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Timbre (pronounced "tam-ber") is that quality of sound which distinguishes one instrument from another. The physical characteristics of sound which are used in the determination of timbre are the waveform of the steady part of the tone (the spectrum) and the way the spectrum changes with time, especially at the onset or attack (the envelope.)
The spectrum of a tone played on an instrument depends on the type of instrument, the individual instrument, the person playing the instrument, and other factors such as volume,pitch of note, and temperature. The spectrum consists on energies at various frequencies which include the fundamental pitch and harmonic overtones (integer multiples of the frequency of fundamental pitch) as well as inharmonic components (not integer multiples.) Note the difference in the spectrum for the same note played by the flute and the violin as illustrated in the following diagrams: (The vertical variable is the intensity level in dB and the horizontal variable is the frequency in kHz.)

The production of sound involves an exciter, a mechanism that applies energy; an oscillator, something to vibrate and supply the spectrum, and a resonator, a structure which response to the oscillations often amplifying the sound and modifying the spectrum due to the material and construction of the resonator. The resonator responds to a wide band of frequencies but not in a uniform way. The response peaks are called formants and play an important part in establishing the timbre identity of an instrument. The oscillator is the controlling factor in the pitch produced by the instrument while the formants of the resonator modify the spectrum produced by the oscillator. The formants do not change, so the waveform produced by the instrument varies somewhat from pitch to pitch.
Consider a violin for an example. The exciter is the bow which excites the string. The string is the oscillator which determines the pitch and spectrum due to the length, tension, and composition of the string. The energy of the vibrating string is transferred though the bridge to the body of the violin which acts as the resonator. The violin body resonates and radiates sound from its entire surface area which amplifies the sound but also modifies its spectrum by emphasizing or de-emphasizing certain overtones.

For more details on the nature of sound follow these links:
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