The harmonic seventh interval, also known as the septimal minor seventh,[2][3]or subminor seventh,[4][5][6]is one with an exact 7:4 ratio[7](about 969 cents).[8]This is somewhat narrower than and is, "particularly sweet",[9]"sweeter in quality" than an "ordinary"[10]just minor seventh, which has an intonation ratio of 9:5[11](about 1018 cents).
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 the four notes (in order) of a purely consonant major chord (root position) with an added minor seventh (or augmented sixth, depending on the tuning system used).
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 (968.826 cents up from the reference or tonic note) rather than a scale-position note, a harmonic seventh is produced by different notes in different tuning systems:
In 5-limit just intonation the harmonic 7th is very near precisely an accute diminished seventh: 7↑.[a]
In multiple slight variations of quarter comma meantone, the harmonic seventh is accurately rendered by the augmented sixth interval (rather than a seventh).[b]
Actual use in musical practice
When played on the natural horn, the note is often adjusted to 16:9 of the root as a compromise (for C maj7♭, the substituted note is B♭-, 996.09 cents), but some pieces call for the pure harmonic seventh, including Britten's Serenade for Tenor, Horn and Strings.[12] 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.[13][14]
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 B♭maj7♭ became "lost chords" (among other chords).
The harmonic seventh differs from the just 5-limit augmented sixth of 225 / 128 by a septimal kleisma ( 225 / 224 , 7.71 cents), or about 1 / 3 Pythagorean comma.[19]The harmonic seventh note is about 1 / 3 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 I7) and functions as a "fully resolved" final chord.[20]
^Sadly, regardless of how accurately it reproduces the interval of a seventh harmonic, a 5-limit justly intoned accute diminished seventh is only a theoretical pitch. The pitch's position in the just tone net is too far from its tonic for both to sit in the same octave. It is a correctly specified note that does exist among the extended network of just intonation pitches, the note cannot be put to practical use: A grave diminished seventh cannot be reached from its tonic in any feasible justly intoned octave.
^In fact, there is a small modification away from exactly quarter comma that adjusts the tuning system to reproduce as an augmented sixth the seventh harmonic exactly: The adjusted quarter comma uses a fifth that is 696.883cents instead of 696.578 cents in conventional quarter comma meantone.
^Hagerman & Sundberg (1980)[17] present empirical data that challenges the accuracy of the claim.
^Horner, Andrew; Ayres, Lydia (2002). Cooking with Csound: Woodwind and brass recipes. A-R Editions. p. 131. ISBN 0-89579-507-8.
^Bosanquet, R.H.M. (1876). An Elementary Treatise on Musical Intervals and Temperament. Houten, NL: Diapason Press. pp. 41–42. ISBN 90-70907-12-7.
^Brabner, John H.F. (1884). The National Encyclopædia. Vol. 13. London, UK. p. 135 – via Google books.{{cite book}}: CS1 maint: location missing publisher (link)
^Fonville, J. (Summer 1991). "Ben Johnston's extended Just Intonation: A guide for interpreters". Perspectives of New Music. 29 (2): 106–137. doi:10.2307/833435. JSTOR 833435.
^"Definition of barbershop harmony". About Us. barbershop.org.
^Richards, Jim, Dr. "The physics of barbershop sound". shop.barbershop.org.{{cite web}}: CS1 maint: multiple names: authors list (link)
^ a bHagerman, B.; Sundberg, J. (1980). "Fundamental frequency adjustment in barbershop singing" (PDF). STL-QPSR (Speech Transmission Laboratory. Quarterly Progress and Status Reports). 21 (1): 28–42. Retrieved 13 August 2021.
^Harrison, Lou (1988). Miller, Leta E. (ed.). Lou Harrison: Selected keyboard and chamber music, 1937–1994. p. xliii. ISBN 978-0-89579-414-7.
^Mathieu, W.A. (1997). Harmonic Experience. Rochester, VT: Inner Traditions International. pp. 318–319. ISBN 0-89281-560-4.
Further reading
Hewitt, Michael (2000). The Tonal Phoenix: A study of tonal progression through the prime numbers three, five, and seven. Orpheus-Verlag. ISBN 978-3922626961.