Harmonics are whole-number multiples of the fundamental frequency of a given pitch.
For example, the fundamental frequency for concert A is 440 hertz. An 880-hertz overtone would be considered the second harmonic, because it is two times the fundamental frequency of concert A.
Typically, even harmonics are perceived as pleasing to the ear and odd harmonics are perceived as harsher, more dissonant tones.
The distortion characteristics of tube microphones tend to emphasize even harmonics, which sound very warm and musical, whereas the distortion characteristics of solid-state microphones tend to emphasize odd harmonics, which are less musically pleasing.
Different instruments playing the same fundamental frequency can have a varying degree of harmonic intensity. Because of this, harmonics heavily impact an instrument's timbre, or sonic characteristics.