13/12 - Revision history

Overthink: fill in temperaments section

2026-01-27T05:30:38Z

fill in temperaments section

← Older revision		Revision as of 05:30, 27 January 2026
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	In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).		In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).

	~~== Temperaments ==~~
	~~{{Todo\|expand\|inline=1}}~~

	== Approximation ==		== Approximation ==
	It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].		It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].
	{{Interval edo approximation\|{{PAGENAME}}}}		{{Interval edo approximation\|{{PAGENAME}}}}

			== Temperaments ==
			13/12 can be used to generate [[bleu]] temperament in the 2.3.7.11.13 subgroup, mapping [[3/2]] to +5 generators, [[7/4]] to +7 generators, [[11/8]] to +4 generators, and [[13/8]] to +6 generators.

			A slightly sharp 13/12 generates [[glacier]] temperament, which equates 5 13/12's to 3/2 like bleu. This temperament has an extension to the 2.3.7.11.13.23.29 subgroup which is more complex but much more accurate than bleu.

	== See also ==		== See also ==
	* [[24/13]] – its [[octave complement]]		* [[24/13]] – its [[octave complement]]

Pailiaq at 20:49, 3 November 2025

2025-11-03T20:49:58Z

← Older revision		Revision as of 20:49, 3 November 2025
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	== Approximation ==		== Approximation ==
	It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].		It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].
			{{Interval edo approximation\|{{PAGENAME}}}}
	== See also ==		== See also ==
	* [[24/13]] – its [[octave complement]]		* [[24/13]] – its [[octave complement]]

Hkm at 22:37, 2 April 2025

2025-04-02T22:37:33Z

← Older revision		Revision as of 22:37, 2 April 2025
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	In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).		In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).

			== Temperaments ==
			{{Todo\|expand\|inline=1}}

			== Approximation ==
	It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].		It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].

Hkm: Material about 17edo should go in the 17edo page, which already has material about chords.

2025-04-02T22:35:28Z

Material about 17edo should go in the 17edo page, which already has material about chords.

← Older revision		Revision as of 22:35, 2 April 2025
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	In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).		In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).

	The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.

	It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].		It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].

Lériendil at 06:33, 20 November 2024

2024-11-20T06:33:55Z

← Older revision		Revision as of 06:33, 20 November 2024
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	The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.		The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.

			It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].

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

Aura at 16:15, 14 December 2023

2023-12-14T16:15:35Z

← Older revision		Revision as of 16:15, 14 December 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = tridecimal neutral second		\| Name = (lesser) tridecimal neutral second
	\| Color name = 3o2, tho 2nd		\| Color name = 3o2, tho 2nd
	\| Sound = jid_13_12_pluck_adu_dr220.mp3		\| Sound = jid_13_12_pluck_adu_dr220.mp3
	}}		}}

	In [[13-limit]] [[just intonation]], '''13/12''' is the '''tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).		In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).

	The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.		The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.

Plumtree: Normalising usage of Infobox Interval

2022-10-25T11:34:45Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 11:34, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 13/12~~
	~~\| Monzo = -2 -1 0 0 0 1~~
	~~\| Cents = 138.57266~~
	\| Name = tridecimal neutral second		\| Name = tridecimal neutral second
	\| Color name = 3o2, tho 2nd		\| Color name = 3o2, tho 2nd
	~~\| FJS name = m2<sup>13</sup>~~
	\| Sound = jid_13_12_pluck_adu_dr220.mp3		\| Sound = jid_13_12_pluck_adu_dr220.mp3
	}}		}}
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	~~[[Category:13-limit]]~~
	[[Category:Second]]		[[Category:Second]]
	[[Category:Neutral second]]		[[Category:Neutral second]]
	~~[[Category:Superparticular]]~~

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:Neutral second]]		[[Category:Neutral second]]
	[[Category:Superparticular]]		[[Category:Superparticular]]
	~~[[Category:Pages with internal sound examples]]~~

Fredg999: Specified the full interval name in the article body

2021-12-12T19:41:49Z

Specified the full interval name in the article body

← Older revision		Revision as of 19:41, 12 December 2021
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	}}		}}

	In [[13-limit]] [[just intonation]], '''13/12''' is a '''neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).		In [[13-limit]] [[just intonation]], '''13/12''' is the '''tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).

	The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.		The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.

Fredg999: Misc. edits, categories

2021-12-12T19:38:19Z

Misc. edits, categories

← Older revision		Revision as of 19:38, 12 December 2021
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 13/12		\| Ratio = 13/12
	\| Monzo = -2 -1 0 0 0 1		\| Monzo = -2 -1 0 0 0 1
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	}}		}}

	In [[13-limit]] [[~~Just Intonation~~]], '''13/12''' is a '''neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th ~~overtone~~ (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).		In [[13-limit]] [[just intonation]], '''13/12''' is a '''neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).

	The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.		The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.
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	[[Category:13-limit]]		[[Category:13-limit]]
	[[Category:~~Interval]]~~		[[Category:Second]]
	~~[[Category:Just interval]]~~
	~~[[Category:Ratio~~]]
	[[Category:Neutral second]]		[[Category:Neutral second]]
	~~[[Category:Second]]~~
	[[Category:Superparticular]]		[[Category:Superparticular]]
	[[Category:Pages with internal sound examples]]		[[Category:Pages with internal sound examples]]