http://www.smu.edu/totw/overtone.htm
http://www.music.ecu.edu/courses/brass/OVERTONE_SERIES.HTML

Two reasonably simple explanations above will attempt to explain the overtone series. The overtones were known even before Pythagorus. Pythagorus and Fourier (sp) wrote treatises to explain the idea. Simply put, modern harmony manipulates traditional harmony to make the dissonances or the out of tune notes in the overtone series sound correct or more palatable to the ear. (very noticeable in horns and on the average guitar above the 7th fret) Equally noticeable with computer software and hardware if not properly controlled.
Hope this helps a little.