Though the phrase tone color is often used as a synonym for timbre, colors of the optical spectrum are not generally explicitly associated with particular sounds. Rather, the sound of an instrument may be described as "warm" or "harsh" or other terms, perhaps suggesting that tone color has more in common with the sense of touch than of sight. People who experience synaesthesia, however, may see certain colors when they hear particular instruments
The physical characteristics of sound which are used in the determination of timbre are spectrum and envelope.
Spectra
Each note produced by a musical instrument is made of a number of distinct frequencies, measured in hertz (Hz). The lowest frequency is called the fundamental and the pitch produced by this frequency is used to name the note. For example, in western music, instruments are normally tuned to A = 440 Hz.
However, the richness of the sound is produced by the combination of this fundamental with a series of harmonics and/or partials (also collectively called overtones). Most western instruments produce harmonic sounds, and these can be calculated by multiplying the fundamental by an increasing series of numbers - x2, x3, x4, etc (whole number multiples). However many instruments produce inharmonic tones, and may contain overtones which are not whole number multiples, these being the partials.
Therefore, when the orchestral tuning note is played, the sound is a combination of 440 Hz, 880 Hz, 1320 Hz, 1760 Hz and so on. The balance of the amplitudes of the different frequencies is responsible for giving each instrument its characteristic sound, which is exploited by FM synthesis.
William Sethares argues in Tuning, Timbre, Spectrum, Scale that just intonation and the western equal tempered scale are derived from the harmonic spectra/timbre of most western instruments. Similarly the specific inharmonic timbre of Thai metallophones would produce the seven tone near equal temperament they do indeed employ, and the five note sometimes near equal tempered slendro scale provides the most consonance in the combination of the inharmonic spectra of Balinese metallophones with harmonic instruments such as the stringed rebab.
There are two additional points that should be noted:
Envelope
The timbre of a sound is also greatly effected by the following factors: attack, decay, sustain, release, and transients. For instance, if one takes the attack off of the sound of a piano or trumpet, one much less readily identifies the sound correctly, since the sound of the hammer hitting the strings or the first blat of the players lips are highly characteristic of those instruments.
Timbre is often cited as one of the fundamental aspects of music.