7/4 - Revision history

AraMax at 10:17, 21 May 2025

2025-05-21T10:17:58Z

← Older revision		Revision as of 10:17, 21 May 2025
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	\| es =		\| es =
	\| ja =		\| ja =
			\| ro = 7/4 (ro)
	}}		}}
	{{Infobox Interval		{{Infobox Interval

Sintel at 21:16, 1 May 2025

2025-05-01T21:16:38Z

← Older revision		Revision as of 21:16, 1 May 2025
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	{{Wikipedia\|Harmonic seventh}}		{{Wikipedia\|Harmonic seventh}}

	Frequency ratio '''7/4''', measuring approximately 968.8 [[cent]]s, named '''harmonic seventh''' or '''natural seventh''', represents the interval between the 4th and 7th harmonics in the [[harmonic series]]. It is also called a '''septimal (sub)minor seventh''' – the word "septimal" referring to the presence of a 7 as the highest [[prime]] in the ratio, and the word "subminor" referring to the harmonic seventh's narrowness compared with a traditional minor seventh (such as [[9/5]] or [[16/9]], [[12edo]]'s 1000-cent interval, or a minor seventh found in a meantone system). It is traditionally seen as a seventh, though it may show up as a sixth in ~~rare uses, specifically as the sum of 11/8 and a 14/11 neomajor third as per [[User:Aura/Aura's Ideas on Functional Harmony #Basic Paradiatonic Functions\|this example]]~~.		Frequency ratio '''7/4''', measuring approximately 968.8 [[cent]]s, named '''harmonic seventh''' or '''natural seventh''', represents the interval between the 4th and 7th harmonics in the [[harmonic series]]. It is also called a '''septimal (sub)minor seventh''' – the word "septimal" referring to the presence of a 7 as the highest [[prime]] in the ratio, and the word "subminor" referring to the harmonic seventh's narrowness compared with a traditional minor seventh (such as [[9/5]] or [[16/9]], [[12edo]]'s 1000-cent interval, or a minor seventh found in a meantone system). It is traditionally seen as a minor seventh, though it may show up as an augmented sixth in some cases.

	7/4 has seen use in blues music, barbershop quartet music, and some musical traditions of the world, but has mostly not been recognized as a "[[consonance]]" in Western music theory. In most [[Just Intonation]] systems, the harmonic seventh is treated as a fundamental consonance in its own right, with its own distinct quality.		7/4 has seen use in blues music, barbershop quartet music, and some musical traditions of the world, but has mostly not been recognized as a "[[consonance]]" in Western music theory. In most [[Just Intonation]] systems, the harmonic seventh is treated as a fundamental consonance in its own right, with its own distinct quality.

VectorGraphics at 16:57, 14 April 2025

2025-04-14T16:57:42Z

← Older revision		Revision as of 16:57, 14 April 2025
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	{{Wikipedia\|Harmonic seventh}}		{{Wikipedia\|Harmonic seventh}}

	Frequency ratio '''7/4''', measuring approximately 968.8 [[cent]]s, named '''harmonic seventh''' or '''natural seventh''', represents the interval between the 4th and 7th harmonics in the [[harmonic series]]. It is also called a '''septimal minor ~~seventh''' or '''subminor~~ seventh''' – the word "septimal" referring to the presence of a 7 as the highest [[prime]] in the ratio, and the word "subminor" referring to the harmonic seventh's narrowness compared with a traditional minor seventh (such as [[9/5]] or [[16/9]], [[12edo]]'s 1000-cent interval, or a minor seventh found in a meantone system). It is traditionally seen as a seventh, though it may show up as a sixth in rare uses, specifically as the sum of 11/8 and a 14/11 neomajor third as per [[User:Aura/Aura's Ideas on Functional Harmony #Basic Paradiatonic Functions\|this example]].		Frequency ratio '''7/4''', measuring approximately 968.8 [[cent]]s, named '''harmonic seventh''' or '''natural seventh''', represents the interval between the 4th and 7th harmonics in the [[harmonic series]]. It is also called a '''septimal (sub)minor seventh''' – the word "septimal" referring to the presence of a 7 as the highest [[prime]] in the ratio, and the word "subminor" referring to the harmonic seventh's narrowness compared with a traditional minor seventh (such as [[9/5]] or [[16/9]], [[12edo]]'s 1000-cent interval, or a minor seventh found in a meantone system). It is traditionally seen as a seventh, though it may show up as a sixth in rare uses, specifically as the sum of 11/8 and a 14/11 neomajor third as per [[User:Aura/Aura's Ideas on Functional Harmony #Basic Paradiatonic Functions\|this example]].

	7/4 has seen use in blues music, barbershop quartet music, and some musical traditions of the world, but has mostly not been recognized as a "[[consonance]]" in Western music theory. In most [[Just Intonation]] systems, the harmonic seventh is treated as a fundamental consonance in its own right, with its own distinct quality.		7/4 has seen use in blues music, barbershop quartet music, and some musical traditions of the world, but has mostly not been recognized as a "[[consonance]]" in Western music theory. In most [[Just Intonation]] systems, the harmonic seventh is treated as a fundamental consonance in its own right, with its own distinct quality.

BudjarnLambeth: /* See also */ link

2024-10-26T23:59:09Z

CompactStar at 00:18, 1 September 2024

2024-09-01T00:18:18Z

← Older revision		Revision as of 00:18, 1 September 2024
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	== Harmonic seventh chord ==		== Harmonic seventh chord ==
	7:4 appears in an otonal tetrad that forms the basis of much JI music, commonly called a "harmonic seventh chord". It consists of a major triad (4:5:6) plus a harmonic seventh: 4:5:6:7(:8). This tetrad, a hallmark of blues and barbershop harmony, not to mention modern Just Intonation practice, represents a sequence of overtones from the fourth to the seventh. (8, being a doubling of 4, represents an octave above the root.) The intervals between adjacent members of the chord decrease in size:		7:4 appears in an otonal tetrad that forms the basis of much JI music, commonly called a "harmonic seventh chord". It consists of a ptolemaic major triad (4:5:6) plus a harmonic seventh: 4:5:6:7(:8). This tetrad, a hallmark of blues and barbershop harmony, not to mention modern Just Intonation practice, represents a sequence of overtones from the fourth to the seventh. (8, being a doubling of 4, represents an octave above the root.) The intervals between adjacent members of the chord decrease in size:

	{\| class="wikitable"		{\| class="wikitable"

CompactStar at 00:17, 1 September 2024

2024-09-01T00:17:52Z

← Older revision		Revision as of 00:17, 1 September 2024
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	In [[Meantone family #Septimal meantone\|meantone systems]] – which are generated by repeatedly stacking a slightly flattened (from just) [[perfect fifth]] such that four fifths gives a near-just major third of 5/4 – there is sometimes a good approximation of the harmonic seventh in the form of an augmented sixth. [[Quarter-comma meantone]] (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh falling somewhere between 16/9 and 9/5. The augmented sixth appears in tonal harmony in the augmented sixth chord. The so-called [[German sixth chord]], in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).		In [[Meantone family #Septimal meantone\|meantone systems]] – which are generated by repeatedly stacking a slightly flattened (from just) [[perfect fifth]] such that four fifths gives a near-just major third of 5/4 – there is sometimes a good approximation of the harmonic seventh in the form of an augmented sixth. [[Quarter-comma meantone]] (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh falling somewhere between 16/9 and 9/5. The augmented sixth appears in tonal harmony in the augmented sixth chord. The so-called [[German sixth chord]], in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).

	Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents – about 22 cents flat of 7:4, and so less effective as a consonance. Systems on the flat end of reasonable meantone tunings, flatter than [[19edo]], have the augmented sixth closer to [[12/7]], while the diminished seventh is closer to [[7/4]]. Mapping the harmonic seventh to A6 is known as [[septimal meantone]] and mapping it to d7 is known as [[flattone]].		Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents – about 22 cents flat of 7:4, and so less effective as a consonance. Systems on the flat end of reasonable meantone tunings, flatter than [[19edo]], have the augmented sixth closer to [[12/7]], while the diminished seventh is closer to 7/4. Mapping the harmonic seventh to A6 is known as [[septimal meantone]] and mapping it to d7 is known as [[flattone]].

	== Approximations by EDOs ==		== Approximations by EDOs ==

CompactStar at 00:17, 1 September 2024

2024-09-01T00:17:45Z

← Older revision		Revision as of 00:17, 1 September 2024
Line 58:		Line 58:
	In [[Meantone family #Septimal meantone\|meantone systems]] – which are generated by repeatedly stacking a slightly flattened (from just) [[perfect fifth]] such that four fifths gives a near-just major third of 5/4 – there is sometimes a good approximation of the harmonic seventh in the form of an augmented sixth. [[Quarter-comma meantone]] (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh falling somewhere between 16/9 and 9/5. The augmented sixth appears in tonal harmony in the augmented sixth chord. The so-called [[German sixth chord]], in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).		In [[Meantone family #Septimal meantone\|meantone systems]] – which are generated by repeatedly stacking a slightly flattened (from just) [[perfect fifth]] such that four fifths gives a near-just major third of 5/4 – there is sometimes a good approximation of the harmonic seventh in the form of an augmented sixth. [[Quarter-comma meantone]] (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh falling somewhere between 16/9 and 9/5. The augmented sixth appears in tonal harmony in the augmented sixth chord. The so-called [[German sixth chord]], in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).

	Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents – about 22 cents flat of 7:4, and so less effective as a consonance.		Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents – about 22 cents flat of 7:4, and so less effective as a consonance. Systems on the flat end of reasonable meantone tunings, flatter than [[19edo]], have the augmented sixth closer to [[12/7]], while the diminished seventh is closer to [[7/4]]. Mapping the harmonic seventh to A6 is known as [[septimal meantone]] and mapping it to d7 is known as [[flattone]].

	== Approximations by EDOs ==		== Approximations by EDOs ==

FloraC: /* Meantone augmented sixth */ move part of this to the German sixth chord page

2024-08-15T14:34:03Z

Meantone augmented sixth: move part of this to the German sixth chord page

← Older revision		Revision as of 14:34, 15 August 2024
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	{{See also\| Meantone }}		{{See also\| Meantone }}

	In [[Meantone family #Septimal meantone\|meantone systems]] – which are generated by repeatedly stacking a slightly ~~flatted~~ (from just) [[perfect fifth]] such that four fifths gives a near-just [[major third]] – there is sometimes a good approximation of the harmonic seventh in the form of an "augmented sixth". [[Quarter-comma meantone]] (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh (falling somewhere between 16:9 and 9:5). The augmented sixth appears in tonal harmony in the "augmented sixth chord~~," and is treated as a rare and special dissonance~~. The so-called "German sixth", in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8)~~. In Just Intonation, this augmented sixth is likely to be [[225/128]] – the Neapolitan augmented sixth~~.		In [[Meantone family #Septimal meantone\|meantone systems]] – which are generated by repeatedly stacking a slightly flattened (from just) [[perfect fifth]] such that four fifths gives a near-just major third of 5/4 – there is sometimes a good approximation of the harmonic seventh in the form of an augmented sixth. [[Quarter-comma meantone]] (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh falling somewhere between 16/9 and 9/5. The augmented sixth appears in tonal harmony in the augmented sixth chord. The so-called [[German sixth chord]], in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).

	Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents – about 22 cents flat of 7:4, and so less effective as a consonance.		Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents – about 22 cents flat of 7:4, and so less effective as a consonance.

FloraC: +twelfth complement

2023-08-14T11:26:38Z

+twelfth complement

← Older revision		Revision as of 11:26, 14 August 2023
Line 54:		Line 54:

	== Meantone augmented sixth ==		== Meantone augmented sixth ==
			{{See also\| Meantone }}

	In [[Meantone family #Septimal meantone\|meantone systems]] – which are generated by repeatedly stacking a slightly flatted (from just) [[perfect fifth]] such that four fifths gives a near-just [[major third]] – there is sometimes a good approximation of the harmonic seventh in the form of an "augmented sixth". [[Quarter-comma meantone]] (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh (falling somewhere between 16:9 and 9:5). The augmented sixth appears in tonal harmony in the "augmented sixth chord," and is treated as a rare and special dissonance. The so-called "German sixth", in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8). In Just Intonation, this augmented sixth is likely to be [[225/128]] – the Neapolitan augmented sixth.		In [[Meantone family #Septimal meantone\|meantone systems]] – which are generated by repeatedly stacking a slightly flatted (from just) [[perfect fifth]] such that four fifths gives a near-just [[major third]] – there is sometimes a good approximation of the harmonic seventh in the form of an "augmented sixth". [[Quarter-comma meantone]] (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh (falling somewhere between 16:9 and 9:5). The augmented sixth appears in tonal harmony in the "augmented sixth chord," and is treated as a rare and special dissonance. The so-called "German sixth", in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8). In Just Intonation, this augmented sixth is likely to be [[225/128]] – the Neapolitan augmented sixth.

	Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents – about 22 cents flat of 7:4, and so less effective as a consonance.		Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents – about 22 cents flat of 7:4, and so less effective as a consonance.

	~~{{See also\| Meantone }}~~

	== Approximations by EDOs ==		== Approximations by EDOs ==
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	== See also ==		== See also ==
	* [[8/7]] – its [[octave complement]]		* [[8/7]] – its [[octave complement]]
			* [[12/7]] – its [[twelfth complement]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	[[Category:Seventh]]		[[Category:Seventh]]
	[[Category:Subminor seventh]]		[[Category:Subminor seventh]]

Aura at 19:50, 13 May 2023

2023-05-13T19:50:03Z

← Older revision		Revision as of 19:50, 13 May 2023
Line 12:		Line 12:
	{{Wikipedia\|Harmonic seventh}}		{{Wikipedia\|Harmonic seventh}}

	Frequency ratio '''7/4''', measuring approximately 968.8 [[cent]]s, named '''harmonic seventh''' or '''natural seventh''', represents the interval between the 4th and 7th harmonics in the [[harmonic series]]. It is also called a '''septimal minor seventh''' or '''subminor seventh''' – the word "septimal" referring to the presence of a 7 as the highest [[prime]] in the ratio, and the word "subminor" referring to the harmonic seventh's narrowness compared with a traditional minor seventh (such as [[9/5]] or [[16/9]], [[12edo]]'s 1000-cent interval, or a minor seventh found in a meantone system). It is traditionally seen as a seventh, though it may show up as a sixth in rare uses, specifically as the sum of 11/8 and a 14/11 neomajor third. [[User:Aura/Aura's Ideas on Functional Harmony #~~Interstep~~ Functions\|~~One such~~ example]].		Frequency ratio '''7/4''', measuring approximately 968.8 [[cent]]s, named '''harmonic seventh''' or '''natural seventh''', represents the interval between the 4th and 7th harmonics in the [[harmonic series]]. It is also called a '''septimal minor seventh''' or '''subminor seventh''' – the word "septimal" referring to the presence of a 7 as the highest [[prime]] in the ratio, and the word "subminor" referring to the harmonic seventh's narrowness compared with a traditional minor seventh (such as [[9/5]] or [[16/9]], [[12edo]]'s 1000-cent interval, or a minor seventh found in a meantone system). It is traditionally seen as a seventh, though it may show up as a sixth in rare uses, specifically as the sum of 11/8 and a 14/11 neomajor third as per [[User:Aura/Aura's Ideas on Functional Harmony #Basic Paradiatonic Functions\|this example]].

	7/4 has seen use in blues music, barbershop quartet music, and some musical traditions of the world, but has mostly not been recognized as a "[[consonance]]" in Western music theory. In most [[Just Intonation]] systems, the harmonic seventh is treated as a fundamental consonance in its own right, with its own distinct quality.		7/4 has seen use in blues music, barbershop quartet music, and some musical traditions of the world, but has mostly not been recognized as a "[[consonance]]" in Western music theory. In most [[Just Intonation]] systems, the harmonic seventh is treated as a fundamental consonance in its own right, with its own distinct quality.

← Older revision		Revision as of 23:59, 26 October 2024
Line 197:		Line 197:
	* [[8/7]] – its [[octave complement]]		* [[8/7]] – its [[octave complement]]
	* [[12/7]] – its [[twelfth complement]]		* [[12/7]] – its [[twelfth complement]]
			* [[Ed7/4]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	[[Category:Seventh]]		[[Category:Seventh]]
	[[Category:Subminor seventh]]		[[Category:Subminor seventh]]