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 identifying 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 proportions of subjects using a pitch-class-controlled or a spectral-envelope-controlled mode of responding. Evidence was found to indicate that the largest proportion of subjects using a 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 proportion 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, described 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 pretest, 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 results suggest that the bulk of those subjects eliminated in past Tritone Paradox experiments that employed a pure-tone pre-test, may have been subjects who were far more likely to use a spectral-envelope controlled mode of responding. / Thesis / Doctor of Philosophy (PhD)

Thesis (M.M.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / 2999-01-01

Thesis (Ph.D.) -- McMaster University, 2002. / Includes bibliographical references (leaves 250-253). Also available via World Wide Web.

Charles Ives is commonly referred to as the "Father of American Music." The implication is one that Ives himself would agree with, that he wrote purely American ideas from his own environment without reference to other styles or methods, in particular the widespread European tradition. Some composers, like Aaron Copland and Roger Sessions, created an American sonority by incorporating the concepts of musical construction they studied at the Paris Conservatoire. Ives, conversely, received no instruction in Europe, but the techniques so prevalent in the music of the French art song are found in certain songs written by Ives. Though he claimed no European influence, however, he used the late nineteenth century French song style in some of his songs, and he also borrowed tunes from the French composers. This study identifies significant trademarks of eighteenth century French song and the stylistic traits associated with a variety of prominent composers of the time. Ives's childhood musical influences, his church position, and his studies at Yale University will establish a relationship between Ives and the French musical ideas. The primary source for his songs is his collection entitled 114 Songs. Ives gathered his songs and put them into one collection which included Four French Songs. Through the analysis of several songs, including the four French songs written by Ives and three comparisons of songs by Ives with songs by French composers, it becomes evident that Ives was influenced, to a certain extent, by French music and used many techniques of the style.

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