Subharmonic

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. 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. The hybrid term subharmonic is used in music 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.). As such, one way to define subharmonics is that they are '...integral submultiples of the fundamental (driving) frequency'. 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 nonlinear system', there are '...only fairly restricted conditions' that will lead to the 'nonlinear phenomenon known as subharmonic generation'. 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. The overtone series can be produced physically in two ways—either by overblowing a wind instrument, or by dividing a monochord string. If a monochord string is lightly damped at the halfway point, then at 1/3, then 1/4, 1/5, etc., then the string will produce the overtone series, which includes the major triad. If instead, the length of the string is doubled in the opposite ratios, the undertones series is produced. Similarly, on a wind instrument, if the holes are equally spaced, each successive hole covered will produce the next note in the undertone series. In addition, undertones can be made through the use of a simple oscillator such as a tuning fork. If the oscillator is gently forced to vibrate against a sheet of paper 'it will naturally make contact at various audible modes of vibration.' Because the tuning fork produces a sine tone, it normally vibrates at its fundamental frequency (e.g. 440 Hz), but 'momentarily', it will make contact only at every other oscillation (220 Hz), or at every third oscillation (147 Hz), and so on. This produces audible 'subharmonic spectra', (e.g. 1:1 yields A4 (440 Hz), 1:2 yields A3 (220 Hz), 1:3 yields D3 (147 Hz), 1:4 yields A2 (110 Hz), 1:5 yields F2 (88 Hz), etc.). José Sotorrio claims it is possible to sustain these 'subspectra' using a sine wave generator through a speaker cone making contact with a flexible (flappable) surface, and also on string instruments 'through skillful manipulation of the bow', but that this rarely sustains noticeably beyond the 'sub-octave or twelfth'. String quartets by composers George Crumb and Daniel James Wolf, as well as works by violinist and composer Mari Kimura, include undertones, 'produced by bowing with great pressure to create pitches below the lowest open string on the instrument.' These require string instrument players to bow with sufficient pressure that the strings vibrate in a manner 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. Subharmonics can be produced by signal amplification through loudspeakers.They are also a common effect in both digital and analog signal processing. Octave effect processors, in effect, use the undertone series to create an artificial bass line for an instrument by synthesizing a subharmonic tone at a fixed interval to the input. Subharmonic synthesizer systems used in audio production and mastering work on the same principle.