Introduction 5
chapter 15 connects with the many-dimensional manifolds earlier considered by the math-
ematician Bernhard Riemann. Riemann ’ s unfinished work on the mechanism of the ear
affected Helmholtz ’ s ensuing response, which used studies of sound and color to present
an empirical basis for Riemann ’ s hypotheses. Einstein drew on these results to shape his
world-geometry.
At the same time, the study of spectra brought the music of the spheres to the atomic
level. Chapter 16 explores the acoustical underpinnings of G. Johnstone Stoney and Johann
Balmer ’ s search for the order in elemental spectra. Balmer ’ s basic formula for the spectral
lines of hydrogen emerged from musical presuppositions and analogies. In the following
years, Max Planck investigated a complex harmonium just before he began studying black-
body radiation in 1894. Though Helmholtz assumed that “ natural ” tuning would win out
over the convention of equal temperament, Planck ’ s performance experiments with cho-
ruses showed otherwise. Chapter 17 describes the relation between Planck ’ s surprising
musical findings and the “ chorus ” of resonators he subsequently introduced to determine
the universal spectrum of black bodies.
Planck ’ s colleagues, such as Werner Heisenberg, often considered their musical experi-
ences to be formative of their relation to physics. As chapter 18 shows, even the unmusi-
cal Erwin Schr ö dinger found himself relying on musical analogies as he formulated his
wave mechanics. The continuing development of string theory reengages the mathematics
of vibration, though the reality of the strings rests on analogy built on analogy. The
Pythagorean theme of harmony remains potent in contemporary physics, though its har-
monies are more and more unhearable, ever more embedded in its mathematical formal-
ism. Even so, the quest for these harmonies preceded and succeeded the profound changes
in the “ new philosophy ” around the seventeenth century. Mathematics and physics,
ancient as well as modern, have been and remain closely linked to essentially musical
concepts, whose continuities may have been more significant than the changes generally
ascribed to the “ scientific revolution. ” To put it provocatively, that “ revolution ” may more
nearly have been a phase in the restoration and augmentation of the ancient project of
musicalizing the world than a change in the basic project of natural philosophy. I hope
that bringing forward these overarching musical themes will allow us to see science in
a new light, compared to standard accounts based on disruptive “ revolutions ” and “ para-
digm shifts. ”^5
I have not attempted anything like a complete history of the connections between music
and science but have chosen cases in which music led the way.^6 I have restricted myself
to what we now call physics and mathematics, noting throughout the actual terms used by
the actors themselves, terms generally quite different from ours.^7 About 1830, William
Whewell advocated the use of the terms “ scientist ” and “ physicist, ” but Michael Faraday
did not care for them and called himself simply a philosopher, as did those who preceded
him (sometimes qualifying their pursuit as “ natural philosophy ” ). Using and assessing the
terms and language of the historical actors is essential to approaching their meaning, which