Subharmonic
Encyclopedia
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) and 110 Hz (1/4). Thus, they are a mirror image of the harmonic series
.
It is incorrect and a common misconception to imply that subharmonic series are perfect ratios of 1/n when in fact they are sum and difference frequencies of the original fundamentals. Subharmonics are well known and were called combination tone
s by physisist Hermann von Helmholtz
and 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.
Subharmonics can be produced by signal amplification through loudspeakers. They are naturally produced by bells, giving them their distinct sound.
String quartet
s 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 string vibrates in modes with frequencies corresponding to subharmonics. It is also possible to produce several subharmonics on the saxophone in a similar way to producing regular harmonics.
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
below the fundamental frequency
Fundamental frequency
The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the lowest frequency of a periodic waveform. In terms of a superposition of sinusoids The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the...
of an oscillator in a ratio of 1/n, with n a positive integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
number. For example, if the fundamental frequency of an oscillator is 440 Hz, sub-harmonics include 220 Hz (1/2) and 110 Hz (1/4). Thus, they are a mirror image of the harmonic series
Harmonic series (music)
Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
.
It is incorrect and a common misconception to imply that subharmonic series are perfect ratios of 1/n when in fact they are sum and difference frequencies of the original fundamentals. Subharmonics are well known and were called combination tone
Combination tone
A combination tone, also called a sum tone or a difference tone , can be any of at least three similar psychoacoustic phenomena. When two tones are played simultaneously, a listener can sometimes perceive an additional tone whose frequency is a sum or difference of the two frequencies...
s by physisist Hermann von Helmholtz
Hermann von Helmholtz
Hermann Ludwig Ferdinand von Helmholtz was a German physician and physicist who made significant contributions to several widely varied areas of modern science...
and formally described by musician Giuseppe Tartini
Giuseppe Tartini
Giuseppe Tartini was an Italian baroque composer and violinist.-Biography:Tartini was born in Piran, a town on the peninsula of Istria, in the Republic of Venice to Gianantonio – native of Florence – and Caterina Zangrando, a descendant of one of the oldest aristocratic Piranian families.It...
. 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.
Subharmonics can be produced by signal amplification through loudspeakers. They are naturally produced by bells, giving them their distinct sound.
String quartet
String quartet
A string quartet is a musical ensemble of four string players – usually two violin players, a violist and a cellist – or a piece written to be performed by such a group...
s by composers George Crumb
George Crumb
George Crumb is an American composer of contemporary classical music. He is noted as an explorer of unusual timbres, alternative forms of notation, and extended instrumental and vocal techniques. Examples include seagull effect for the cello , metallic vibrato for the piano George Crumb (born...
and Daniel James Wolf
Daniel James Wolf
Daniel James Wolf is an American composer.- Studies :Wolf studied composition with Gordon Mumma, Alvin Lucier, and La Monte Young, as well as musical tunings with Erv Wilson and Douglas Leedy and ethnomusicology . Important contacts with Lou Harrison, John Cage, Walter Zimmermann...
as well as works by violinist and composer Mari Kimura
Mari Kimura
is a Japanese violinist and composer best known for her use of subharmonics, which, achieved through special bowing techniques, allow pitches below the instrument's normal range...
require string instrument players to bow with sufficient pressure that the string vibrates in modes with frequencies corresponding to subharmonics. It is also possible to produce several subharmonics on the saxophone in a similar way to producing regular harmonics.
See also
- HarmonicHarmonicA harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...
- Harmonic series (music)Harmonic series (music)Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
- OvertoneOvertoneAn overtone is any frequency higher than the fundamental frequency of a sound. The fundamental and the overtones together are called partials. Harmonics are partials whose frequencies are whole number multiples of the fundamental These overlapping terms are variously used when discussing the...
- Subharmonic mixer
- Subharmonic synthesizerSubharmonic synthesizerA subharmonic synthesizer is a device or system that generates subharmonics of an input signal. The nth subharmonic of a signal of fundamental frequency F is a signal with frequency F/n...
- Combination toneCombination toneA combination tone, also called a sum tone or a difference tone , can be any of at least three similar psychoacoustic phenomena. When two tones are played simultaneously, a listener can sometimes perceive an additional tone whose frequency is a sum or difference of the two frequencies...