color name = 31o3, thiwo 3rd		\| 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 ~~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 [[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.		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.

Xenllium at 12:32, 27 April 2025

2025-04-27T12:32:33Z

← Older revision		Revision as of 12:32, 27 April 2025
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Name = tricesimoprimal ultramajor third, tricesimoprimal semidiminished fourth		\| Name = (greater) tricesimoprimal ultramajor third, (greater) tricesimoprimal semidiminished fourth
	\| Color name = 31o3, thiwo 3rd		\| Color name = 31o3, thiwo 3rd
	\| Sound = jid_31_24_pluck_adu_dr220.mp3		\| Sound = jid_31_24_pluck_adu_dr220.mp3

Lériendil at 12:17, 18 March 2025

2025-03-18T12:17:26Z

← Older revision		Revision as of 12:17, 18 March 2025
Line 4:		Line 4:
	\| 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 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, ~~wherein~~ it is equated to its complement relative to [[5/3]], that is, [[40/31]].		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 ==

Lériendil at 03:42, 18 March 2025

2025-03-18T03:42:15Z

← Older revision		Revision as of 03:42, 18 March 2025
Line 4:		Line 4:
	\| 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 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, ~~where~~ it is equated to its complement relative to [[5/3]], that is, [[40/31]].		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, wherein it is equated to its complement relative to [[5/3]], that is, [[40/31]].

	== Approximation ==		== Approximation ==

Lériendil at 03:38, 18 March 2025

2025-03-18T03:38:15Z

← Older revision		Revision as of 03:38, 18 March 2025
Line 4:		Line 4:
	\| 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 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, ~~especially for~~ the [[5-limit]] [[sensipent]] temperament, where it is equated to its complement relative to [[5/3]], that is, [[40/31]].		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, where it is equated to its complement relative to [[5/3]], that is, [[40/31]].

	== Approximation ==		== Approximation ==

Lériendil at 23:22, 17 March 2025

2025-03-17T23:22:15Z

← Older revision		Revision as of 23:22, 17 March 2025
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	== Approximation ==		== Approximation ==
	31/24 is ~~very closely~~ approximated by [[~~65edo~~\|24\65]] and [[~~19edo~~\|7\19]].		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 ==		== See also ==

Lériendil at 23:09, 9 March 2025

2025-03-09T23:09:36Z

← Older revision		Revision as of 23:09, 9 March 2025
Line 4:		Line 4:
	\| 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 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, especially for 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, especially for the [[5-limit]] [[sensipent]] temperament, where it is equated to its complement relative to [[5/3]], that is, [[40/31]].

	== Approximation ==		== Approximation ==

MisterShafXen at 13:44, 5 February 2025

2025-02-05T13:44:11Z

← Older revision		Revision as of 13:44, 5 February 2025
Line 7:		Line 7:

	== Approximation ==		== Approximation ==
	31/24 is very closely approximated by [[65edo\|24\65]].		31/24 is very closely approximated by [[65edo\|24\65]] and [[19edo\|7\19]].

	== See also ==		== See also ==

Inthar: /* Approximation */ correct link

2024-08-29T11:16:28Z

Approximation: correct link

← Older revision		Revision as of 11:16, 29 August 2024
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	== Approximation ==		== Approximation ==
	31/24 is very closely approximated by [[~~24edo~~\|24\65]].		31/24 is very closely approximated by [[65edo\|24\65]].

	== See also ==		== See also ==

FloraC: +relation to nearby Pythagorean intervals

2024-07-26T06:33:56Z

+relation to nearby Pythagorean intervals

← Older revision		Revision as of 06:33, 26 July 2024
Line 4:		Line 4:
	\| 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 semidiminished fourth'''. It can be used as a [[generator]] tuning for the [[sensi]] temperament, especially for 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, especially for the [[5-limit]] [[sensipent]] temperament.

	== Approximation ==		== Approximation ==