16/13 - Revision history

Overthink: 13/8 is the octave-reduced form of 13/1

2026-05-30T17:11:54Z

13/8 is the octave-reduced form of 13/1

← Older revision		Revision as of 17:11, 30 May 2026
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	}}		}}

	In [[13-limit]] [[just intonation]], '''16/13''', the '''(greater) tridecimal neutral third''', is a 13-limit-based interval measuring about 359.5¢. It is the inversion of [[13/8]], the 13th harmonic.		In [[13-limit]] [[just intonation]], '''16/13''', the '''(greater) tridecimal neutral third''', is a 13-limit-based interval measuring about 359.5¢. It is the inversion of [[13/8]], the [[octave reduction\|octave-reduced]] 13th harmonic.

	16/13 differs from the Pythagorean major third [[81/64]] by [[1053/1024]], about 48¢, from the classic major third [[5/4]] by [[65/64]], about 27¢, from the undecimal neutral third [[11/9]] by [[144/143]], about 12¢, and from the rastmic neutral third [[27/22]] by [[352/351]], about 4.9¢. A [[List_of_root-3rd-P5_triads_in_JI\|root-3rd-P5 triad]] featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, [[39/32]], which measures about 342.5¢. The interval between these two intervals is [[512/507]], about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th harmonic of the [[harmonic series]].		16/13 differs from the Pythagorean major third [[81/64]] by [[1053/1024]], about 48¢, from the classic major third [[5/4]] by [[65/64]], about 27¢, from the undecimal neutral third [[11/9]] by [[144/143]], about 12¢, and from the rastmic neutral third [[27/22]] by [[352/351]], about 4.9¢. A [[List_of_root-3rd-P5_triads_in_JI\|root-3rd-P5 triad]] featuring 16/13 is 26:32:39, which introduces another tridecimal neutral third, [[39/32]], which measures about 342.5¢. The interval between these two intervals is [[512/507]], about 17¢. While 16/13 is utonal, 39/32 is otonal, as it is the 39th harmonic of the [[harmonic series]].
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	16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]].		16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]].

	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|16/13}}		{{Interval edo approximation\|16/13}}

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

2025-11-03T13:15:24Z

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

← Older revision		Revision as of 13:15, 3 November 2025
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	16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]].		16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]].
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 16/13}}		{{Interval edo approximation\|16/13}}
	== See also ==		== See also ==
	* [[13/8]] – its [[octave complement]]		* [[13/8]] – its [[octave complement]]

Pailiaq at 07:07, 3 November 2025

2025-11-03T07:07:29Z

← Older revision		Revision as of 07:07, 3 November 2025
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	16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]].		16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]].
			== Approximation ==
			{{Interval_Edo_Approximation \| 16/13}}
	== See also ==		== See also ==
	* [[13/8]] – its [[octave complement]]		* [[13/8]] – its [[octave complement]]

Lucius Chiaraviglio: Fix ttypo

2025-05-15T09:05:01Z

Fix ttypo

← Older revision		Revision as of 09:05, 15 May 2025
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	16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.		16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.

	16/13 is near the border-region between neutral ~~thrds~~ and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]].		16/13 is near the border-region between neutral thirds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]].

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

CompactStar at 23:41, 8 March 2023

2023-03-08T23:41:49Z

← Older revision		Revision as of 23:41, 8 March 2023
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	16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.		16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.

	16/13 is near the border-region between neutral thrds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds while still sounding slightly darker than a major third like [[5/4]].		16/13 is near the border-region between neutral thrds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds, while still sounding slightly darker than a major third like [[5/4]].

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

CompactStar at 23:40, 8 March 2023

2023-03-08T23:40:33Z

← Older revision		Revision as of 23:40, 8 March 2023
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	16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.		16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.

	16/13 is near the border-region between neutral thrds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds while still sounding darker than a major third like [[5/4]].		16/13 is near the border-region between neutral thrds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds while still sounding slightly darker than a major third like [[5/4]].

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

CompactStar at 23:40, 8 March 2023

2023-03-08T23:40:12Z

← Older revision		Revision as of 23:40, 8 March 2023
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	16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.		16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.

	16/13 is near the border-region between neutral thrds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds while still ~~not~~ sounding like a [[5/4]] ~~major third~~.		16/13 is near the border-region between neutral thrds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds while still sounding darker than a major third like [[5/4]].

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

CompactStar at 23:39, 8 March 2023

2023-03-08T23:39:50Z

← Older revision		Revision as of 23:39, 8 March 2023
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	16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.		16/13 is a fraction of a cent away from the neutral third found in the 10''n'' family of edos.

			16/13 is near the border-region between neutral thrds and submajor thirds, so it has a bright edge to it compared to narrower neutral thirds while still not sounding like a [[5/4]] major third.

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

Plumtree: Normalising usage of Infobox Interval

2022-10-25T11:26:56Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 11:26, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 16/13~~		\| Name = (greater) tridecimal neutral third, octave-reduced 13th subharmonic
	~~\| Monzo = 4 0 0 0 0 -1~~
	~~\| Cents = 359.47234~~
	\| Name = (greater) tridecimal neutral third, ~~<br>~~octave-reduced 13th subharmonic
	\| Color name = 3u3, thu 3rd		\| Color name = 3u3, thu 3rd
	~~\| FJS name = M3<sub>13</sub>~~
	\| Sound = jid_16_13_pluck_adu_dr220.mp3		\| Sound = jid_16_13_pluck_adu_dr220.mp3
	}}		}}
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	* [[Gallery of Just Intervals]]		* [[Gallery of Just Intervals]]

	~~[[Category:13-limit]]~~
	[[Category:Third]]		[[Category:Third]]
	[[Category:Neutral third]]		[[Category:Neutral third]]
	~~[[Category:Octave-reduced subharmonics]]~~

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

2022-02-22T23:46:42Z

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:Neutral third]]		[[Category:Neutral third]]
	[[Category:Octave-reduced subharmonics]]		[[Category:Octave-reduced subharmonics]]
	~~[[Category:Pages with internal sound examples]]~~