20/13 - Revision history

FloraC: Fix redundant hyphen

2026-01-22T16:29:14Z

Fix redundant hyphen

← Older revision		Revision as of 16:29, 22 January 2026
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	\| Sound = jid_20_13_pluck_adu_dr220.mp3		\| Sound = jid_20_13_pluck_adu_dr220.mp3
	}}		}}

	'''20/13''', the '''tridecimal semitenth''', is a [[13-limit]] [[interseptimal]] interval measuring about 745.8 [[cent]]s. It falls in an ambiguous zone between a narrow minor sixth such as [[14/9]] and a sharp fifth such as [[32/21]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes.		'''20/13''', the '''tridecimal semitenth''', is a [[13-limit]] [[interseptimal]] interval measuring about 745.8 [[cent]]s. It falls in an ambiguous zone between a narrow minor sixth such as [[14/9]] and a sharp fifth such as [[32/21]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes.

	In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), 20/13 is a fifth, as it is a [[3/2\|perfect fifth (3/2)]] plus an instance of [[40/39]], which is a [[2187/2048\|Pythagorean apotome]] minus a stack consisting of an [[81/80\|syntonic comma (81/80)]] and a [[1053/1024\|tridecimal quartertone (1053/1024)]], none of which changes the [[scale\|scale degree]]. It functions as such in voicings of the harmonic thirteenth chord, [[4:5:6:7:9:11:13]].		In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), 20/13 is a fifth, as it is a [[3/2\|perfect fifth (3/2)]] plus an instance of [[40/39]], which is a [[2187/2048\|Pythagorean apotome]] minus a stack consisting of an [[81/80\|syntonic comma (81/80)]] and a [[1053/1024\|tridecimal quartertone (1053/1024)]], none of which changes the [[scale\|scale degree]]. It functions as such in voicings of the harmonic thirteenth chord, [[4:5:6:7:9:11:13]].

	However, 20/13 also appears in voicings of the relatively-simple [[10:13:15]] triad, which consists of [[13/10]] and [[15/13]] that stack to make a [[3/2]] perfect fifth. This makes 20/13 function as an inframinor sixth (if the chord is not taken as a suspension).		However, 20/13 also appears in voicings of the relatively simple [[10:13:15]] triad, which consists of [[13/10]] and [[15/13]] that stack to make a [[3/2]] perfect fifth. This makes 20/13 function as an inframinor sixth (if the chord is not taken as a suspension).

	20/13 is the targeted as the wolf fifth in [[Gene Ward Smith]]'s [[Ratwolf]] scale.		20/13 is the targeted as the wolf fifth in [[Gene Ward Smith]]'s [[Ratwolf]] scale.

FloraC: Elaborate on its ambiguous quality

2026-01-22T16:27:38Z

Elaborate on its ambiguous quality

← Older revision		Revision as of 16:27, 22 January 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = Barbados sixth~~, ratwolf wolf fifth~~, tridecimal semitenth		\| Name = Barbados sixth, tridecimal semitenth
	\| Color name = 3uy5, thuyo 5th		\| Color name = 3uy5, thuyo 5th
	\| Sound = jid_20_13_pluck_adu_dr220.mp3		\| Sound = jid_20_13_pluck_adu_dr220.mp3
	}}		}}

	'''20/13''', the '''tridecimal semitenth''', is a [[13-limit]] [[interseptimal]] interval measuring about ~~746~~ [[cent]]s.		'''20/13''', the '''tridecimal semitenth''', is a [[13-limit]] [[interseptimal]] interval measuring about 745.8 [[cent]]s. It falls in an ambiguous zone between a narrow minor sixth such as [[14/9]] and a sharp fifth such as [[32/21]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes.

			In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), 20/13 is a fifth, as it is a [[3/2\|perfect fifth (3/2)]] plus an instance of [[40/39]], which is a [[2187/2048\|Pythagorean apotome]] minus a stack consisting of an [[81/80\|syntonic comma (81/80)]] and a [[1053/1024\|tridecimal quartertone (1053/1024)]], none of which changes the [[scale\|scale degree]]. It functions as such in voicings of the harmonic thirteenth chord, [[4:5:6:7:9:11:13]].

			However, 20/13 also appears in voicings of the relatively-simple [[10:13:15]] triad, which consists of [[13/10]] and [[15/13]] that stack to make a [[3/2]] perfect fifth. This makes 20/13 function as an inframinor sixth (if the chord is not taken as a suspension).

			20/13 is the targeted as the wolf fifth in [[Gene Ward Smith]]'s [[Ratwolf]] scale.

	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|20/13}}		{{Interval edo approximation\|20/13}}

	== See also ==		== See also ==
	* [[13/10]] – its [[octave complement]]		* [[13/10]] – its [[octave complement]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]


	~~{{stub}}~~

	[[Category:Interseptimal intervals]]		[[Category:Interseptimal intervals]]

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

2025-11-03T13:03:16Z

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

← Older revision		Revision as of 13:03, 3 November 2025
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	'''20/13''', the '''tridecimal semitenth''', is a [[13-limit]] [[interseptimal]] interval measuring about 746 [[cent]]s.		'''20/13''', the '''tridecimal semitenth''', is a [[13-limit]] [[interseptimal]] interval measuring about 746 [[cent]]s.
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 20/13}}		{{Interval edo approximation\|20/13}}
	== See also ==		== See also ==
	* [[13/10]] – its [[octave complement]]		* [[13/10]] – its [[octave complement]]

Pailiaq at 07:34, 3 November 2025

2025-11-03T07:34:26Z

← Older revision		Revision as of 07:34, 3 November 2025
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	'''20/13''', the '''tridecimal semitenth''', is a [[13-limit]] [[interseptimal]] interval measuring about 746 [[cent]]s.		'''20/13''', the '''tridecimal semitenth''', is a [[13-limit]] [[interseptimal]] interval measuring about 746 [[cent]]s.
			== Approximation ==
			{{Interval_Edo_Approximation \| 20/13}}
	== See also ==		== See also ==
	* [[13/10]] – its [[octave complement]]		* [[13/10]] – its [[octave complement]]

BudjarnLambeth: Stub

2024-12-15T00:51:34Z

Stub

← Older revision		Revision as of 00:51, 15 December 2024
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	* [[13/10]] – its [[octave complement]]		* [[13/10]] – its [[octave complement]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]


			{{stub}}

	[[Category:Interseptimal intervals]]		[[Category:Interseptimal intervals]]
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	[[Category:Fifth]]		[[Category:Fifth]]
	[[Category:Superfifth]]		[[Category:Superfifth]]
	~~{{todo\| expand }}~~

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

2023-04-28T03:27:00Z

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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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	[[Category:Interseptimal]]		[[Category:Interseptimal intervals]]
	[[Category:Cocytic]]		[[Category:Cocytic]]
	[[Category:Sixth]]		[[Category:Sixth]]

Plumtree: Normalising usage of Infobox Interval

2022-10-25T12:07:41Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 12:07, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 20/13~~		\| Name = Barbados sixth, ratwolf wolf fifth, tridecimal semitenth
	~~\| Monzo = 2 0 1 0 0 -1~~
	~~\| Cents = 745.78605~~
	\| Name = Barbados sixth, ~~<br>~~ratwolf wolf fifth, ~~<br>~~tridecimal semitenth
	\| Color name = 3uy5, thuyo 5th		\| Color name = 3uy5, thuyo 5th
	~~\| FJS name = A5<sup>5</sup><sub>13</sub>~~
	\| Sound = jid_20_13_pluck_adu_dr220.mp3		\| Sound = jid_20_13_pluck_adu_dr220.mp3
	}}		}}
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

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

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

2022-02-22T23:46:43Z

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:Fifth]]		[[Category:Fifth]]
	[[Category:Superfifth]]		[[Category:Superfifth]]
	~~[[Category:Pages with internal sound examples]]~~

	{{todo\| expand }}		{{todo\| expand }}

Fredg999: Categories

2021-12-15T18:25:48Z

Fredg999: Misc. edits, categories

2021-12-15T17:31:00Z

Misc. edits, categories

← Older revision		Revision as of 17:31, 15 December 2021
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 20/13		\| Ratio = 20/13
	\| Monzo = 2 0 1 0 0 -1		\| Monzo = 2 0 1 0 0 -1
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	[[Category:13-limit]]		[[Category:13-limit]]
	~~[[Category:Interval]]~~
	~~[[Category:Ratio]]~~
	[[Category:Interseptimal]]		[[Category:Interseptimal]]
	[[Category:Cocytic]]		[[Category:Cocytic]]

← Older revision		Revision as of 18:25, 15 December 2021
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	[[Category:Fifth]]		[[Category:Fifth]]
	[[Category:Superfifth]]		[[Category:Superfifth]]
			[[Category:Pages with internal sound examples]]

	{{todo\| expand }}		{{todo\| expand }}