14/11 - Revision history

FloraC: Fix a link

2026-01-16T09:03:32Z

Fix a link

← Older revision		Revision as of 09:03, 16 January 2026
Line 9:		Line 9:
	In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]].		In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]].

	However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function sometimes as a major third, hence the names. Indeed, 14/11 is the simplest [[neogothic major and minor\|neogothic major third]]. It falls between [[5/4]] and [[9/7]], and is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7). It is [[56/55]] sharp of [[5/4]], and [[99/98]] flat of [[9/7]]. As such, it is used to form the gentle major triad, [[22:28:33]]<ref group="note">This is a [[minor minthmic chord]] where 14/11 and [[13/11]] sum to a perfect fifth. Shown here is the simplest JI representation. </ref>. Compare this to 22:28:32 ([[11:14:16]]), which has the much more dissonant [[16/11]] as the outside interval in place of [[3/2]]; 11:14:16 can be voiced as 8:11:14 however, which is less dissonant. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2{{c}}) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4{{c}}). The fact that 14/11 functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.		However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function sometimes as a major third, hence the names. Indeed, 14/11 is the simplest [[neogothic major and minor\|neogothic major third]]. It falls between [[5/4]] and [[9/7]], and is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7). It is [[56/55]] sharp of [[5/4]], and [[99/98]] flat of [[9/7]]. As such, it is used to form the gentle major triad, [[22:28:33]]<ref group="note">This is a [[minor minthmic chords\|minor minthmic chord]] where 14/11 and [[13/11]] sum to a perfect fifth. Shown here is the simplest JI representation. </ref>. Compare this to 22:28:32 ([[11:14:16]]), which has the much more dissonant [[16/11]] as the outside interval in place of [[3/2]]; 11:14:16 can be voiced as 8:11:14 however, which is less dissonant. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2{{c}}) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4{{c}}). The fact that 14/11 functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.

	== Approximation ==		== Approximation ==

FloraC: Paragraphing

2026-01-16T09:03:01Z

Paragraphing

← Older revision		Revision as of 09:03, 16 January 2026
Line 7:		Line 7:
	In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', a major or supermajor third of about 417.5 [[cent]]s. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].		In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', a major or supermajor third of about 417.5 [[cent]]s. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].

	In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]]. However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function sometimes as a major third, hence the names.		In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]].

	Indeed, 14/11 is the simplest [[neogothic major and minor\|neogothic major third]]. It falls between [[5/4]] and [[9/7]], and is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7). It is [[56/55]] sharp of [[5/4]], and [[99/98]] flat of [[9/7]]. As such, it is used to form the gentle major triad, [[22:28:33]]<ref group="note">This is a [[minor minthmic chord]] where 14/11 and [[13/11]] sum to a perfect fifth. Shown here is the simplest JI representation. </ref>. Compare this to 22:28:32 ([[11:14:16]]), which has the much more dissonant [[16/11]] as the outside interval in place of [[3/2]]; 11:14:16 can be voiced as 8:11:14 however, which is less dissonant. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2{{c}}) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4{{c}}). The fact that 14/11 functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.		However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function sometimes as a major third, hence the names. Indeed, 14/11 is the simplest [[neogothic major and minor\|neogothic major third]]. It falls between [[5/4]] and [[9/7]], and is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7). It is [[56/55]] sharp of [[5/4]], and [[99/98]] flat of [[9/7]]. As such, it is used to form the gentle major triad, [[22:28:33]]<ref group="note">This is a [[minor minthmic chord]] where 14/11 and [[13/11]] sum to a perfect fifth. Shown here is the simplest JI representation. </ref>. Compare this to 22:28:32 ([[11:14:16]]), which has the much more dissonant [[16/11]] as the outside interval in place of [[3/2]]; 11:14:16 can be voiced as 8:11:14 however, which is less dissonant. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2{{c}}) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4{{c}}). The fact that 14/11 functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.

	== Approximation ==		== Approximation ==

FloraC: Rework as many chord examples here are substructures of the harmonic eleventh chord, where notating 14/11 as a fourth makes sense. The assumption that fourths must be greater than thirds is a loaded one.

2026-01-16T09:01:38Z

Rework as many chord examples here are substructures of the harmonic eleventh chord, where notating 14/11 as a fourth makes sense. The assumption that fourths must be greater than thirds is a loaded one.

← Older revision		Revision as of 09:01, 16 January 2026
Line 7:		Line 7:
	In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', a major or supermajor third of about 417.5 [[cent]]s. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].		In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', a major or supermajor third of about 417.5 [[cent]]s. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].

	In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function ~~more often~~ as a major third, hence the names.		In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]]. However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function sometimes as a major third, hence the names.

	14/11 is the simplest [[neogothic major and minor\|neogothic major third]]. It falls between [[5/4]] and [[9/7]], and is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7). It is [[56/55]] sharp of [[5/4]], and [[99/98]] flat of [[9/7]]. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2{{c}}) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4{{c}}. The fact that ~~this interval~~ functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.		Indeed, 14/11 is the simplest [[neogothic major and minor\|neogothic major third]]. It falls between [[5/4]] and [[9/7]], and is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7). It is [[56/55]] sharp of [[5/4]], and [[99/98]] flat of [[9/7]]. As such, it is used to form the gentle major triad, [[22:28:33]]<ref group="note">This is a [[minor minthmic chord]] where 14/11 and [[13/11]] sum to a perfect fifth. Shown here is the simplest JI representation. </ref>. Compare this to 22:28:32 ([[11:14:16]]), which has the much more dissonant [[16/11]] as the outside interval in place of [[3/2]]; 11:14:16 can be voiced as 8:11:14 however, which is less dissonant. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2{{c}}) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4{{c}}). The fact that 14/11 functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.

	Despite being around a third in size, due to being notated as an imperfect fourth in many systems, many chords involving it are awkward to notate in terms of diatonic degrees. For example, in [[11:14:16:20]], if [[16/11]] is considered a type of fifth and 14/11 is considered a type of third, then [[8/7]] would be considered a type of third, which is awkward due to its size, but actually makes sense if its inversion 7/4 sometimes considered a sixth. It also appears in the chord [[7:9:11:14]], which consists of three thirds stacked to an octave, but in a diatonic system three thirds would stack to a type of seventh, so one of the intervals would have to be considered a type of fourth instead. In FJS and other systems, 14/11 is considered an imperfect fourth, but 9/7 is wider than it, so it may be considered a diminished fourth in this context instead. In short, this interval shows that diatonic interval classification is far from perfect, and such ambiguity also occurs with [[13/10]] and [[7/5]].

	~~It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament~~.

	== Approximation ==		== Approximation ==
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	== External links ==		== External links ==
	* [http://dkeenan.com/Music/NobleMediant.txt ''The Noble Mediant''] by Margo Schulter and David Keenan		* [http://dkeenan.com/Music/NobleMediant.txt ''The Noble Mediant''] by Margo Schulter and David Keenan

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

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

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

2026-01-16T08:07:48Z

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

← Older revision		Revision as of 08:07, 16 January 2026
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	}}		}}

	In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', ~~or '''[[Neogothic major and minor\|neogothic]] major third,'''~~ a major or supermajor third of about 417.5¢. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].		In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', a major or supermajor third of about 417.5 [[cent]]s. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].

	In many notation systems based on the [[3-~~limit~~]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8¢) by a [[896/891\|pentacircle comma (896/891)]], which makes it function more often as a major third, hence the names.		In many notation systems based on the [[5L 2s\|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function more often as a major third, hence the names.

	14/11 ~~can function as a~~ [[neogothic\|~~neo-Gothic~~]] ~~major third, as it~~ falls between [[5/4]] and [[9/7]]~~. Indeed~~, it is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7)~~, and~~ is [[56/55]] sharp of [[5/4]], [[99/98]] flat of [[9/7]]. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2¢) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4¢. The fact that this interval functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh- as opposed to merely a subminor seventh.		14/11 is the simplest [[neogothic major and minor\|neogothic major third]]. It falls between [[5/4]] and [[9/7]], and is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7). It is [[56/55]] sharp of [[5/4]], and [[99/98]] flat of [[9/7]]. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2{{c}}) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4{{c}}. The fact that this interval functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.

	Despite being around a third in size, due to being notated as an imperfect fourth in many systems, many chords involving it are awkward to notate in terms of diatonic degrees. For example, in [[11:14:16:20]], if [[16/11]] is considered a type of fifth and 14/11 is considered a type of third, then [[8/7]] would be considered a type of third, which is awkward due to its size, but actually makes sense if its inversion 7/4 sometimes considered a sixth. It also appears in the chord [[7:9:11:14]], which consists of three thirds stacked to an octave, but in a diatonic system three thirds would stack to a type of seventh, so one of the intervals would have to be considered a type of fourth instead. In FJS and other systems, 14/11 is considered an imperfect fourth, but 9/7 is wider than it, so it may be considered a diminished fourth in this context instead. In short, this interval shows that diatonic interval classification is far from perfect, and such ambiguity also occurs with [[13/10]] and [[7/5]].		Despite being around a third in size, due to being notated as an imperfect fourth in many systems, many chords involving it are awkward to notate in terms of diatonic degrees. For example, in [[11:14:16:20]], if [[16/11]] is considered a type of fifth and 14/11 is considered a type of third, then [[8/7]] would be considered a type of third, which is awkward due to its size, but actually makes sense if its inversion 7/4 sometimes considered a sixth. It also appears in the chord [[7:9:11:14]], which consists of three thirds stacked to an octave, but in a diatonic system three thirds would stack to a type of seventh, so one of the intervals would have to be considered a type of fourth instead. In FJS and other systems, 14/11 is considered an imperfect fourth, but 9/7 is wider than it, so it may be considered a diminished fourth in this context instead. In short, this interval shows that diatonic interval classification is far from perfect, and such ambiguity also occurs with [[13/10]] and [[7/5]].

	It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.		It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.

	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|14/11}}		{{Interval edo approximation\|14/11}}

	== See also ==		== See also ==
	* [[11/7]] – its [[octave complement]]		* [[11/7]] – its [[octave complement]]

Overthink: Expanded paragraph on diatonic classification

2025-11-05T23:40:38Z

Expanded paragraph on diatonic classification

← Older revision		Revision as of 23:40, 5 November 2025
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	14/11 can function as a [[neogothic\|neo-Gothic]] major third, as it falls between [[5/4]] and [[9/7]]. Indeed, it is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7), and is [[56/55]] sharp of [[5/4]], [[99/98]] flat of [[9/7]]. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2¢) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4¢. The fact that this interval functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh- as opposed to merely a subminor seventh.		14/11 can function as a [[neogothic\|neo-Gothic]] major third, as it falls between [[5/4]] and [[9/7]]. Indeed, it is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7), and is [[56/55]] sharp of [[5/4]], [[99/98]] flat of [[9/7]]. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2¢) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4¢. The fact that this interval functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh- as opposed to merely a subminor seventh.

	Despite being around a third in size, due to being notated as an imperfect fourth in many systems, many chords involving it are awkward to notate in terms of diatonic degrees. For example, in [[11:14:16:20]], if [[16/11]] is considered a type of fifth and 14/11 is considered a type of third, then [[8/7]] would be considered a type of third, which is awkward due to its size, but actually makes sense if its inversion 7/4 sometimes considered a sixth.		Despite being around a third in size, due to being notated as an imperfect fourth in many systems, many chords involving it are awkward to notate in terms of diatonic degrees. For example, in [[11:14:16:20]], if [[16/11]] is considered a type of fifth and 14/11 is considered a type of third, then [[8/7]] would be considered a type of third, which is awkward due to its size, but actually makes sense if its inversion 7/4 sometimes considered a sixth. It also appears in the chord [[7:9:11:14]], which consists of three thirds stacked to an octave, but in a diatonic system three thirds would stack to a type of seventh, so one of the intervals would have to be considered a type of fourth instead. In FJS and other systems, 14/11 is considered an imperfect fourth, but 9/7 is wider than it, so it may be considered a diminished fourth in this context instead. In short, this interval shows that diatonic interval classification is far from perfect, and such ambiguity also occurs with [[13/10]] and [[7/5]].

	It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.		It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.

Overthink: added note on diatonic notation of chords

2025-11-05T17:10:13Z

added note on diatonic notation of chords

← Older revision		Revision as of 17:10, 5 November 2025
Line 10:		Line 10:

	14/11 can function as a [[neogothic\|neo-Gothic]] major third, as it falls between [[5/4]] and [[9/7]]. Indeed, it is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7), and is [[56/55]] sharp of [[5/4]], [[99/98]] flat of [[9/7]]. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2¢) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4¢. The fact that this interval functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh- as opposed to merely a subminor seventh.		14/11 can function as a [[neogothic\|neo-Gothic]] major third, as it falls between [[5/4]] and [[9/7]]. Indeed, it is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7), and is [[56/55]] sharp of [[5/4]], [[99/98]] flat of [[9/7]]. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2¢) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4¢. The fact that this interval functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh- as opposed to merely a subminor seventh.

			Despite being around a third in size, due to being notated as an imperfect fourth in many systems, many chords involving it are awkward to notate in terms of diatonic degrees. For example, in [[11:14:16:20]], if [[16/11]] is considered a type of fifth and 14/11 is considered a type of third, then [[8/7]] would be considered a type of third, which is awkward due to its size, but actually makes sense if its inversion 7/4 sometimes considered a sixth.

	It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.		It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.

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

2025-11-03T13:04:53Z

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

← Older revision		Revision as of 13:04, 3 November 2025
Line 13:		Line 13:
	It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.		It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 14/11}}		{{Interval edo approximation\|14/11}}
	== See also ==		== See also ==
	* [[11/7]] – its [[octave complement]]		* [[11/7]] – its [[octave complement]]

Pailiaq at 07:14, 3 November 2025

2025-11-03T07:14:56Z

← Older revision		Revision as of 07:14, 3 November 2025
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	It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.		It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.
			== Approximation ==
			{{Interval_Edo_Approximation \| 14/11}}
	== See also ==		== See also ==
	* [[11/7]] – its [[octave complement]]		* [[11/7]] – its [[octave complement]]

VectorGraphics at 01:07, 2 June 2025

2025-06-02T01:07:48Z

← Older revision		Revision as of 01:07, 2 June 2025
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	}}		}}

	In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', or '''neogothic major third,''' a major or supermajor third of about 417.5¢. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].		In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', or '''[[Neogothic major and minor\|neogothic]] major third,''' a major or supermajor third of about 417.5¢. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].

	In many notation systems based on the [[3-limit]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8¢) by a [[896/891\|pentacircle comma (896/891)]], which makes it function more often as a major third, hence the names.		In many notation systems based on the [[3-limit]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8¢) by a [[896/891\|pentacircle comma (896/891)]], which makes it function more often as a major third, hence the names.

VectorGraphics: regardless of that, this is still the neogothic major third

2025-04-16T15:58:52Z

regardless of that, this is still the neogothic major third

← Older revision		Revision as of 15:58, 16 April 2025
Line 5:		Line 5:
	}}		}}

	In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', a major or supermajor third of about 417.5¢. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].		In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', or '''neogothic major third,''' a major or supermajor third of about 417.5¢. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].

	In many notation systems based on the [[3-limit]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8¢) by a [[896/891\|pentacircle comma (896/891)]], which makes it function more often as a major third, hence the names.		In many notation systems based on the [[3-limit]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3\|perfect fourth (4/3)]] minus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8¢) by a [[896/891\|pentacircle comma (896/891)]], which makes it function more often as a major third, hence the names.