Acknowledgments

This textbook stands on the shoulders of centuries of inquiry conducted at the intersection of physics and music — an intersection that has been considered both illegitimate (by those who believe the disciplines have nothing to say to each other) and inevitable (by those who have actually spent time in both).

We owe an immense debt to Hermann von Helmholtz, whose 1863 masterwork On the Sensations of Tone remains one of the most rigorous and comprehensive investigations of the physical and perceptual foundations of music ever written. Helmholtz's insistence that the physics of sound and the psychology of musical perception must be studied together, not separately, established the intellectual program that this textbook continues.

To Jean-Baptiste Joseph Fourier, whose theorem that any periodic function can be decomposed into sinusoidal components now underlies virtually every technology for analyzing, recording, transmitting, and compressing sound. The elegance of Fourier's insight — that complexity is always a sum of simplicities — is one of the great gifts of mathematical physics.

To Jean-Philippe Rameau, whose Traité de l'harmonie (1722) first systematically grounded music theory in the physics of the overtone series, proposing that the major triad is not a cultural convention but a natural phenomenon. Rameau was wrong about several things, but his instinct that music theory needed a physical foundation was prescient.

To Arnold Schoenberg, who proved by creative experiment that the tonal system is not physical necessity but cultural construction — and thereby clarified the question of what in music IS physically grounded.

To the modern researchers in psychoacoustics and music cognition whose work informs Part VI of this book: Albert Bregman, whose work on auditory scene analysis revealed how the brain constructs musical objects; David Huron, whose ITPRA theory of musical expectation is the most complete psychological account of musical tension and release available; Diana Deutsch, whose decades of research on musical illusions and perception have mapped the gap between acoustic signal and musical experience; and Isabelle Peretz and Robert Zatorre, whose neuroimaging work has revealed what music does in the brain.

To the developers and maintainers of the open-source software communities that make computational music analysis possible: the librosa team, whose Python library for audio and music analysis has democratized spectrographic research; the scipy and numpy communities, without which Python could not do the mathematics this book requires; and the broader ecosystem of open-source scientific Python that has made computational science accessible to students everywhere.

To the physicists who have thought seriously about music: John R. Pierce, Juan G. Roederer, Neville H. Fletcher and Thomas D. Rossing, whose textbooks on the physics of musical instruments remain definitive references; and Max Mathews, who built the first computer music programs at Bell Labs and proved that the physics of sound could be synthesized from first principles in code.

Finally, to you, the reader. You have chosen to take seriously the possibility that two domains usually kept apart might illuminate each other. That choice is itself a form of intellectual courage. This book is for you.