13/11 - Revision history

FloraC: Fix references

2026-01-16T09:26:46Z

Fix references

← Older revision		Revision as of 09:26, 16 January 2026
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	== External links ==		== External links ==
	* [http://dkeenan.com/Music/NobleMediant.txt ''The Noble Mediant''] by Margo Schulter and David Keenan, the earliest description of 13/11 as the "neo-Gothic" minor third		* [http://dkeenan.com/Music/NobleMediant.txt ''The Noble Mediant''] by Margo Schulter and David Keenan, the earliest description of 13/11 as the "neo-Gothic" minor third

			== Notes ==
			<references group="note"/>

	[[Category:Third]]		[[Category:Third]]

FloraC: "Neogothic" is used as an interval region these days.

2026-01-16T09:25:13Z

"Neogothic" is used as an interval region these days.

← Older revision		Revision as of 09:25, 16 January 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = tridecimal ~~minor third, neogothic~~ minor third, major minthmic minor third		\| Name = tridecimal minor third, major minthmic minor third
	\| Color name = 3o1u3, tholu 3rd		\| Color name = 3o1u3, tholu 3rd
	\| Sound = jid_13_11_pluck_adu_dr220.mp3		\| Sound = jid_13_11_pluck_adu_dr220.mp3
	}}		}}

	In [[13-limit]] [[just intonation]], '''13/11''' is ~~the~~ '''tridecimal minor third''', ~~'''neogothic minor third''' or~~ '''major minthmic minor third''', measuring about 289.2¢. It is the difference between the [[11/1\|11th]] and [[13/1\|13th]] [[harmonic]]s. The (octave-reduced) 11th harmonic ([[11/8]], about 551.3¢) and 13th harmonic ([[13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third – it is a [[352/351\|major minthma (352/351)]] narrower than the [[32/27\|Pythagorean minor third (32/27)]]. It can ~~even~~ function as such in a 13-limit [[neogothic]] minor triad of 22:26:33, with a [[3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.		In [[13-limit]] [[just intonation]], '''13/11''' is a '''tridecimal minor third''', specifically the '''major minthmic minor third''', measuring about 289.2 [[cent]]s. It is the difference between the [[11/1\|11th]] and [[13/1\|13th]] [[harmonic]]s. The octave-reduced 11th harmonic ([[11/8]], about 551.3{{c}}) and 13th harmonic ([[13/8]], about 840.5{{c}}) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third – it is a [[352/351\|major minthma (352/351)]] narrower than the [[32/27\|Pythagorean minor third (32/27)]]. It is the simplest [[neogothic major and minor\|neogothic minor third]], and can function as such in a 13-limit neogothic minor triad of [[22:26:33]], with a [[3/2]] perfect fifth between 33 and 22<ref group="note">This is a [[minor minthmic chords\|minor minthmic chord]] where 13/11 and [[14/11]] sum to a perfect fifth. Shown here is the simplest JI representation. </ref>. Compare this to 22:26:32 ([[11:13:16]]), which has the much more dissonant [[16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as [[5:6:7]].

	13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6/5]] and [[7/6]], as it can be given as (6+7)/(5+6). This puts it in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13+7)/(11+6) = [[20/17]], the septendecimal subminor third, about 281.4¢) and between 13/11 and 6/5 (which yields (13+6)/(11+5) = [[19/16]], the overtone minor third of [[19-limit]] JI, about 297.5¢). (See the diagram below.)		13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6/5]] and [[7/6]], as it can be given as (6 + 7)/(5 + 6). This puts it in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13 + 7)/(11 + 6) = [[20/17]], the septendecimal subminor third, about 281.4{{c}}) and between 13/11 and 6/5 (which yields (13 + 6)/(11 + 5) = [[19/16]], the overtone minor third of [[19-limit]] JI, about 297.5{{c}}). See the diagram below.

	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|-		\|-
	! ~~subminor~~ and minor third		! Subminor and minor third
	\| 7/6 <br> 266.9¢		\| 7/6 <br> 266.9{{c}}
	\| colspan="7" \|		\| colspan="7" \|
	\| 6/5 <br> 315.6¢		\| 6/5 <br> 315.6{{c}}
	\|-		\|-
	! ~~interval~~ in between		! Interval in between
	\|		\|
	\| colspan="3" \| <<		\| colspan="3" \| <<
	\| [[36/35\|36:35]] <br> 48.7¢		\| [[36/35\|36:35]] <br> 48.7{{c}}
	\| colspan="3" \| >>		\| colspan="3" \| >>
	\|		\|
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	\| colspan="9" \|		\| colspan="9" \|
	\|-		\|-
	! ~~add~~ mediant (13/11)		! Add mediant (13/11)
	\| 7/6 <br> 266.9¢		\| 7/6 <br> 266.9{{c}}
	\| colspan="3" \|		\| colspan="3" \|
	\| 13/11 <br> 289.2¢		\| 13/11 <br> 289.2{{c}}
	\| colspan="3" \|		\| colspan="3" \|
	\| 6/5 <br> 315.6¢		\| 6/5 <br> 315.6{{c}}
	\|-		\|-
	! ~~intervals~~ in between		! Intervals in between
	\|		\|
	\| <<		\| <<
	\| [[78/77\|78:77]] <br> 22.3¢		\| [[78/77\|78:77]] <br> 22.3{{c}}
	\| >>		\| >>
	\|		\|
	\| <<		\| <<
	\| [[66/65\|66:65]] <br> 26.4¢		\| [[66/65\|66:65]] <br> 26.4{{c}}
	\| >>		\| >>
	\|		\|
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	\| colspan="9" \|		\| colspan="9" \|
	\|-		\|-
	! ~~add~~ mediants (20/17 and 19/16)		! Add mediants (20/17 and 19/16)
	\| 7/6 <br> 266.9¢		\| 7/6 <br> 266.9{{c}}
	\|		\|
	\| [[20/17]] <br> 281.4¢		\| [[20/17]] <br> 281.4{{c}}
	\|		\|
	\| '''13/11''' <br> '''289.2¢'''		\| '''13/11''' <br> '''289.2{{c}}'''
	\|		\|
	\| [[19/16]] <br> 297.5¢		\| [[19/16]] <br> 297.5{{c}}
	\|		\|
	\| 6/5 <br> 315.6¢		\| 6/5 <br> 315.6{{c}}
	\|-		\|-
	! ~~intervals~~ in between		! Intervals in between
	\|		\|
	\| << [[120/119\|120:119]] >> <br> 14.5¢		\| << [[120/119\|120:119]] >> <br> 14.5{{c}}
	\|		\|
	\| << [[221/220\|221:220]] >> <br> 7.9¢		\| << [[221/220\|221:220]] >> <br> 7.9{{c}}
	\|		\|
	\| << [[209/208\|209:208]] >> <br> 8.3¢		\| << [[209/208\|209:208]] >> <br> 8.3{{c}}
	\|		\|
	\| << [[96/95\|96:95]] >> <br> 18.1¢		\| << [[96/95\|96:95]] >> <br> 18.1{{c}}
	\|		\|
	\|}		\|}
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	== Approximation ==		== Approximation ==
	This interval is well approximated by [[17edo\|4\17]] (282.353 cents), and even better, by [[29edo\|7\29]] (289.655 cents).		This interval is well approximated by [[17edo\|4\17]] (282.353 cents), and even better, by [[29edo\|7\29]] (289.655 cents).

	{{Interval edo approximation\|13/11}}		{{Interval edo approximation\|13/11}}

	== See also ==		== See also ==
	* [[22/13]] – its [[octave complement]]		* [[22/13]] – its [[octave complement]]

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

2025-11-03T13:11:35Z

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

← Older revision		Revision as of 13:11, 3 November 2025
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	== Approximation ==		== Approximation ==
	This interval is well approximated by [[17edo\|4\17]] (282.353 cents), and even better, by [[29edo\|7\29]] (289.655 cents).		This interval is well approximated by [[17edo\|4\17]] (282.353 cents), and even better, by [[29edo\|7\29]] (289.655 cents).
	{{~~Interval_Edo_Approximation~~ \| 13/11}}		{{Interval edo approximation\|13/11}}
	== See also ==		== See also ==
	* [[22/13]] – its [[octave complement]]		* [[22/13]] – its [[octave complement]]

Pailiaq at 06:59, 3 November 2025

2025-11-03T06:59:49Z

← Older revision		Revision as of 06:59, 3 November 2025
Line 72:		Line 72:
	== Approximation ==		== Approximation ==
	This interval is well approximated by [[17edo\|4\17]] (282.353 cents), and even better, by [[29edo\|7\29]] (289.655 cents).		This interval is well approximated by [[17edo\|4\17]] (282.353 cents), and even better, by [[29edo\|7\29]] (289.655 cents).
			{{Interval_Edo_Approximation \| 13/11}}
	== See also ==		== See also ==
	* [[22/13]] – its [[octave complement]]		* [[22/13]] – its [[octave complement]]

FloraC: Fix negligence

2025-04-16T13:49:24Z

Fix negligence

← Older revision		Revision as of 13:49, 16 April 2025
Line 5:		Line 5:
	}}		}}

	In [[13-limit]] [[just intonation]], '''13/11''' is the '''tridecimal minor third''', '''neogothic minor third''' or '''major minthmic minor third''', measuring about 289.2¢. It is the difference between the [[11/1\|11th]] and [[13/1\|13th]] [[harmonic]]s. The (octave-reduced) 11th harmonic ([[11/8]], about 551.3¢) and 13th harmonic ([[13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third – it is a [[352/351\|major minthma (352/351)]] narrower than the [[32/27\|Pythagorean minor third (32/27)]]. It can even function as such in a 13-limit [[neogothic~~\|neo-Gothic~~]] minor triad of 22:26:33, with a [[3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.		In [[13-limit]] [[just intonation]], '''13/11''' is the '''tridecimal minor third''', '''neogothic minor third''' or '''major minthmic minor third''', measuring about 289.2¢. It is the difference between the [[11/1\|11th]] and [[13/1\|13th]] [[harmonic]]s. The (octave-reduced) 11th harmonic ([[11/8]], about 551.3¢) and 13th harmonic ([[13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third – it is a [[352/351\|major minthma (352/351)]] narrower than the [[32/27\|Pythagorean minor third (32/27)]]. It can even function as such in a 13-limit [[neogothic]] minor triad of 22:26:33, with a [[3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.

	13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6/5]] and [[7/6]], as it can be given as (6+7)/(5+6). This puts it in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13+7)/(11+6) = [[20/17]], the septendecimal subminor third, about 281.4¢) and between 13/11 and 6/5 (which yields (13+6)/(11+5) = [[19/16]], the overtone minor third of [[19-limit]] JI, about 297.5¢). (See the diagram below.)		13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6/5]] and [[7/6]], as it can be given as (6+7)/(5+6). This puts it in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13+7)/(11+6) = [[20/17]], the septendecimal subminor third, about 281.4¢) and between 13/11 and 6/5 (which yields (13+6)/(11+5) = [[19/16]], the overtone minor third of [[19-limit]] JI, about 297.5¢). (See the diagram below.)

VectorGraphics: "neogothic" is usually written as one word

2025-04-16T08:40:42Z

"neogothic" is usually written as one word

← Older revision		Revision as of 08:40, 16 April 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = tridecimal minor third, ~~neo-Gothic~~ minor third, major minthmic minor third		\| Name = tridecimal minor third, neogothic minor third, major minthmic minor third
	\| Color name = 3o1u3, tholu 3rd		\| Color name = 3o1u3, tholu 3rd
	\| Sound = jid_13_11_pluck_adu_dr220.mp3		\| Sound = jid_13_11_pluck_adu_dr220.mp3
	}}		}}

	In [[13-limit]] [[just intonation]], '''13/11''' is the '''tridecimal minor third''', '''~~neo-Gothic~~ minor third''' or '''major minthmic minor third''', measuring about 289.2¢. It is the difference between the [[11/1\|11th]] and [[13/1\|13th]] [[harmonic]]s. The (octave-reduced) 11th harmonic ([[11/8]], about 551.3¢) and 13th harmonic ([[13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third – it is a [[352/351\|major minthma (352/351)]] narrower than the [[32/27\|Pythagorean minor third (32/27)]]. It can even function as such in a 13-limit [[neogothic\|neo-Gothic]] minor triad of 22:26:33, with a [[3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.		In [[13-limit]] [[just intonation]], '''13/11''' is the '''tridecimal minor third''', '''neogothic minor third''' or '''major minthmic minor third''', measuring about 289.2¢. It is the difference between the [[11/1\|11th]] and [[13/1\|13th]] [[harmonic]]s. The (octave-reduced) 11th harmonic ([[11/8]], about 551.3¢) and 13th harmonic ([[13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third – it is a [[352/351\|major minthma (352/351)]] narrower than the [[32/27\|Pythagorean minor third (32/27)]]. It can even function as such in a 13-limit [[neogothic\|neo-Gothic]] minor triad of 22:26:33, with a [[3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.

	13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6/5]] and [[7/6]], as it can be given as (6+7)/(5+6). This puts it in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13+7)/(11+6) = [[20/17]], the septendecimal subminor third, about 281.4¢) and between 13/11 and 6/5 (which yields (13+6)/(11+5) = [[19/16]], the overtone minor third of [[19-limit]] JI, about 297.5¢). (See the diagram below.)		13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6/5]] and [[7/6]], as it can be given as (6+7)/(5+6). This puts it in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13+7)/(11+6) = [[20/17]], the septendecimal subminor third, about 281.4¢) and between 13/11 and 6/5 (which yields (13+6)/(11+5) = [[19/16]], the overtone minor third of [[19-limit]] JI, about 297.5¢). (See the diagram below.)

Lucius Chiaraviglio: Add missing word

2025-01-19T00:22:57Z

Add missing word

← Older revision		Revision as of 00:22, 19 January 2025
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	In [[13-limit]] [[just intonation]], '''13/11''' is the '''tridecimal minor third''', '''neo-Gothic minor third''' or '''major minthmic minor third''', measuring about 289.2¢. It is the difference between the [[11/1\|11th]] and [[13/1\|13th]] [[harmonic]]s. The (octave-reduced) 11th harmonic ([[11/8]], about 551.3¢) and 13th harmonic ([[13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third – it is a [[352/351\|major minthma (352/351)]] narrower than the [[32/27\|Pythagorean minor third (32/27)]]. It can even function as such in a 13-limit [[neogothic\|neo-Gothic]] minor triad of 22:26:33, with a [[3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.		In [[13-limit]] [[just intonation]], '''13/11''' is the '''tridecimal minor third''', '''neo-Gothic minor third''' or '''major minthmic minor third''', measuring about 289.2¢. It is the difference between the [[11/1\|11th]] and [[13/1\|13th]] [[harmonic]]s. The (octave-reduced) 11th harmonic ([[11/8]], about 551.3¢) and 13th harmonic ([[13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third – it is a [[352/351\|major minthma (352/351)]] narrower than the [[32/27\|Pythagorean minor third (32/27)]]. It can even function as such in a 13-limit [[neogothic\|neo-Gothic]] minor triad of 22:26:33, with a [[3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.

	13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6/5]] and [[7/6]], as it can be given as (6+7)/(5+6). This puts in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13+7)/(11+6) = [[20/17]], the septendecimal subminor third, about 281.4¢) and between 13/11 and 6/5 (which yields (13+6)/(11+5) = [[19/16]], the overtone minor third of [[19-limit]] JI, about 297.5¢). (See the diagram below.)		13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6/5]] and [[7/6]], as it can be given as (6+7)/(5+6). This puts it in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13+7)/(11+6) = [[20/17]], the septendecimal subminor third, about 281.4¢) and between 13/11 and 6/5 (which yields (13+6)/(11+5) = [[19/16]], the overtone minor third of [[19-limit]] JI, about 297.5¢). (See the diagram below.)

	{\| class="wikitable center-all"		{\| class="wikitable center-all"

BudjarnLambeth: Category:Taxicab-2 intervals

2024-12-01T22:58:23Z

Category:Taxicab-2 intervals

← Older revision		Revision as of 22:58, 1 December 2024
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	[[Category:Gentle]]		[[Category:Gentle]]
	[[Category:Neo-gothic]]		[[Category:Neo-gothic]]
			[[Category:Taxicab-2 intervals]]

BudjarnLambeth: /* See also */ link

2024-10-26T23:54:44Z

FloraC: Recategorize

2024-09-30T08:45:27Z

Recategorize

← Older revision		Revision as of 08:45, 30 September 2024
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	[[Category:Third]]		[[Category:Third]]
	[[Category:Minor third]]		[[Category:Minor third]]
	[[Category:Over-11]]		[[Category:Over-11 intervals]]
	[[Category:Major minthmic]]		[[Category:Major minthmic]]
	[[Category:Gentle]]		[[Category:Gentle]]
	[[Category:Neo-gothic]]		[[Category:Neo-gothic]]

← Older revision		Revision as of 23:54, 26 October 2024
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	* [[33/26]] – its [[fifth complement]]		* [[33/26]] – its [[fifth complement]]
	* [[44/39]] – its [[fourth complement]]		* [[44/39]] – its [[fourth complement]]
			* [[Ed13/11]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Gentle chords]]		* [[Gentle chords]]