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Vassilakis, P.N. (1998).  A single model explaining the first and second pitch-shift effects as alternative manifestations of a single phenomenon.  Proceedings of the 5th ICMPC: 107-114.  Seoul, Korea: Seoul National University.

Abstract [full paper]
  
The 1st pitch-shift effect describes the relationship between pitch and center frequency of complex stimuli with equally spaced frequency components and fixed frequency spacing. The 2nd pitch shift effect describes a drop in the perceived pitch of a complex stimulus with fixed center frequency, when the frequency spacing among its components is slightly increased. The present study demonstrates that the model explaining the 1st pitch-shift effect, introduced by de Boer (1956, Doctoral dissertation, Univ. of Amsterdam) and modified here based on Smoorenburg’s argument (1970, JASA, 48(4/2): 1055-1060), predicts, without further modification, the second pitch-shift effect as well.
The same model also predicts that the perceived pitch of a complex stimulus will not always drop when increasing the frequency spacing among its components, but may rise depending on the structure of the initial stimulus. To test this prediction a perceptual experiment was conducted using nine synthesized complex stimuli. For eight of the stimuli the model predicted a rise in pitch with increasing frequency spacing while for the ninth stimulus the opposite was predicted. The results indicate that
a) the pitch of a complex stimulus and the frequency spacing between its components do not necessarily have to move in opposite directions and
b) the specific direction of pitch change can be predicted in each case by the same model that explains the first pitch shift effect.
The proposed single model is therefore able to predict the pitch of any complex stimulus with equally spaced components a) regardless of whether it has resulted from shifting (1st pitch-shift effect) or stretching (2nd pitch-shift effect) the components of some complex spectrum and b) without the restrictions for fixed frequency spacing (1st pitch shift effect) or fixed center frequency (2nd pitch-shift effect). The results of an experiment testing this more general claim are presented and its implications are discussed.

  


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