Harmonic
Definition
One of the pure tones that combine to make a complex sound — whole-number multiples of the fundamental frequency.
Technical definition
The nth harmonic has frequency f_n = n·f_1, where f_1 is the fundamental. On a string fixed at both ends, harmonics correspond to standing-wave modes with n half-wavelengths fitting the string length.
Example
A guitar's A string vibrates at 110 Hz (fundamental) plus 220, 330, 440 Hz and more — the mix of these harmonics is what makes it sound like a guitar and not a flute.
Common confusion
‘Harmonic’ and ‘overtone’ are often used interchangeably but differ: the 2nd harmonic is the 1st overtone. The fundamental counts as the 1st harmonic but is not an overtone.