This is Your Brain on Music – Professor Daniel Levitin

All natural objects in the world have several modes of vibration.  A piano string actually vibrates at several different rates at once.  The same thing is true of bells that we hit with a hammer, drums that we hit with our hands, or flutes that we blow air into; the air molecules vibrate at several rates simultaneously, not just a single rate……….

Surprisingly, these other frequencies are often mathematically related to each other in a very similar way; as integer multiples of one another.  So if you pluck a string and its slowest vibration frequency is one hundred times per second, the other vibration frequencies will be 2 X 100 [200Hz], 3 X 100 [300 Hz] etc.  If you blow into a flute or a recorder and cause vibrations at 310 Hz, additional vibrations will be occurring at twice, three times, four times etc, this rate 620 Hz, 930 Hz, 1240 Hz etc When an instrument creates energy at frequencies that are integer multiples such as this, we say that the sound is harmonic, and we refer to the pattern of energy at different frequencies as the OVERTONE series