Subharmonic

This article is about frequencies in dynamics. For subharmonic functions in mathematics, see Subharmonic function.
5-limit Otonality and Utonality: overtone and "undertone" series,[1] partials 1-5 numbered  Play Otonality ,  Play Utonality ,  Play major chord on C , and  Play minor chord on F .

The term subharmonic is used in music and dynamics in a few different ways. In its pure sense, the term subharmonic refers strictly to any member of the subharmonic series (1/1, 1/2, 1/3, 1/4, etc.). When the subharmonic series is used to refer to frequency relationships, it is written with f representing some highest known reference frequency (f/1, f/2, f/3, f/4, etc.). The complex tones of acoustic instruments do not produce partials that resemble the subharmonic series. However, such tones can be produced artificially with audio software and electronics. Subharmonics can be contrasted with harmonics. While harmonics can "...occur in any linear system", there are "...only fairly restricted conditions" that will lead to the "nonlinear phenomenon known as subharmonic generation." [2] One way to define subharmonics is that they are "...integral submultiples of the fundamental (driving) frequency." [3]

In a second sense, subharmonic does not relate to the subharmonic series, but instead describes an instrumental technique for lowering the pitch of an acoustic instrument below what would be expected for the resonant frequency of that instrument, such as a violin string that is driven and damped by increased bow pressure to produce a fundamental frequency lower than the normal pitch of the same open string. The human voice can also be forced into a similar driven resonance, also called “undertone singing” (which similarly has nothing to do with the undertone series), to extend the range of the voice below what is normally available. However, the frequency relationships of the component partials of the tone produced by the acoustic instrument or voice played in such a way still resemble the harmonic series, not the subharmonic series. In this sense, “subharmonic” is a term created by reflection from the second sense of the term “harmonic”, which in that sense refers to an instrumental technique for making an instrument’s pitch seem higher than normal by eliminating some lower partials by damping the resonator at the antinodes of vibration of those partials (such as placing a finger lightly on a string at certain locations).

In a very loose third sense, “subharmonic” is sometimes used or misused to represent any frequency lower than some other known frequency or frequencies, no matter what the frequency relationship is between those frequencies and no matter the method of production.

Frequencies

Subharmonic frequencies are frequencies below the fundamental frequency of an oscillator in a ratio of 1/n, with n a positive integer number. For example, if the fundamental frequency of an oscillator is 440 Hz, sub-harmonics include 220 Hz (1/2), ~146.6 Hz (1/3) and 110 Hz (1/4). Thus, they are a mirror image of the harmonic series, the undertone series.

Loudspeakers

Subharmonics can be produced by signal amplification through loudspeakers.[4]

Music examples

String quartets by composers George Crumb and Daniel James Wolf as well as works by violinist and composer Mari Kimura require string instrument players to bow with sufficient pressure that the strings vibrate [5] causing the sound waves to modulate and demodulate by the instruments resonating horn with frequencies corresponding to subharmonics. The tritare, a guitar with Y shaped strings, cause subharmonics too. This can also be achieved by the extended technique of crossing two strings as some experimental jazz guitarists have developed. Also third bridge preparations on guitars cause timbres consisting of sets of high pitched overtones combined with a subharmonic resonant tone of the unplugged part of the string.

See also

References

  1. ↑ Rehding, Alexander (2003). Hugo Riemann and the Birth of Modern Musical Thought, p.16. ISBN 978-0-521-82073-8. Goes to partial nine, unnumbered.
  2. ↑ Dallos, Peter (2012). The Auditory Periphery Biophysics and Physiology. Elsevier. p. 2012.
  3. ↑ Dallos, Peter (2012). The Auditory Periphery Biophysics and Physiology. Elsevier. p. 2012.
  4. ↑ Barry Truax, ed (1999). Handbook for Acoustic Ecology. World Soundscape Project, Simon Fraser University.
  5. ↑ Edward Rothstein (April 21, 1994). "A Violinist Tests Limits In Music Of Her Time". New York Times. Retrieved 2008-09-15.

Further reading

External links

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