11. Harmonics

When the frequencies of the partials are whole-number multiples of the fundamental frequency, those frequencies are harmonics.

For instance, if the fundamental frequency is 100 Hz, the harmonic frequencies would be 200 Hz, 300 Hz, 400 Hz, and so on. If the fundamental frequency is 440 Hz, the harmonic frequencies would include 880 Hz, 1320 Hz, 1760 Hz, 2200 Hz, etc.

Furthermore, each harmonic is identified ordinally; this means that the fundamental is called the first harmonic, the first partial is called the second harmonic, the second partial is the third harmonic, and so on.

Example 11-1: Frequencies contained in a specified harmonic series change in accordance with changes of the fundamental frequency.

This relationship between the fundamental frequency and the upper partials is called the harmonic series. The makeup of the specific harmonics in any given waveform is called the harmonic spectrum, or spectrum.

The term overtone is often mentioned in discussions about harmonics and harmonic series. An overtone is any harmonic other than the fundamental. This often leads to confusion because the first overtone is the second harmonic, and the second overtone is the third harmonic, etc. A partial, however, is not necessarily a harmonic; a partial may be a non-harmonic sine wave component higher in frequency than the fundamental. These terms, however, are often used rather loosely in the literature about electronic music.

Accordingly, you should study any discussion of the terms harmonic, overtone and partial with care to understand how a particular author is using them. In Electronic Music Interactive, the term "harmonic" is used consistently throughout.

The harmonic series is the basis for the sound of many acoustic instruments, and is commonly used in music synthesis to create waveforms. The sawtooth, triangle, square, and rectangle waves are some of the complex periodic waveforms whose harmonic spectra are based on the harmonic series.