Doctoral work

Mathematical and Mechanical Studies of Music in Late Seventeenth-Century England: D.Phil., Oxford, 2006 (faculty of history)

This thesis describes the development of the quadrivial discipline of 'harmonics' in late seventeenth-century England, examining writings which apply a primarily mathematical, mechanical, or experimental approach to the study of music, with particular attention to their technical content.

After an overview of the rationale, content, and problems of earlier mathematical studies of music, I survey the context for late-seventeenth-century English work, including: earlier sources' visibility; awareness of changes in musical style; new mechanical explanations for consonance; and the major early-seventeenth-century works of Mersenne, Kircher, and Descartes.

Next, four strands of seventeenth-century development are traced: quantification and representation of pitch and their use of mathematical innovations including logarithms; theories of sound and hearing and the anatomy of the ear; musical experiments; and discussions of music in natural philosophy. Broadly mathematical writers considered in detail include Mercator, Newton, Pietro Mengoli, John Birchensha, and Thomas Salmon.

I ask general questions about the nature of musical science in this period. Key points which emerge are: the study of music continued to be widely considered a branch of mathematics and contained real mathematical innovation; there was widespread uncertainty and scepticism about the ability of the musical hearing to produce reliable knowledge; natural philosophers put music to a wide variety of uses in their writings, including as a mechanical analogy and as a formal cause; and there was uncertainty and disagreement about the proper shape which the study of music should take, including the role of the senses and of experiment, and therefore about the validity of particular authors' work.

Connections between these points are made in my final chapter, pointing towards further work on the late development of these issues and on more general changes in mathematics' use and meaning.

A a book based on this doctoral thesis is in preparation for Ashgate.