Definition and background:
The natural pure sounds that are a part of any musical tone; the overtones that are present with any fundamental tone. That is, the series of sounds heard when any note is sounded, consisting of the original note, which is the fundamental or first harmonic, then the tone an octave above that called the first overtone (also called the second harmonic), then the fifth above the first overtone, then the perfect fourth above that, then the major third above that, etc., in increasingly smaller intervals. High notes that are achieved on instruments of the violin family when the performer lightly places his finger exactly in the middle of the vibrating string.The harmonic tones produced by a vibration that go to make up the aural spectrum of any particular note, or grouping of notes.
Chime-like sounds achieved in two ways: 1) natural harmonics - by touching a string at any equidistant division of the string length (typically 5th, 7th, and 12th fret), directly above the fret with left hand, and striking hard with the right-hand fingers or pick near the bridge where there is more string resistance; or 2) artificial harmonics - touching a string with the index finger of the right hand twelve frets higher than any fretted note and plucking the string with either the thumb or third finger of the right hand
The term is sometimes loosely used for the fundamental frequencies of the series of notes which can be sounded by a player on a brass instrument with a given setting of any slide or valves. These, however, form only an approximation to a harmonic series
Whole number multiples of the frequency that determines the timbre recognition of an instrument's sound.
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Wikipedia - Glossary of Musical Terminology
Virginia Tech Multimedia Music Dictionary
ORB -- Medieval Music Glossary