Harmonic Overtones and Resonance

A sine wave is a pure tone composed of a single frequency. Most sounds that occur in nature are a mixture of many different frequencies, each of which is a separate sine wave. Sounds made by musical instruments consist of a fundamental and a series of overtones. The fundamental is the perceived pitch of the note and is usually the lowest frequency tone in the series. Harmonic overtones occur at frequencies that are integer multiples of the fundamental.

The fundamental is also called the first harmonic. The second harmonic is twice the frequency of the fundamental and is one octave up the musical scale. The third harmonic is three times the frequency of the fundamental and is one and a half octaves up the musical scale from the fundamental.

When multiple sine waves are mixed together they unite to form a complex waveform. The two charts below show a fundamental and third harmonic mixed together. The first chart shows two sine waves, and the second chart shows the complex waveform.