combination tone, in musical acoustics, faint tone produced in the inner ear by two simultaneously sounded musical tones. Because such tones are caused by the ear rather than by the external source of the sound, they are sometimes called subjective, or resultant, tones. There are two varieties: difference tones (D) and summation tones (S), generated respectively by the frequency differential of the two pitches or the sum of their frequencies. The most commonly heard are difference tones lying below the original pitches; these were discovered by the celebrated violinist-composer Giuseppe Tartini (1692–1770), who regarded the “third tone” as an excellent means of correcting faulty intonations of double stops on the violin.

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. Other, more-complex waveforms, such as those produced by singing voices, also occasionally produce combination tones.

A similar subjective phenomenon, aural harmonics, results from the ear’s distortion of a single pure tone. The distortions produce frequencies in the ear corresponding to multiples of the original frequency (2f, 3f, 4f,…), and aural harmonics thus have the same pitch as externally produced harmonics.

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This article was most recently revised and updated by William L. Hosch.
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beat, in physics, the pulsation caused by the combination of two waves of slightly different frequencies. The principle of beats for sound waves can be demonstrated on a piano by striking a white key and an adjacent black key at the bass end of the keyboard. The resulting sound is alternately soft and loud—that is, having characteristic pulsations, or throbs, called beats. Toward the treble end of the keyboard, the beat frequency is greater because the difference in frequency of adjacent keys is more than at the lower end. The Figure depicts two waves n1 and n2 with respective frequencies of 24 and 30 vibrations per second (hertz); the beat frequency N is their difference, 6 beats per second.

The phenomenon of beats is employed in various ways. For example, in the tuning of instruments, if a tuning fork and piano key of the same note are struck simultaneously and no beat is heard, then they are of identical pitch. Ultrasonic vibrations (having a frequency higher than is audible), such as the vocal sounds made by bats and dolphins, may be detected by superimposing a sound of different frequency to produce audible beats. The principle is also used in the superheterodyne reception of radio waves, in which a low-frequency signal from an oscillator is beat against an incoming high-frequency radio signal to produce an intermediate (beat) frequency that can be amplified to produce audible signals.

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