harmonic series

In music, the harmonic series refers to the set of frequencies that are integer multiples of a fundamental frequency. These frequencies are also known as harmonics or overtones. For example, if the fundamental frequency is 100 Hz, the harmonic series would include 100 Hz, 200 Hz, 300 Hz, 400 Hz, and so on.1

The concept of harmonic series has roots in ancient Greece, where mathematicians like Pythagoras explored numerical relationships in music. The specific mathematical sequence 1, 1/2, 1/3, 1/4, ... is also called the harmonic series, and its partial sums grow infinitely large.23

Musical instruments produce sounds with a fundamental frequency and various harmonics, which contribute to their unique tone quality or timbre. The bore shape of instruments influences which harmonics are present, affecting the resulting sound. For instance, instruments like flutes and violins produce all harmonics, while clarinets emphasize odd harmonics.41