ASA 1 - Cancelled Harmonics


This demonstration illustrates Fourier analysis of a complex tone consisting of 20 harmonics of a 200-Hz fundamental. The demonstration also illustrates how our auditory system, like our other senses, has the ability to listen to complex sounds in different modes. When we listen analytically, we hear the different components separately; when we listen holistically, we focus on the whole sound and pay little or no attention to the components.

When the relative amplitudes of all 20 harmonics remain steady (even if the total intensity changes), we tend to hear them holistically. However, when one of the harmonics is turned off and on, it stands out clearly. The same is true if one of the harmonics is given a "vibrato" (i.e., its frequency, its amplitude, or its phase is modulated at a slow rate).


R.Plomp (1964), "The ear as a frequency analyzer," J. Acoust. Soc. Am. 36, 1628-367.

H. Duifhuis (1970), "Audibility of high harmonics in a periodic pulse," J. Acoust. Soc. Am. 48, 888-93.

Time Delay


A complex tone is presented, followed by several cancellations and restorations of a particular harmonic. This is done for harmonics 1 through 10.