Dissecting the magic of music

In attempting to describe inter-relationships between her three topics, Penelope Gouk has taken on a new and difficult task. Her book has three distinct parts. The first, the most original and revealing, uses terms from projective geometry (not a name Gouk uses) as metaphors to show how disciplinary, social and cognitive domains were related to music, natural magic and science in 17th-century England, and how these relationships changed with time. The result goes beyond common linear narratives that wander across a boundary between two established academic areas.

The second part is a short demonstration, illustrated by diagrams, to show that arithmetical and geometric structures of musical harmony and speculative cosmology were significant in the development of science.

The third part comprises three narratives on the importance of music and natural magic in the early activities of the Royal Society and in the work of Hooke and Newton.

Gouk describes the first part of the book as an experiment, but it is not so in the scientific sense. It is more a contrivance, or invention. A reader who practises in the discipline from which Gouk takes some of her vocabulary must discard meanings of familiar and often mathematically defined terms and recognise their metaphorical value in a new context. It is no surprise to find that Gouk's narrative is most effective when the topic is most nearly geometric: the maps of knowledge constructed by John Dee, Johannes Alstead and Ephraim Chambers, and one derived from Bacon's writings. Temporal changes in the cognitive relationships between music, natural magic and science over the 150 years spanned by these four maps are seen clearly. But different relationships between the three main subjects also come into existence when each knowledge map is transformed by projection through practitioners' social positions, or who taught them, or who their patrons were. Gouk's drawing-out and presentation of these and other complex relationships are the most important and valuable attributes of the book.

The three chapters in the third part are less successful. In seeking her "goal to demonstrate how the social practice of making music had a direct and perceivable effect on experimental scientific knowledge, mediated via their shared relationship with natural magic" Gouk pushes the evidence too far, particularly where Hooke is concerned. Although some of Newton's thought still seems mysterious and can be described as typical of a Pythagorean magus, nearly all Hooke's work can be seen as predominantly mechanical and empirical. Gouk's temporal projections and mappings are all prospective, which may explain why she has arrived at unqualified conclusions (such as that Hooke followed Dee's speculative tradition, and Hooke's entire philosophy was founded on correspondence between the macrocosm and the microcosm) that are very hard to accept.

In an epilogue, Gouk asks: "Where did natural magic go?" Although not explicitly part of the author's plan, an added value of this book is that it encourages speculation about the limits of science. Many elements in the sequence of energy transformations in space and time between the brain of musician and the brain of a listener can now be identified and measured by neuroscience, physiology and acoustics. But at each end of that sequence is an individual's conscious mind.

Is science capable of explaining the complete process, or will musicianship and its appreciation remain forever occult, accessible only to the performer and listener at each magical instant?

M. A. R. Cooper is professor of engineering surveying, City University.