Acoustic bass of pipe organ


The so-called acoustic bass of pipe organs (cf.  [104]  p. 400) is produced by a trick of organ manufacturers and organ players, respectively, which has been known for more than 200 years. As the name indicates, the trick is concerned with producing low notes, i.e., in the bass range. It was early discovered that the simultaneous sounding of two pipes in a fifth interval, e.g. C_4 - G_4, gives the aural impression that essentially  one note is being played, and that the pitch of that note is an octave below the lower note of the dyad, i.e. in the example, C_3.  Although the sound of such a dyad is not fully equivalent to that of a real pipe of corresponding size (in fact the effect is fairly subtle [66] ),  the trick can be employed in small organs for which implementation of real bass pipes is impossible due to cost and/or lack of space.

The explanation of the "acoustic-bass effect" has been far from obvious. Physicists tended to suppose that by some kind of nonlinearity the two simultaneous sound waves would yield a difference tone, i.e. another sound wave with a frequency equal to the difference between the frequencies of the two pipes. When, for instance, the lower pipe of the dyad gives a 200-Hz wave, the second, being a fifth higher in frequency, gives 300 Hz. The difference is 100 Hz, i.e., one octave below the first pipe's frequency. However, even at the high sound intensities which can be produced by organ pipes, the nonlinearity of the air is small, such that the intensity of a difference tone can only be quite small. Since in the bass region the ear gets less and less sensitive when frequency decreases, it is unlikely that such a difference wave can be heard at all.

A convincing explanation emerges from contemporary knowledge on the perception of pitch, in particular from the fact that a harmonic complex tone evokes a pitch that essentially corresponds to its fundamental frequency eventhough the fundamental (as a component of the Fourier spectrum) may be so weak in intensity that it is below the threshold of hearing (see topic virtual pitch). In fact the two tones of the fifth-dyad can as well be viewed as the second and third harmonics (e.g. 200 and 300 Hz) of a missing fundamental (100 Hz). According to that explanation, the "acoustic bass" emerges from a kind of inference process in the auditory system which produces a virtual pitch the equivalent frequency of which is subharmonic to the frequencies actually sounding. As I have pointed out on various occasions (e.g. [104] ), that process is analogous to the perception of virtual contours in vision. We have verified this [66] by comparison of experimental results on the acoustic bass of a pipe organ with predictions of the virtual-pitch theory. I am sure that the phenomenon of acoustic bass is of exactly the same type as perception of the "fundamental notes" (roots, basse fondamentale) of musical chords.

In the light of these findings, the phenomenon of "acoustic bass" turns out to be, in a sense, quite "the opposite of" acoustic; it rather is of a psychological nature. It should be noted, however, that such criticism of the term probably is not fair, as in former Centuries the term acoustic was not confined to the physical aspects of sound.


Author: Ernst Terhardt terhardt@ei.tum.de - Feb. 11, 2000


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