Undertone series

In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones must be produced in unusual ways. While the overtone series is based upon arithmetic multiplication of frequencies, resulting in a harmonic series, the undertone series is based on arithmetic division.^[1]

^ ^a ^b Nattiez, Jean-Jacques (1990) [1987]. Musicologie générale et sémiologue [Music and Discourse: Toward a Semiology of Music]. Translated by Abbate, Carolyn. Princeton, New Jersey: Princeton University Press. p. 202. ISBN 0-691-02714-5. Nattiez shows the undertone series on E, as Riemann (Handbuch der Harmonielehre, 10th ed., 1929, p. 4) and D'Indy (Cours de composition musicale, vol. I, 1912, p. 100) had done.

[Nattiez-1] Nattiez, Jean-Jacques (1990) [1987]. Musicologie générale et sémiologue [Music and Discourse: Toward a Semiology of Music]. Translated by Abbate, Carolyn. Princeton, New Jersey: Princeton University Press. p. 202. ISBN 0-691-02714-5. Nattiez shows the undertone series on E, as Riemann (Handbuch der Harmonielehre, 10th ed., 1929, p. 4) and D'Indy (Cours de composition musicale, vol. I, 1912, p. 100) had done.

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