Harmonic seventh
Encyclopedia
The harmonic seventh interval , also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio (about 969 cents
). This is somewhat narrower than and is "sweeter in quality" than an "ordinary" minor seventh
, which has a just-intonation ratio of 9:5 (1017.596 cents), or an equal-temperament ratio of 1000 cents (25/6:1). The harmonic seventh may be derived from the harmonic series
as the interval between the seventh harmonic and the fourth harmonic.
Composer Ben Johnston
uses a small "7" as an accidental to indicate a note is lowered 49 cents
(1018-969=49), or an upside-down "7" to indicate a note is raised 49 cents. Thus, in C major, "the seventh partial," or harmonic seventh, is notated as B with "7" written above the flat. The harmonic seventh is also used by Barbershop Quartet
singers when they tune dominant seventh chords
(harmonic seventh chord
), and is an essential aspect of the Barbershop style.
The harmonic seventh differs from the augmented sixth
by 224/225
(7.71 cents), or about one-third of a comma
. The harmonic seventh note is about a sixth-tone
flatter than an equal tempered minor seventh (≈ 31 cents). When this flatter seventh is used, the dominant seventh chord's "need to resolve" down a fifth is weak or non-existent. This chord is often used on the tonic (written as I7) and functions as a "fully resolved" final chord.
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
). This is somewhat narrower than and is "sweeter in quality" than an "ordinary" minor seventh
Minor seventh
In classical music from Western culture, a seventh is a musical interval encompassing seven staff positions , and the minor seventh is one of two commonly occurring sevenths. The minor quality specification identifies it as being the smallest of the two: the minor seventh spans ten semitones, the...
, which has a just-intonation ratio of 9:5 (1017.596 cents), or an equal-temperament ratio of 1000 cents (25/6:1). The harmonic seventh may be derived from the harmonic series
Harmonic series (music)
Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
as the interval between the seventh harmonic and the fourth harmonic.
Composer Ben Johnston
Ben Johnston
Benjamin Burwell Johnston, Jr. is a composer of contemporary music in the just intonation system.-Johnston's music:...
uses a small "7" as an accidental to indicate a note is lowered 49 cents
Septimal quarter tone
A septimal quarter-tone is an interval with the ratio of 36:35 , which is the difference between the septimal minor third and the Just minor third , or about 48.77 cents wide. The name derives from the interval being the 7-limit approximation of a quarter tone...
(1018-969=49), or an upside-down "7" to indicate a note is raised 49 cents. Thus, in C major, "the seventh partial," or harmonic seventh, is notated as B with "7" written above the flat. The harmonic seventh is also used by Barbershop Quartet
Barbershop music
Barbershop vocal harmony, as codified during the barbershop revival era , is a style of a cappella, or unaccompanied vocal music characterized by consonant four-part chords for every melody note in a predominantly homophonic texture...
singers when they tune dominant seventh chords
Dominant seventh chord
In music theory, a dominant seventh chord, or major minor seventh chord,is a chord composed of a root, major third, perfect fifth, and minor seventh. It can be also viewed as a major triad with an additional minor seventh...
(harmonic seventh chord
Harmonic seventh chord
The harmonic seventh chord is a major triad plus the harmonic seventh interval . This interval is somewhat narrower than and is "sweeter in quality" than an "ordinary" minor seventh, which has a just-intonation ratio of 9:5 , or an equal-temperament ratio of 1000 cents...
), and is an essential aspect of the Barbershop style.
The harmonic seventh differs from the augmented sixth
Augmented sixth
In classical music from Western culture, an augmented sixth is an interval produced by widening a major sixth by a chromatic semitone. For instance, the interval from C to A is a major sixth, nine semitones wide, and both the intervals from C to A, and from C to A are augmented sixths, spanning...
by 224/225
Septimal kleisma
In music, the ratio 225/224 is called the septimal kleisma .It is a minute comma type interval of approximately 7.7 cents. Factoring it into primes gives 2−5 32 52 7−1, which can be rewritten 2−1 2 . That says that it is the amount that two major thirds of 5/4 and a septimal...
(7.71 cents), or about one-third of a comma
Pythagorean comma
In musical tuning, the Pythagorean comma , named after the ancient mathematician and philosopher Pythagoras, is the small interval existing in Pythagorean tuning between two enharmonically equivalent notes such as C and B , or D and C...
. The harmonic seventh note is about a sixth-tone
Sixth-tone
A sixth-tone is a musical interval approximately one-third of a half-step, thus producing 36 pitches per octave. See:*Just sixth-tone*Pythagorean sixth-tone*Septimal sixth-tone*36 equal temperamentSee also:*Ptolemy's enharmonic*Septimal diesis...
flatter than an equal tempered minor seventh (≈ 31 cents). When this flatter seventh is used, the dominant seventh chord's "need to resolve" down a fifth is weak or non-existent. This chord is often used on the tonic (written as I7) and functions as a "fully resolved" final chord.