Definition and background:
Overtones or harmonics are the natural parts of any pitch heard when it is sounded. That is to say, that each pitch that we hear contains addition pitches within it that are termed overtones or harmonics. The relative strength or weakness of these overtones determines the tone color or timbre of the pitch. This is why no two instruments sound alike. When a pitch is played, the main note heard is the fundamental (the note itself), but there is also present a series of other pitches above it called overtones or harmonics. The first overtone is an octave above the fundamental, the second is an octave and a fifth above the fundamental, the third is two octaves, the fourth is two octaves and a third, and so on, with each following overtone closer to the last than the last was to the tone before it. The series of overtones ( harmonic series) for the fundamental pitch C would consist of C-C 3-G 3-C 4-E 4 G 4-B-Flat 4*-C 5-D 5 E 5-F-Sharp 5*-G 5-A 5*-B Flat 5*-B 5-C 6. a tone that is present in the sounding of a fundamental, due to the physics of the production of musical tones
A word sometimes used for the spectral components (q.v.) of a sustained sound higher than the fundamental. Confusion is sometimes introduced by using the term 'overtone' when wishing to identify specific members of the series. For clarity it is preferable to speak of harmonics - the second harmonic is at twice the frequency of the fundamental, the third harmonic at three times, etc
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Wikipedia - Glossary of Musical Terminology
Virginia Tech Multimedia Music Dictionary
ORB -- Medieval Music Glossary