Harmonic seventh


The harmonic seventh interval, also known as the septimal minor seventh,
or subminor seventh,
is one with an exact 7:4 ratio
.
This is about 32 cents narrower, with a more stable and consonant sound, than a minor seventh in equal temperament, and is up to 49 cents narrower than and is, "particularly sweet",
"sweeter in quality" than an "ordinary"
just minor seventh, which has an intonation ratio of 9:5
.
[File:Harmonic seventh on C.png|thumb|left|Harmonic seventh, septimal seventh]
The harmonic seventh arises from the harmonic series as the interval between the fourth harmonic and the seventh harmonic; in that octave, harmonics 4, 5, 6, and 7 constitute the four notes of a purely consonant major chord with an added minor seventh.

Fixed pitch: Not a scale note

Although the word "seventh" in the name suggests the seventh note in a scale, and although the seventh pitch up from the tonic is indeed used to form a harmonic seventh in a few tuning systems, the harmonic seventh is a pitch relation to the tonic, not an ordinal note position in a scale. As a pitch relation rather than a scale-position note, a harmonic seventh is produced by different notes in different tuning systems:
When played on the natural horn, the note is often adjusted to 16:9 of the root as a compromise, but some pieces call for the pure harmonic seventh, including Britten's Serenade for Tenor, Horn and Strings. Composer Ben Johnston uses a small "7" as an accidental to indicate a note is lowered 49 cents , and is considered an essential aspect of the barbershop style.
In quarter-comma meantone tuning, standard in the Baroque and earlier, the augmented sixth is 965.78 cents – only 3 cents below 7:4, well within normal tuning error and vibrato.
Pipe organs were the last fixed-tuning instrument to adopt equal temperament. With the transition of organ tuning from meantone to equal-temperament in the late 19th and early 20th centuries the formerly harmonic Gmaj7 and Bmaj7 became "lost chords".
The harmonic seventh differs from the just 5-limit augmented sixth of by a septimal kleisma, or about.
The harmonic seventh note is about flatter than an equal-tempered minor seventh. 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 and functions as a "fully resolved" final chord.
The twenty-first harmonic is the harmonic seventh of the dominant, and would then arise in chains of secondary dominants in styles using harmonic sevenths, such as barbershop music.