The dominant-7th chord is formally a chord containing 4 notes, built upward in pitch from the root with the intervals of a major-3rd, minor-3rd, and another minor-3rd, resulting in the chord-members identified as root, 3rd, 5th, and 7th. The actual intervals above the root are thus the major-3rd, perfect-5th, and minor-7th.
The dominant-7th chord arises naturally as the chord whose root is the fifth note, designated by Roman numeral "V" and called the "dominant", of the diatonic major-scale -- its common abbreviation is thus "V7". For example:
key of C-major: C D E F G A B C D E F G I II III IV V VI VII I II III IV V | | | | root 3rd 5th 7th \______/ \___/ \____/ maj-3rd min-3rd min-3rd
The dominant-7th chord plays an important role in musical harmony, especially at divisions of the formal structure, because of its use in cadences. In traditional music-theory it is considered to be a dissonant chord in need of resolution, specifically the resolution of the tritone which is included within the chord, as in the B:F interval in the chord illustrated above; note that the use of the word "tritone" here is in the loose sense, which designates both the true tritone (augmented-4th) and its inversion (diminished-5th). The normal resolution is for the 3rd of the chord to move upward one diatonic-semitone to the tonic of the key (I), and for the 7th of the chord to move downward one diatonic-semitone to the 3rd of the tonic chord (III), so in the above example B-->C and F-->E. Thus the most dissonant interval normally used in tonal music is resolved to the most consonant, and by the shortest distance in voice-leading, and additionally by contrary motion, which is felt to be a stronger resolution than oblique or similar motion.
key of C-major: G A B C D E F G * * * * * G dominant-7th chord (V) \ / | * * * C major chord (I)
Traditionally, in the meantone tunings which have been standard in Western theory and practice, the dominant-7th actually has been composed of discordant intervals, particularly the minor-7th. But in more recent times, many composers working in just-intonation (JI) have come to think of the dominant-7th chord as a consonant entity with the 7th of the chord tuned as the harmonic-7th of ratio 7:4. This usage parallels the use of the dominant-7th chords in blues music, in which every chord is a dominant-7th, but where they are normally tuned in 12-edo as played on a guitar.
In 12-edo pc-set theory, the dominant-7th chord is classified as follows:
interval-string prime interval-vector Solomon Forte (is) form (iv) catalog # set-name 3324 0368 012111 065 4-27[b]
Below is a diagram illustrating the prime-form and interval-string:
0 1 2 3 4 5 6 7 8 9 A B 0 = 12-edo degree integers (pcs) B C D E F G A B = diatonic C-major scale, rotated to most compact arrangement * * * * * = chord notes 0 3 6 8 = prime-form (pcs) \_3_/ \_3_/ \2/ \__4__/ = interval-string (ics)
The interval-vector is self-evident:
0 3 6 8 0 = pcs (prime-form) \_3_/ \_3_/ \2/ \__4__/ \ \___5___/ = instances of intervals \____6____/ / interval interval- semitones vector 1 0 none 2 1 F:G = 6,8 3 2 B:D = 0,3 and D:F = 3,6 4 1 G:B = 8,0 5 1 D:G = 3,8 6 1 B:F = 0,6
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