The whole-number multiples of a fundamental frequency, f, 2f, 3f and so on, which a string or air column sounds together.
Also called: overtone series, harmonics, series of partials
The harmonic series is the set of frequencies that are whole-number multiples of a fundamental: f, 2f, 3f, 4f, and so on. A string, pipe or air column that sounds a note produces these partials alongside the fundamental. With a fundamental of 110 Hz, the series reads 110, 220, 330, 440, 550 and 660 Hz. The second partial is an octave above, the third is an octave and a fifth above, and the fourth is two octaves above. Intervals between neighbouring partials use simple ratios such as 3:2 and 4:3, which is why the octave, fifth, fourth and major third come first in the series. The series is an ideal. Real strings and bells have partials that drift from exact multiples, and piano tuners stretch the octaves to follow the upper partials.
Acoustics & Sound
A vibrating string or air column sounds a fundamental and a set of partials at whole-number multiples of it. Here are the first sixteen, their cents, and where they differ from equal temperament.