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, "particularly sweet", "sweeter in quality" than an "ordinary" just minor seventh, which has an intonation ratio of 9:5 (about 1018 cents). Harmonic seventh on C

The harmonic seventh arises from the harmonic series as the interval between the fourth harmonic (second octave of the fundamental) and the seventh harmonic; in that octave, harmonics 4, 5, 6, and 7 constitute a purely consonant major chord with added seventh (root position). When played on the

natural horn The natural horn is a musical instrument that is the predecessor to the modern-day (French) horn (differentiated by its lack of valves). Throughout the seventeenth and eighteenth century the natural horn evolved as a separation from the trump ...

, as a compromise the note is often adjusted to 16:9 of the root (for C maj⁷, the substituted note is B, 996.09 cents), but some pieces call for the pure harmonic seventh, including

Britten Edward Benjamin Britten, Baron Britten (22 November 1913 – 4 December 1976, aged 63) was an English composer, conductor, and pianist. He was a central figure of 20th-century British music, with a range of works including opera, other ...

's ''

Serenade for Tenor, Horn and Strings The ''Serenade for Tenor, Horn and Strings'', Op. 31, is a song cycle written in 1943 by Benjamin Britten for tenor, solo horn and a string orchestra. Composed during the Second World War at the request of the horn player Dennis Brain, it is a ...

''. 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 note with "7" written above the flat. Septimal major second on B7b

The harmonic seventh is also expected from

barbershop quartet A barbershop quartet is a group of four singers who sing music in the barbershop style, characterized by four-part harmony without instrumental accompaniment, or a cappella. The four voices are: the lead, the vocal part which typically carries t ...

singers when they tune

dominant seventh chord In music theory, a dominant seventh chord, or major minor seventh chord, is a seventh chord, usually built on the fifth degree of the major scale, and composed of a root, major third, perfect fifth, and minor seventh. Thus it is a major triad tog ...

s (

harmonic seventh chord The harmonic seventh chord is a major triad plus the harmonic seventh interval (ratio of 7:4, about 968.826 centsBosanquet, Robert Holford Macdowall (1876). ''An elementary treatise on musical intervals and temperament'', pp. 41-42. Diapason ...

), and is considered an essential aspect of the barbershop style. Origin of seconds and thirds in harmonic series

In ¼ comma meantone tuning, standard in the

Baroque The Baroque (, ; ) is a style of architecture, music, dance, painting, sculpture, poetry, and other arts that flourished in Europe from the early 17th century until the 1750s. In the territories of the Spanish and Portuguese empires including t ...

and earlier, the augmented sixth is 965.78 cents – only 3 cents below 7:4, well within normal tuning error and

vibrato Vibrato (Italian language, Italian, from past participle of "wikt:vibrare, vibrare", to vibrate) is a musical effect consisting of a regular, pulsating change of pitch (music), pitch. It is used to add expression to vocal and instrumental music. ...

Pipe organs The pipe organ is a musical instrument that produces sound by driving pressurized air (called ''wind'') through the organ pipes selected from a keyboard. Because each pipe produces a single pitch, the pipes are provided in sets called ''ranks' ...

were the last fixed-tuning instrument to adopt

equal temperament An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...

. With the transition of organ tuning from meantone to equal-temperament in the late 19th and early 20th centuries the formerly harmonic G_maj⁷ and B_maj⁷ became "lost chords" (among other chords). The harmonic seventh differs from the Pythagorean

augmented sixth In classical music from Western culture, an augmented sixth () is an interval produced by widening a major sixth by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . Specific example of an A6 not g ...

by 225/224 (7.71 cents), or about ⅓

comma The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline ...

. The harmonic seventh note is about ⅓ semitone (≈ 31 cents) 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 (written as ) and functions as a "fully resolved" final chord. Mathieu, W. A. (1997). ''Harmonic Experience'', pp. 318–319. Rochester, Vermont: Inner Traditions International. . The twenty-first harmonic (470.78 cents) is the harmonic seventh of the dominant, and would then arise in chains of

secondary dominant A secondary chord is an analytical label for a specific harmonic device that is prevalent in the tonal idiom of Western music beginning in the common practice period: the use of diatonic functions for tonicization. Secondary chords are a typ ...

s (known as the Ragtime progression) in styles using harmonic sevenths, such as barbershop music.

Notes

Further reading