Pitch Class and Envelope Effects in the Tritone Paradox Are Mediated by Differently Pronounced Frequency Preference Regions - Malek, Stephanie (Frontiers in Psychology, 2018)
Shepard tones (octave-complex tones) are well defined in pitch chroma, but ambiguous in pitch height. Pitch-direction judgments on Shepard tones depend on the clockwise distance of the pitch classes on the pitch-class circle, indicating the proximity principle in auditory perception. The tritone paradox emerges when two Shepard tones that form a tritone interval are presented successively. In this case, no proximity cue is available and judgments depend on the first tone and vary from person to person. A common explanation for the tritone paradox is the assumption of a specific pitch-class comparison mechanism based on a pitch-class template that is differently orientated from person to person. In contrast, psycho-acoustic approaches (e.g. the Terhardt Virtual Pitch Theory) explain it with common pitch-processing mechanisms. The present paper proposes a probabilistic threshold model, which estimates Shepard-tone pitch height by a probabilistic fundamental-frequency extraction. Frequency components are filtered when their amplitudes are beneath specific random-distributed threshold values, whose expected values are determined by a threshold function. The lowest non-filtered component is dedicated to the pitch height. The model is designed for tone pairs and provides occurrence probabilities for descending judgments. In a pitchmatching pretest, 12 Shepard tones (generated under a cosine envelope centered at 261 Hz) were compared to pure tones, whose frequencies were adjusted by an up-down staircase method. Matched frequencies corresponded to frequency components and were ambiguous in octave position. In order to test the model, Shepard tones were generated under 6 cosine envelopes centered over a wide frequency range (65.41, 261, 370, 440, 523.25, 1244.51 Hz). The model predicted pitch-class- and envelope effects. Steep threshold functions, associated with a pronounced frequency-preference region, caused pronounced pitch-class effects; flat threshold functions, associated with no or a small frequency-preference region, caused pronounced envelope effects. The model provides an alternative explanation to the pitch-class-template theory and serves as a psycho-acoustic framework for Shepard tones.