Difference Tones
Consider the two waves starting in unison, f1 − f2 = 0. As the difference between f1 and f2 increases, the speed increases. Beyond a certain proximity (usually about 15 Hz), beating becomes undetectable and a roughness is heard instead, after which the two pitches are perceived as separate. If the beating frequency rises to the point that the envelope becomes audible (usually, much more than 20 Hz), it is called a difference tone. The violinist Giuseppe Tartini was the first to describe it, dubbing it il Terzo Suono (Italian for "the third sound"). Playing pure harmonies (i.e., a frequency pair of a simple proportional relation, like 4/5 or 5/6, as in just intonation major and minor third respectively) on the two upper strings of a violin, such as the C above middle C against an open E-string, will produce a clearly audible C two octaves lower.
An interesting listening experiment is to start from a perfect unison and then very slowly and regularly increase the pitch of one tone. When one tone starts to split out from the former twin-note, a slow rumbling can be heard, gradually increasing into an audible tone.
Read more about this topic: Beat (acoustics)
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