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Vassilakis, P.N. (1998).  The first pitch-shift effect as a Doppler effect: a simple physical explanation to a complex perceptual phenomenon.  J. Acoust. Soc. Am., 104(3/2): 1799 (presented at the 136th meeting of the Acoustical Society of America, Norfolk, VA).

Abstract
  
The first pitch-shift effect describes the relationship between pitch and center frequency of complex stimuli with equally spaced components and fixed frequency spacing (: f₀). It is described mathematically by a saw-tooth function in a model introduced by de Boer [Doctoral dissertation, University of Amsterdam, (1956)]. Researchers usually favor a more ambiguous frequency-shift/pitch-shift relationship that better justifies the generally accepted explanation (: perceptual detection of a wave signal’s time-fine-structure). Pilot experiments, however, indicate that:
a) The patterned pitch ambiguities reported by previous studies may be artifacts of experimental design, not a challenge to de Boer’s model.
b) No model accounts for the present study’s reported pitch for frequency shifts: f₀/2.

The explanation introduced presently argues that:
a) Modulations resulting from wave superposition are waves themselves, with velocity (V_Group) that is independent from the velocity of their constituent components (V_Phase).
b) Uniform frequency shifts of a complex wave’s components change the relationship between V_Group and V_Phase, changing the effective frequency of the emerging modulations relative to a fixed point in the medium of propagation.
These relative speed/frequency changes predict pitch shifts that agree with observation, (including frequency-shifts: f₀/2), making the first pitch-shift effect a version of the Doppler effect.