Box BThe Sweet Sound of Distortion

As early as the first half of the eighteenth century, musical composers such as Giuiseppe Tartini and W. A. Sorge discovered that upon playing pairs of tones, other tones not present in the original stimulus are also heard. These combination tones, fc, are mathematically related to the played tones, f1 and f2 (f2 > f1), by the formula

Image ch13e1.jpg

where m and n are positive integers. Combination tones have been used for a variety of compositional effects, as they can strengthen the harmonic texture of a chord. Furthermore, organ builders sometimes use the difference tone (f2-f1) created by two smaller organ pipes to produce the extremely low tones that would otherwise require building one especially large pipe.

Modern experiments indicate that this distortion product is actually due to the nonlinear properties of the inner ear. M. Ruggero and his colleagues placed small glass beads (10–30 mm in diameter) on the basilar membrane of an anesthetized animal and then determined the velocity of the basilar membrane in response to different combinations of tones by measuring the Doppler shift of laser light reflected from the beads. When two tones were played into the ear, the basilar membrane vibrated not only at those two frequencies, but also at other frequencies predicted by the above formula.

Related experiments on hair cells studied in vitro suggest that these nonlinearities result from the properties of the mechanical linkage of the transduction apparatus. By moving the hair bundle sinusoidally with a metal-coated glass fiber, A. J. Hudspeth and his co-workers found that the hair bundle exerts a force at the same frequency. However, when two sinusoids were applied simultaneously, the forces exerted by the hair bundle occurred not only at the primary frequencies, but at several combination frequencies as well. These distortion products are due to the transduction apparatus, since blocking the transduction channels causes the forces exerted at the combination frequencies to disappear, even though the forces at the primary frequencies remain unaffected. It seems that the tip links add a certain extra springiness to the hair bundle in the small range of motions over which the transduction channels are changing between closed and open states. If nonlinear distortions of basilar membrane vibrations arise from the properties of the hair bundle, then it is likely that hair cells can indeed influence basilar membrane motion, thereby accounting for the cochlea's extreme sensitivity. Apparently, when we hear difference tones, we are paying the price in distortion for an exquisitely fast and sensitive transduction mechanism.

References

  1. Planchart A. E. A study of the theories of Giuseppe Tartini. J. Music Theory. (1960);4(1):32–61.
  2. Robles L., Ruggero M. A., Rich N. C. Two-tone distortion in the basilar membrane of the cochlea. Nature. (1991);439:413– 414. [PMC free article: PMC3579518] [PubMed: 1992342]
  3. Jaramillo F., Markin V. S., Hudspeth A. J. Auditory illusions and the single hair cell. Nature. (1993);364:527–529. [PubMed: 8336792]

From: The Inner Ear

Cover of Neuroscience
Neuroscience. 2nd edition.
Purves D, Augustine GJ, Fitzpatrick D, et al., editors.
Sunderland (MA): Sinauer Associates; 2001.
Copyright © 2001, Sinauer Associates, Inc.

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