Difference tone

A combination tone (also called resultant or subjective tone) is a psychoacoustic phenomenon of an additional tone or tones that are artificially perceived when two real tones are sounded at the same time. Their discovery is credited to the violinist Giuseppe Tartini (although he was not the first, see Sorge) and so are also called Tartini tones.

There are two types of combination tones: sum tones whose frequencies are found by adding the frequencies of the real tones and difference tones whose frequencies are the difference between the frequencies of the real tones. "Combination tones are heard when two pure tones (i.e., tones produced by simple harmonic sound waves having no overtones), differing in frequency by about 50 cycles per second or more, sound together at sufficient intensity."

Combination tones can also be produced electronically by combining two signals in a circuit that has nonlinear distortion, such as an amplifier subject to clipping or a ring modulator.

One way a difference tone can be heard is when two tones with fairly complete sets of harmonics make a just fifth. This can be explained as an example of the missing fundamental phenomenon. If ${\displaystyle f}$ is the missing fundamental frequency, then ${\displaystyle 2f}$ would be the frequency of the lower tone, and its harmonics would be ${\displaystyle 4f,6f,8f,}$ etc. Since a fifth corresponds to a frequency ratio of 2:3, the higher tone and its harmonics would then be ${\displaystyle 3f,6f,9f,}$ etc. When both tones are sounded, there are components with frequencies of ${\displaystyle 2f,3f,4f,6f,8f,9f,}$ etc. The missing fundamental is heard because so many of these components refer to it.

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