Harmonic seventh

harmonic seventh
InverseSeptimal major second
Name
Other namesseptimal minor seventh, subminor seventh, acute diminished just seventh, quarter comma augmented sixth
Abbreviationm 7, H 7, min 7, accdim 7, Aug 6
Size
Semitones~9.7
Interval class~2.3
Just interval7:4[1]
Cents
Just intonation968.826

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 seventh, septimal seventh

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).

  1. ^ Haluska, Jan (2003). "Harmonic seventh". The Mathematical Theory of Tone Systems. CRC Press. p. xxiii. ISBN 0-8247-4714-3.
  2. ^ Gann, Kyle (1998). "Anatomy of an octave". kylegann.com. Just Intonation Explained.
  3. ^ Partch, Harry (1979). Genesis of a Music. p. 68. ISBN 0-306-80106-X.
  4. ^ 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.
  5. ^ 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.
  6. ^ Ellis, A.J. (1877). "On the measurement and settlement of musical pitch". Journal of the Society of Arts. 25 (1279): 664–687. JSTOR 41335396.
  7. ^ Horner, Andrew; Ayres, Lydia (2002). Cooking with Csound: Woodwind and brass recipes. A-R Editions. p. 131. ISBN 0-89579-507-8.
  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.
  9. ^ 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)
  10. ^ Breakspeare, Eustace J. (1886–1887). "On certain novel aspects of harmony". Proceedings of the Musical Association. Royal Musical Association / Oxford University Press. p. 119.
  11. ^ Perrett, Wilfrid (1931–1932). "The heritage of Greece in music". Proceedings of the Musical Association. Royal Musical Association / Oxford University Press. p. 89.