4 Introduction
Throughout his life, the great mathematician Leonhard Euler spent most of his free time
on music, to which he devoted his first book. Chapter 9 shows how he reformulated the
ordering of musical intervals, implying a mathematical basis for the greater “ sadness ” of
minor chords, compared to major. For this purpose, Euler devised a “ degree of agreeable-
ness ” that indexed musical intervals and chords. This work on numerical factorization and
ratios immediately preceded his subsequent interest in number theory. Having devised a
new kind of index, Euler was prepared to put forward indices that would address novel
issues like the K ö nigsberg bridge problem and the construction of polyhedra, basic con-
cepts of what we now call topology. Euler also applied musical ideas and analogies with
sound to the wave theory of light, as chapter 10 describes. He took the analogy with sound
so far as to postulate light “ overtones ” and “ undertones ” based on musical theories, though
undertones lacked any experimental justification. Euler ’ s later musical writings include
his reflections on “ ancient ” versus “ modern ” music through their use of different chords.
He also used music as the centerpiece in his popular account of science.
Building on the work of Euler, Thomas Young advanced the wave theory of sound and
light. Chapter 11 describes how Young found his way to music against the strictures of his
Quaker milieu. His newfound passions for music and dance informed his studies of sound
and languages. At many points, his understanding of sound influenced and shaped his
approach to light, including the decisive experiments that established its wave nature.
When Young turned to the decipherment of Egyptian hieroglyphics, he relied on sound
and phonology. His final suggestions about the transverse nature of light waves again
turned on the comparison with sound.
Those who followed Euler ’ s wave theory of light often reengaged its relation to sound.
The study of electricity and magnetism resonated with ongoing initiatives in light and
sound, reflecting also wider philosophical ideas about the unity of nature. Chapter 12
examines the intertwined studies of electricity and acoustics by Georg Christoph Lichten-
berg, Johann Ritter, and Ernst Chladni. The search to unify the forces of nature often relied
on analogies with sound, which in turn looked to electricity for new tools. In the aftermath
of Young ’ s work, waves became a newly attractive explanatory approach to the problems
of electricity. Building directly on Chladni ’ s sound figures, Hans Christian Ø rsted discov-
ered the synthesis of what he called “ electromagnetism. ” Ø rsted brought a new unity to
the two formerly separate forces of electricity and magnetism, advancing the unitive hopes
of Naturphilosophie, the German Romantic tradition of natural philosophy. This dialogue
between sound and electricity also affected Charles Wheatstone and Michael Faraday.
Chapter 13 shows how their unusual collaboration led Wheatstone to discover telegraphy
and Faraday to the intensive investigations of sound immediately preceding and preparing
his discovery of electromagnetic induction.
Chapter 14 considers how Hermann von Helmholtz ’ s studies of vision and hearing drew
on his deep interest in music and art. The dialogue between these arts and their respective
senses fed strongly into his investigations into the possible “ spaces ” of experience, which