harmonics
In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc. Harmonics come from the mathematical ability through fourier decomposition of any periodic signal into sine waves with frequencies integer multiples of the fundamental frequency.
Many driven oscillators, including the human voice, a bowed violin string, or a Cepheid variable star, naturally tend to be periodic, and thus can be decomposed into harmonics.
Most passive oscillators, such as a plucked guitar string or a struck drum head or struck bell, naturally oscillate at several frequencies known as overtones. When the oscillator is long and thin, such as a guitar string, a trumpet, or a chime, the overtones are integer multiples of the fundamental frequency. Hence, these devices can mimic the sound of singing and are often incorporated into music. Overtones whose frequency is not an integer multiple of the fundamental are called inharmonic and are often perceived as unpleasant.
The untrained human ear typically does not perceive harmonics as separate notes. Instead, they are perceived as the timbre of the tone. In a musical context, overtones which are not exactly integer multiples of the fundamental are known as inharmonics. Inharmonics which are not close to harmonics are known as partials. Bells have more clearly perceptible partials than most instruments. Antique singing bowls are well known for their unique quality of producing multiple harmonic overtones or multiphonics.
The tight relation between overtones and harmonics in music, often leads to their being used synonymously in a strictly musical context, but they are counted differently leading to some possible confusion. This chart demonstrates how they are counted:
1f 440 Hz fundamental frequency first harmonic
2f 880 Hz first overtone second harmonic
3f 1320 Hz second overtone third harmonic
4f 1760 Hz third overtone fourth harmonic