(Ph.D. diss., University of Texas at Austin, 1999; UMI 9956952)
Abstract...
The coincidence theory was a theory of consonance advocated by many of the scientists of the period 1550-1800, including Galileo, Mersenne, Descartes, and Euler. It was the first truly scientific explanation of consonance, addressing the way that sound waves interact with each other either constructively or destructively. Within the present century, historians of music and science have turned their attention to the coincidence theory and the important role it played in both fields in the 17th century. Many of these same authors have charged the theory with having had serious faults. However, an investigation of modern scientific evidence reveals that these alleged problems are either answerable or irrelevant to the coincidence theory. Furthermore, a survey of the major theories of consonance since the 18th century shows that the premises of the coincidence theory pervade and underlie many of these more recent theories. Examples of such theories include those of Helmholtz, Lipps, Boomsliter and Creel, and Terhardt. In the process of establishing these theses, many relevant secondary issues are addressed. For example, this dissertation contains a discussion of the different meanings of the word consonance, the relationship between integer ratios and musical intervals, and the similarities between pitch perception and rhythmic perception. Also, several different versions of the coincidence theory are identified and evaluated.