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von Békésy has shown that listening for 2 min to an 800-Hz tone at a sound pressure of 10 dynes/cm2 both reduces the loudness of subsequently heard tones near 800 Hz and produces a pitch shift, so that tones higher than 800 Hz seem still higher and lower tones seem still lower. [G. von Békésy, Physik Z. 30, 115 (1929); reprinted in G. von Békésy, Experiments in Hearing, edited by E. G. Wever (McGraw–Hill, New York, 1960), pp. 354–368.]
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Fletcher's original measurements using this method were quite variable. However, Scharf, in reviewing recent studies on the critical band in audition, concludes that, "Despite the apparent confusion of intensity discrimination and masking, masking by narrow-band noise can provide adequate estimates of critical bandwidth, as evidenced by the overall agreement of Greenwood's, Hamilton's, and van der Brink's measures with all the other measures of the critical band." Pp. 167–168 in B. Scharf, in Foundations of Modern Auditory Theory, Vol. 1, edited by J. V. Tobias (Academic, New York, 1970), pp. 157–202.
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If a sinusoidal grating L0[1+m cos(2π ƒ0x+Ø)] does not extend to infinity in the x direction, but is truncated by an aperture of width A, such that ƒ (x) = [m cos (2π ƒ0x+Ø)] rect (x/A), when the constant term is neglected, where rect [Equation] then F(ƒ), the Fourier transform of ƒ(x), will be the convolution of the Fourier transform of the grating and aperture functions, yielding [Equation] If A = N / ƒ0, where N is the number of cycles of the grating that fell in aperture A, then at ƒ = ƒ0/3 (i.e., 1.5 octave below ƒ0) for Ø= 0, ƒ0= 2.5 cycles/deg, and A = 2.5 deg; N = 6.25 and F (ƒ)/F (ƒ0)=-23 dB. For other references, see D. H. Kelly, J. Opt. Soc. Am. 60, 98 (1970).
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