How can two musical notes produce a third low tone?

Two sustained high notes can sometimes be accompanied by a faint lower tone that neither player intended. A difference tone can occur at the difference between their frequencies. It is one example of a combination tone associated with nonlinear response.

In a perfectly linear system, adding pure 800-hertz and 1,000-hertz waves produces only those two frequencies in its spectrum. A repeating pattern in their combined waveform does not by itself mean that a separate 200-hertz pressure component has appeared in the air.

A nonlinear element changes that result. In a simple illustrative response containing a squared-input term, multiplying the two oscillations creates sum and difference components. The difference here is 1,000 − 800 = 200 hertz. Nonlinear behavior can occur in an instrument or sound equipment, producing a real extra sound component.

The auditory system is also nonlinear, so a listener may experience a difference tone that is not present as that frequency in the incoming air-pressure signal. The strength and even audibility of the effect depend on the sounds and the listener. It is distinct from slowly beating loudness between nearby pitches.

This makes an illuminating distinction: what exists in the incoming signal, what a physical system generates, and what a listener perceives need not be identical descriptions of the same musical moment.