13/8 - Revision history

Overthink: /* Approximation */- redundant parameter

2026-05-30T17:13:51Z

Approximation: - redundant parameter

← Older revision		Revision as of 17:13, 30 May 2026
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	This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[golden ratio]]. In this case, 13/8 is ~7.4 [[cent\|¢]] sharp of the golden ratio.		This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[golden ratio]]. In this case, 13/8 is ~7.4 [[cent\|¢]] sharp of the golden ratio.
	{{Interval edo approximation~~\|{{PAGENAME}}~~}}		{{Interval edo approximation}}

	== See also ==		== See also ==
	* [[16/13]] – its [[octave complement]]		* [[16/13]] – its [[octave complement]]

Overthink: Grammar

2026-05-30T17:12:55Z

Grammar

← Older revision		Revision as of 17:12, 30 May 2026
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	}}		}}

	'''13/8''' is the '''(lesser) tridecimal neutral sixth''', which measures about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit]] [[just intonation]], 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3/2]] and [[7/4]], separated from each by the [[superparticular]] ratios [[13/12]] and [[14/13]], respectively. The word "lesser" is added when necessary to differentiate it from [[64/39]], another tridecimal neutral sixth. It may also be treated as a type of augmented fifth, as the sum of [[5/4]] and [[13/10]].		'''13/8''' is the '''(lesser) tridecimal neutral sixth''', which measures about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit]] [[just intonation]], 13/8, as the octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3/2]] and [[7/4]], separated from each by the [[superparticular]] ratios [[13/12]] and [[14/13]], respectively. The word "lesser" is added when necessary to differentiate it from [[64/39]], another tridecimal neutral sixth. It may also be treated as a type of augmented fifth, as the sum of [[5/4]] and [[13/10]].

	13/8 differs from the Pythagorean minor sixth [[128/81]] by [[1053/1024]], about 48¢, from the classic minor sixth [[8/5]] by [[65/64]], about 27¢, from the undecimal neutral sixth [[18/11]] by [[144/143]], about 12¢, and from the rastmic neutral sixth [[44/27]] by [[352/351]], about 4.9¢.		13/8 differs from the Pythagorean minor sixth [[128/81]] by [[1053/1024]], about 48¢, from the classic minor sixth [[8/5]] by [[65/64]], about 27¢, from the undecimal neutral sixth [[18/11]] by [[144/143]], about 12¢, and from the rastmic neutral sixth [[44/27]] by [[352/351]], about 4.9¢.

	== Approximation ==		== Approximation ==

Pailiaq at 20:48, 3 November 2025

2025-11-03T20:48:33Z

← Older revision		Revision as of 20:48, 3 November 2025
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	This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[golden ratio]]. In this case, 13/8 is ~7.4 [[cent\|¢]] sharp of the golden ratio.		This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[golden ratio]]. In this case, 13/8 is ~7.4 [[cent\|¢]] sharp of the golden ratio.
			{{Interval edo approximation\|{{PAGENAME}}}}
	== See also ==		== See also ==
	* [[16/13]] – its [[octave complement]]		* [[16/13]] – its [[octave complement]]

Plumtree: Normalising usage of Infobox Interval

2022-10-25T11:53:07Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 11:53, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 13/8~~
	~~\| Monzo = -3 0 0 0 0 1~~
	~~\| Cents = 840.52766~~
	\| Name = (lesser) tridecimal neutral sixth		\| Name = (lesser) tridecimal neutral sixth
	\| Color name = 3o6, tho 6th		\| Color name = 3o6, tho 6th
	~~\| FJS name = m6<sup>13</sup>~~
	\| Sound = jid_13_8_pluck_adu_dr220.mp3		\| Sound = jid_13_8_pluck_adu_dr220.mp3
	}}		}}
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	~~[[Category:13-limit]]~~
	[[Category:Sixth]]		[[Category:Sixth]]
	[[Category:Neutral sixth]]		[[Category:Neutral sixth]]
	[[Category:Golden ratio approximations]]		[[Category:Golden ratio approximations]]
	~~[[Category:Octave-reduced harmonics]]~~

KingHyperio at 13:35, 28 April 2022

2022-04-28T13:35:59Z

← Older revision		Revision as of 13:35, 28 April 2022
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	}}		}}

	'''13/8''' is the '''(lesser) tridecimal neutral sixth''', which measures about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit]] [[just intonation]], 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3/2]] and [[7/4]], separated from each by the [[superparticular]] ratios [[13/12]] and [[14/13]], respectively. The word "lesser" is added when necessary to differentiate it from [[64/39]], another tridecimal neutral sixth.		'''13/8''' is the '''(lesser) tridecimal neutral sixth''', which measures about 840.5¢, falling between the categories of minor sixth and major sixth. In [[13-limit]] [[just intonation]], 13/8, as an octave-reduced 13th harmonic, is treated as a basic component of harmony. In the harmonic series and in chords based on it, 13/8 sits between the more familiar consonances of [[3/2]] and [[7/4]], separated from each by the [[superparticular]] ratios [[13/12]] and [[14/13]], respectively. The word "lesser" is added when necessary to differentiate it from [[64/39]], another tridecimal neutral sixth. It may also be treated as a type of augmented fifth, as the sum of [[5/4]] and [[13/10]].

	13/8 differs from the Pythagorean minor sixth [[128/81]] by [[1053/1024]], about 48¢, from the classic minor sixth [[8/5]] by [[65/64]], about 27¢, from the undecimal neutral sixth [[18/11]] by [[144/143]], about 12¢, and from the rastmic neutral sixth [[44/27]] by [[352/351]], about 4.9¢.		13/8 differs from the Pythagorean minor sixth [[128/81]] by [[1053/1024]], about 48¢, from the classic minor sixth [[8/5]] by [[65/64]], about 27¢, from the undecimal neutral sixth [[18/11]] by [[144/143]], about 12¢, and from the rastmic neutral sixth [[44/27]] by [[352/351]], about 4.9¢.

Fredg999: See also greater n6

2022-03-23T15:35:42Z

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

2022-02-22T23:46:40Z

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:Golden ratio approximations]]		[[Category:Golden ratio approximations]]
	[[Category:Octave-reduced harmonics]]		[[Category:Octave-reduced harmonics]]
	~~[[Category:Pages with internal sound examples]]~~

Fredg999: Categories

2022-02-22T17:16:05Z

Fredg999: Categories

2022-02-22T17:13:05Z

Fredg999: Added relation to golden ratio, misc. edits, categories

2021-12-18T18:45:08Z

Added relation to golden ratio, misc. edits, categories

← Older revision		Revision as of 18:45, 18 December 2021
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	{{Infobox Interval		{{Infobox Interval
	~~\| JI glyph =~~
	\| Ratio = 13/8		\| Ratio = 13/8
	\| Monzo = -3 0 0 0 0 1		\| Monzo = -3 0 0 0 0 1
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	== Approximation ==		== Approximation ==
	13/8 is a fraction of a cent away from the neutral sixth found in the [[10edo\|10''n''-edo]] family (7\10).		13/8 is a fraction of a cent away from the neutral sixth found in the [[10edo\|10''n''-edo]] family (7\10).

			This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[golden ratio]]. In this case, 13/8 is ~7.4 [[cent\|¢]] sharp of the golden ratio.

	== See also ==		== See also ==
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	[[Category:13-limit]]		[[Category:13-limit]]
	[[Category:~~Interval ratio]]~~		[[Category:Sixth]]
	~~[[Category:Just interval]]~~
	~~[[Category:Listen~~]]
	[[Category:Neutral sixth]]		[[Category:Neutral sixth]]
	[[Category:~~Sixth~~]]		[[Category:Golden ratio approximations]]
			[[Category:Octave-reduced harmonics]]
			[[Category:Over-2]]
	[[Category:Untwelve]]		[[Category:Untwelve]]
	~~[[Category:Overtone]]~~
	~~[[Category:Over-2]]~~
	[[Category:Pages with internal sound examples]]		[[Category:Pages with internal sound examples]]

← Older revision		Revision as of 15:35, 23 March 2022
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	== See also ==		== See also ==
	* [[16/13]] – its [[octave complement]]		* [[16/13]] – its [[octave complement]]
			* [[64/39]] – the greater tridecimal neutral sixth
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

← Older revision		Revision as of 17:16, 22 February 2022
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	[[Category:Golden ratio approximations]]		[[Category:Golden ratio approximations]]
	[[Category:Octave-reduced harmonics]]		[[Category:Octave-reduced harmonics]]
	~~[[Category:Over-2]]~~
	[[Category:Pages with internal sound examples]]		[[Category:Pages with internal sound examples]]

← Older revision		Revision as of 17:13, 22 February 2022
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	[[Category:Octave-reduced harmonics]]		[[Category:Octave-reduced harmonics]]
	[[Category:Over-2]]		[[Category:Over-2]]
	~~[[Category:Untwelve]]~~
	[[Category:Pages with internal sound examples]]		[[Category:Pages with internal sound examples]]