Date of Award
Doctor of Philosophy (PhD)
Dr. John R. Platt
When tones comprised of six octave-related harmonics are placed in pairs, where the two tones are separated by a tritone, some subjects perceive the direction of pitch change from the first to the second tone as ascending, while other subjects perceive it as descending. This is the basis for what is currently labeled the Tritone Paradox.
The Tritone Paradox was investigated in a set of four experiments that made use of different experimental procedures that employed a 0 - 750 ms silent interval between tones in a trial-pair, different methods of stimulus presentation (i.e. open air or earphone) and 125 - 500 ms stimulus durations. Major emphasis was placed on the implementation of a standardized experimental procedure and the use of a standardized method of analyzing results in a Tritone Paradox experiment. To this end, an analysis method was designed using circular statistics, which resulted in a truly objective method of analyzing and classifying subjects while making use of all subject data. Analyses indicated that peak-pitch class was highly correlated with the angle of a mean vector (AMV) and that the depth of a profile was correlated with the length of a mean vector (LMV). The AMV and LMV may be combined to produce a single summary measure for a subject's performance.
Two modes of responding employed by subjects were identified. Profiles generated using a spectral-envelope-controlled mode of responding are characterized by judgments of tones under one envelope being close to 180° out of phase with judgments made under a spectral envelope centered one half octave away from the other. Profiles generated using a pitch-class-controlled mode of responding are characterized by judgments of tones under one spectral envelope closely resembling judgments of tones made under a spectral envelope centered a tritone away from the first spectral envelope.
Angular-Separation analysis details the difference between the AMV for two separate profiles generated by a subject. This analysis technique is a fast, reliable method for indentifying individual differences in mode of responding between subjects. Angular-Separation analyses were used to verify the presence of 'spectral-envelope-controlled' subjects, which were first described in detail by Repp (1994). These subjects appeared in significant proportions in all conditions. Based on the results of these analyses, the traditional practice of using a single-averaged profile to describe a subject has been questioned. Such a profile does not adequately describe the performance of a subject using a spectral-envelope-controlled mode of responding. The single-averaged profile masks the differences between these subjects and those using a 'pitch-class-controlled' mode of responding, which are the subjects typically described in the literature. Results of the Angular-Separation analysis across Experiments 1 - 4 showed similar proptions of subjects using a pitch-class-controlled or a spectral-envelope-controlled mode of responding. Evidence was found to indicated that the largest proportion of subjects using pitch-class-controlled mode of responding was observed in an experimental condition that used 125-ms stimuli with no silent interval between tones in a pair. Evidence was also found to indicate that the largest proprtion of subjects using a spectral-envelope-controlled mode of responding was observed in an experimental condition that employed 500 ms stimuli with a 500 ms silent interval between tones in a trial pair. It therefore appears that the duration of tones and the duration of a silent interval between tones in a trial pair will influence the mode of responding adopted by a subject in a Tritone Paradox experiment.
The pure-tone pre-test, desribed in the literature as a subject selection tool, was investigated and results indicate that performance on such a pre-test does not predict how consistent a subject's performance will be in a Tritone Paradox task. Although mean LMV decreased as pre-test error scores increased, there was no significant correlation found between individual subjects' error scores and LMV values. This pre-test, however, has some value in predicting some subjects' mode of responding. The vast majority of subjects with three or more errors on a pure-tone pre-test produced profiles that were classified as spectral-envelope controlled. These reults suggest that the bulk of those subjects eliminated in past Tritone Paradox experiments that emploted a pure-tone pre-test, may have been subjects who were far more likely to use spectral-envelope controlled mode of responding.
Gerhardt, Kris, "The Tritone Paradox: An Experimental and Statistical Analysis" (2002). Open Access Dissertations and Theses. Paper 1011.