15/13 - Revision history

Eufalesio: Semifourth and other things

2026-04-10T18:59:35Z

Semifourth and other things

← Older revision		Revision as of 18:59, 10 April 2026
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	\| Sound = jid_15_13_pluck_adu_dr220.mp3		\| Sound = jid_15_13_pluck_adu_dr220.mp3
	}}		}}
	In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢. In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI\|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root. When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second".		In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢, wherein two instances of this fall short of [[4/3]] by [[676/675]].

			In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI\|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root.

			When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second". In extended [[Pythagorean tuning]] it is extremely close to {{Monzo\|43 -27}}.

	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|15/13}}		{{Interval edo approximation\|15/13}}

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:12:14Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:12, 3 November 2025
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	In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢. In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI\|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root. When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second".		In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢. In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI\|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root. When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second".
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 15/13}}		{{Interval edo approximation\|15/13}}
	== See also ==		== See also ==
	* [[26/15]] – its [[octave complement]]		* [[26/15]] – its [[octave complement]]

Pailiaq at 06:58, 3 November 2025

2025-11-03T06:58:23Z

← Older revision		Revision as of 06:58, 3 November 2025
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	}}		}}
	In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢. In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI\|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root. When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second".		In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢. In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI\|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root. When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second".
			== Approximation ==
			{{Interval_Edo_Approximation \| 15/13}}
	== See also ==		== See also ==
	* [[26/15]] – its [[octave complement]]		* [[26/15]] – its [[octave complement]]

FloraC: Recategorize +1

2024-12-01T14:24:59Z

Recategorize +1

← Older revision		Revision as of 14:24, 1 December 2024
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	[[Category:Second]]		[[Category:Second]]
	[[Category:Supermajor second]]		[[Category:Supermajor second]]
	~~[[Category:Taxicab-2 intervals]]~~

FloraC: Recategorize

2024-11-24T08:05:38Z

Recategorize

← Older revision		Revision as of 08:05, 24 November 2024
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	\| Sound = jid_15_13_pluck_adu_dr220.mp3		\| Sound = jid_15_13_pluck_adu_dr220.mp3
	}}		}}

	In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢. In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI\|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root. When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second".		In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢. In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI\|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root. When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second".

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	[[Category:Second]]		[[Category:Second]]
	[[Category:Supermajor second]]		[[Category:Supermajor second]]
	[[Category:Taxicab-2]]		[[Category:Taxicab-2 intervals]]

Fredg999 category edits: Moving from Category:Interseptimal to Category:Interseptimal intervals using Cat-a-lot

2023-04-28T03:27:02Z

Moving from Category:Interseptimal to Category:Interseptimal intervals using Cat-a-lot

← Older revision		Revision as of 03:27, 28 April 2023
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	* [[The Archipelago]]		* [[The Archipelago]]

	[[Category:Interseptimal]]		[[Category:Interseptimal intervals]]
	[[Category:Semifourth]]		[[Category:Semifourth]]
	[[Category:Third]]		[[Category:Third]]

Plumtree: Normalising usage of Infobox Interval

2022-10-25T11:26:11Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 11:26, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 15/13~~
	~~\| Monzo = 0 1 1 0 0 -1~~
	~~\| Cents = 247.74105~~
	\| Name = tridecimal semifourth		\| Name = tridecimal semifourth
	\| Color name = 3uy2, thuyo 2nd		\| Color name = 3uy2, thuyo 2nd
	~~\| FJS name = A2<sup>5</sup><sub>13</sub>~~
	\| Sound = jid_15_13_pluck_adu_dr220.mp3		\| Sound = jid_15_13_pluck_adu_dr220.mp3
	}}		}}
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	* [[The Archipelago]]		* [[The Archipelago]]

	~~[[Category:13-limit]]~~
	[[Category:Interseptimal]]		[[Category:Interseptimal]]
	[[Category:Semifourth]]		[[Category:Semifourth]]

Fredg999 category edits: Removing from Category:Pages with internal sound examples using Cat-a-lot

2022-02-22T23:46:41Z

Removing from Category:Pages with internal sound examples using Cat-a-lot

← Older revision		Revision as of 23:46, 22 February 2022
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	[[Category:Supermajor second]]		[[Category:Supermajor second]]
	[[Category:Taxicab-2]]		[[Category:Taxicab-2]]
	~~[[Category:Pages with internal sound examples]]~~

Fredg999: Misc. edits, categories

2021-12-12T20:19:01Z

Misc. edits, categories

← Older revision		Revision as of 20:19, 12 December 2021
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 15/13		\| Ratio = 15/13
	\| Monzo = 0 1 1 0 0 -1		\| Monzo = 0 1 1 0 0 -1
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	[[Category:13-limit]]		[[Category:13-limit]]
	~~[[Category:Interval]]~~
	[[Category:Interseptimal]]		[[Category:Interseptimal]]
	[[Category:Semifourth]]		[[Category:Semifourth]]

FloraC: Revert part of category changes

2021-04-10T14:51:54Z

Revert part of category changes

← Older revision		Revision as of 14:51, 10 April 2021
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	[[Category:Semifourth]]		[[Category:Semifourth]]
	[[Category:Third]]		[[Category:Third]]
	[[Category:~~Inframinor~~ third]]		[[Category:Subminor third]]
	[[Category:Second]]		[[Category:Second]]
	[[Category:~~Ultramajor~~ second]]		[[Category:Supermajor second]]
	[[Category:Taxicab-2]]		[[Category:Taxicab-2]]
	[[Category:Pages with internal sound examples]]		[[Category:Pages with internal sound examples]]