7/4: Difference between revisions
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| Monzo = -2 0 0 1 | | Monzo = -2 0 0 1 | ||
| Cents = 968.82591 | | Cents = 968.82591 | ||
| Name = harmonic seventh <br> natural seventh | | Name = harmonic seventh, <br>natural seventh | ||
| Color name = z7, zo 7th | | Color name = z7, zo 7th | ||
| FJS name = m7<sup>7</sup> | | FJS name = m7<sup>7</sup> | ||
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Frequency ratio '''7:4''', measuring approximately 968.8 [[cent|cents]], named '''harmonic seventh''' or '''natural seventh''', represents the interval between the 4th and 7th harmonics in the [[overtone series]]. It is also called a | Frequency ratio '''7:4''', measuring approximately 968.8 [[cent|cents]], named '''harmonic seventh''' or '''natural seventh''', represents the interval between the 4th and 7th harmonics in the [[overtone 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|9:5]] or [[16/9|16:9]], [[12edo]]'s 1000-cent interval, or a minor seventh found in a meantone system). | ||
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. | ||
== 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. | 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: | ||
{| class="wikitable" | {| class="wikitable" | ||
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== Meantone Augmented Sixth == | == Meantone Augmented Sixth == | ||
In [[Meantone family|meantone systems]] | 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). | ||
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: [[ | :''See also: [[Wikipedia:Septimal_meantone_temperament|Septimal meantone temperament - Wikipedia]]'' | ||
== Approximations == | == Approximations == | ||
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|- | |- | ||
|[[67edo]] | | [[67edo]] | ||
|1.6617 | | 1.6617 | ||
|9.2780 | | 9.2780 | ||
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|- | |- | ||
|[[41edo]] | | [[41edo]] | ||
|2.9722 | | 2.9722 | ||
|10.1552 | | 10.1552 | ||
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|} | |} | ||
== See also == | |||
* [[8/7]] – its [[octave complement]] | |||
* [[Gallery of just intervals]] | |||
* [[Wikipedia:Harmonic_seventh|Harmonic seventh - Wikipedia]] | |||
[[Category:7-limit]] | |||
[[Category:Harmonic]] | |||
[[Category:Just interval]] | |||
[[Category:Listen]] | |||
[[Category:Overtone]] | |||
[[Category:Theory]] | |||
[[Category:Seventh]] | |||
[[Category:minor seventh]] | |||
[[Category:Over-2]] | |||
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[[de:Naturseptime]] | [[de:Naturseptime]] | ||