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).
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]
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]
Origin of large and small seconds and thirds in harmonic series.[18]
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 Pythagorean augmented sixth by 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. ISBN0-89579-507-8.
^Bosanquet, R.H.M. (1876). An Elementary Treatise on Musical Intervals and Temperament. Houten, NL: Diapason Press. pp. 41–42. ISBN90-70907-12-7.
^ 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)
^ "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)
^ ab Hagerman, 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. ISBN978-0-89579-414-7.
Hewitt, Michael (2000). The Tonal Phoenix: A study of tonal progression through the prime numbers three, five, and seven. Orpheus-Verlag. ISBN978-3922626961.
January 01, 1970
harmonic, seventh, harmonic, seventh, interval, also, known, septimal, minor, seventh, subminor, seventh, with, exact, ratio, about, cents, this, somewhat, narrower, than, particularly, sweet, sweeter, quality, than, ordinary, just, minor, seventh, which, into. 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 harmonic seventhInverseSeptimal major secondNameOther namesseptimal minor seventh subminor seventh acute diminished just seventh quarter comma augmented sixthAbbreviationm 7 H 7 min 7 accdim 7 Aug 6SizeSemitones 9 7Interval class 2 3Just interval7 4 1 CentsJust intonation968 826 Harmonic seventh septimal seventh source source source 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 Contents 1 Fixed pitch Not a scale note 2 Actual use in musical practice 3 Notes 4 See also 5 Citations 6 Further readingFixed pitch Not a scale note editAlthough 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 nbsp 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 edit nbsp Use of the seventh harmonic in the prologue to Britten s Serenade for Tenor Horn and Strings source source source 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 nbsp Inverse septimal major second on B7 source source source The harmonic seventh is also expected from barbershop quartet singers when they tune dominant seventh chords harmonic seventh chord and is considered an essential aspect of the barbershop style 15 16 c 17 nbsp Origin of large and small seconds and thirds in harmonic series 18 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 Pythagorean augmented sixth by 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 The twenty first harmonic 470 78 cents is the harmonic seventh of the dominant and would then arise in chains of secondary dominants known as the Ragtime progression in styles using harmonic sevenths such as barbershop music Notes edit 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 696 883 cents instead of 696 578 cents in conventional quarter comma meantone Hagerman amp Sundberg 1980 17 present empirical data that challenges the accuracy of the claim See also editaugmented sixth quarter comma meantone 31 tone equal temperamentCitations edit Haluska Jan 2003 Harmonic seventh The Mathematical Theory of Tone Systems CRC Press p xxiii ISBN 0 8247 4714 3 Gann Kyle 1998 Anatomy of an octave kylegann com Just Intonation Explained Partch Harry 1979 Genesis of a Music p 68 ISBN 0 306 80106 X von Helmholtz H L F Ellis A J 2007 On the Sensations of Tone Ellis A J translator of English ed editor and author of an extensive appendix reprint ed Cosimo p 456 ISBN 978 1 60206 639 7 Ellis A J 1880 Notes of observations on musical beats Proceedings of the Royal Society of London 30 200 205 520 533 doi 10 1098 rspl 1879 0155 Ellis A J 1877 On the measurement and settlement of musical pitch Journal of the Society of Arts 25 1279 664 687 JSTOR 41335396 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 Encyclopaedia Vol 13 London UK p 135 via Google books a href Template Cite book html title Template Cite book cite book a CS1 maint location missing publisher link Breakspeare Eustace J 1886 1887 On certain novel aspects of harmony Proceedings of the Musical Association Royal Musical Association Oxford University Press p 119 Perrett Wilfrid 1931 1932 The heritage of Greece in music Proceedings of the Musical Association Royal Musical Association Oxford University Press p 89 Fauvel J Flood R Wilson R J 2006 Music and Mathematics Oxford University Press pp 21 22 ISBN 9780199298938 Keislar Douglas Blackwood Easley Eaton John Harrison Lou Johnston Ben Mandelbaum Joel Schottstaedt William Winter 1991 Six American composers on nonstandard tunings Perspectives of New Music 1 29 1 176 211 esp 193 doi 10 2307 833076 JSTOR 833076 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 a href Template Cite web html title Template Cite web cite web a CS1 maint multiple names authors list link a b Hagerman 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 Bosanquet R H M 1876 1877 On some points in the harmony of perfect consonances Proceedings of the Musical Association Royal Musical Association Oxford University Press p 153 Mathieu W A 1997 Harmonic Experience Rochester VT Inner Traditions International pp 318 319 ISBN 0 89281 560 4 Further reading editHewitt Michael 2000 The Tonal Phoenix A study of tonal progression through the prime numbers three five and seven Orpheus Verlag ISBN 978 3922626961 Retrieved from https en wikipedia org w index php title Harmonic seventh amp oldid 1214310476, wikipedia, wiki, book, books, library,
