ASA 34 - Aural Combination Tones


When two or more tones are presented simultaneously, various nonlinear processes in the ear produce combination tones similar to the distortion products heard in Demonstration 33 and many more. The most important combination tones are the difference tones of various orders, with frequencies f2 - f1 and f1 - n(f2 - f1), where n is an integer.

Two prominent difference tones are the quadratic difference tone f2 - f1, (sometimes referred to simply as "the difference tone") and the cubic difference tone 2f1 - f2. If f1, remains constant (at 1000 Hz in this demonstration) while f2 increases, the quadratic difference tone moves upward with f2 while the cubic difference tone moves in the opposite direction. At low levels ( approximately 50 dB), they can be heard from about f2/f1, = 1.2 to 1.4 (solid line in the figure below), but at 80 dB they are audible over nearly an entire octave (f2/f1 = 1 to 2 dashed line in the figure below). In this case, quadratic and cubic difference tones cross over at f2/f1 = 1.5. They are shown on a musical staff in the right half of the figure.

In this demonstration, which follows No. 19 on the "Harvard tapes," tones with frequencies of 1000 and 1200 Hz are first presented. When an 804-Hz tone is added, it beats with the 800-Hz (quadratic) difference tone.

Next, the frequency of the upper tone is slowly increased from f2 = 1200 to 1600 Hz and back again. You should hear the cubic difference tone moving opposite to f2 soon joined by the quadratic difference tone, which first becomes audible at a low pitch and moves in the same direction as f2. They should cross over when f2 = 1500 Hz.

Over part of the frequency range, the quartic difference tone 3f1 - f2 may be audible.


J.L.Goldstein (1967), "Auditory nonlinearity," J. Acoust. Soc. Am. 41, 676-89.

J.L.Hall (1972), "Auditory distortion products f2 - f1 and 2f1 - f2," J. Acoust. Soc. Am. 51, 1863-71.

R.Plomp (1965), "Detectability threshold for combination tones," J. Acoust. Soc. Am. 37, 1110-23.

T.D.Rossing (1982), The Science of Sound (Addison-Wesley, Reading, MA). Chap. 8.

B.Scharf and A.J.M.Houtsma (1986), "Audition 11: Loudness, pitch, localization, aural distortion, pathology," in Handbook of Perception and Human Performance, ed. L.Kaufman, K.Boff and J.Thomas (Wiley, New York).

G.F.Smoorenburg (1972a), "Audibility region of combination tones," J. Acoust. Soc. Am. 52, 603-14.

G.F.Smoorenburg (1972b), "Combination tones and their origin," J. Acoust. Soc. Am. 52, 615-632.

Time Delay


In this demonstration two tones of 1000 and 1200 Hz are presented. When an 804-Hz probe tone is added, it beats with the 800-Hz aural combination tone.

Time Delay


Now the frequency of the upper tone is slowly increased from 1200 to 1600 Hz and then back again.