Subharmonic

This article is about frequencies in dynamics. For subharmonic functions in mathematics, see Subharmonic function.

In music and dynamics, subharmonic frequencies are frequencies below the main frequency of a signal.

Subharmonics are well known and form part of the combination tones, as they are called by physicist Hermann von Helmholtz and were formally described by musician Giuseppe Tartini. In fact the harmonic series is also the set of sums and differences, the only occurrence of integer multiple harmonics is with the trivial case where a single sinusoid interacts with itself or its own harmonic. There are no subharmonic frequencies associated with a single pure tone since the differences of a frequency with itself results in a value of zero, when a single tone is summed with itself or its own harmonic then and only then will it result in "n" integer harmonics. If a subharmonic frequency is desired from a single tone then it can be synthesized at any subharmonic frequency with the usage of frequency divider circuits which rely on the modulation of the single tone with selective amplified noise signals to initialize a feedback circuit.

Any subharmonic frequency or frequencies can be created with a frequency synthesizer by the modulation and subsequent demodulation of two or more signals. If the two signals being combined are separated by less than one octave then some of the frequencies will be subharmonic, that is that the frequencies synthesized will be less than that of the lowest of the frequencies that were initially combined. The reason for this is that complete harmonic series is the infinite set of all combined frequencies of sums and differences as well as the sums and differences of the infinite numbers of the resulting sums and differences. The set of frequencies that comply with the notion of n integer multiple or 1/n integer multiple harmonics is simply a limited subset of the complete set created by imposing strict restrictions on the frequency synthesis process.

Mathematically subharmonics or difference frequencies are the direct result of applying sum to product trigonometric identities when two sinusoids are superposed or added, see List_of_trigonometric_identities.

Subharmonics can be produced by signal amplification through loudspeakers. They are naturally produced by bells, giving them their distinct sound.

String quartets by composers George Crumb and Daniel James Wolf^{[citation needed]} as well as works by violinist and composer Mari Kimura require string instrument players to bow with sufficient pressure that the strings vibrate 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

• Harmonic
• Harmonic series (music)
• Overtone
• Subharmonic mixer
• Subharmonic synthesizer
• Combination tone
• Missing fundamental

References

Other

• Gurewitsch, Matthew (May 13, 2011). "For a Violinist, Success Means a New Low Point". The New York Times. http://www.nytimes.com/2011/05/15/arts/music/the-violinist-mari-kimura-looks-for-low-notes.html?r=1. Retrieved January 23, 2012. 

External links

• Website of Mari Kimura with audio clips
• Article on Mari Kimura
• Article Harmonic and Subharmonic Distortions in Musical Interpretations