Music and the Making of Modern Science

Music and the Making of Modern Science

Peter Pesic
Copyright Date: 2014
Published by: MIT Press
Pages: 360
https://www.jstor.org/stable/j.ctt9qf97s
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  • Book Info
    Music and the Making of Modern Science
    Book Description:

    In the natural science of ancient Greece, music formed the meeting place between numbers and perception; for the next two millennia, Pesic tells us inMusic and the Making of Modern Science, "liberal education" connected music with arithmetic, geometry, and astronomy within a fourfold study, the quadrivium. Peter Pesic argues provocatively that music has had a formative effect on the development of modern science -- that music has been not just a charming accompaniment to thought but a conceptual force in its own right. Pesic explores a series of episodes in which music influenced science, moments in which prior developments in music arguably affected subsequent aspects of natural science. He describes encounters between harmony and fifteenth-century cosmological controversies, between musical initiatives and irrational numbers, between vibrating bodies and the emergent electromagnetism. He offers lively accounts of how Newton applied the musical scale to define the colors in the spectrum; how Euler and others applied musical ideas to develop the wave theory of light; and how a harmonium prepared Max Planck to find a quantum theory that reengaged the mathematics of vibration. Taken together, these cases document the peculiar power of music -- its autonomous force as a stream of experience, capable of stimulating insights different from those mediated by the verbal and the visual. An innovative e-book edition available for iOS devices will allow sound examples to be played by a touch and shows the score in a moving line.

    eISBN: 978-0-262-32438-0
    Subjects: Music, History of Science & Technology

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-viii)
  3. Introduction
    (pp. 1-8)

    Alfred North Whitehead once observed that omitting the role of mathematics in the story of modern science would be like performingHamletwhile “cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming—and a little mad.”¹ If in the story of science mathematics takes the part of Ophelia, music might be compared with Horatio, Hamlet’s friend and companion who helps investigate the ghost, discusses what may lie beyond their philosophies, sings the sweet prince to his rest, and tells his story.

    This book will examine some...

  4. 1 Music and the Origins of Ancient Science
    (pp. 9-20)

    Music entered deeply into the making of modern science because it was already a central element of ancient philosophy. Greek concepts of number and cosmos were the foundations to which their successors looked, even when they turned toward new directions.¹ The ancient Greek wordmousikēdenoted all the activities of the Muses, vocal and instrumental art as well as the arts of poetry and dance, which the followers of Pythagoras then connected with their teaching thatall is number, thereby also implying that all ismusic. This fundamental connection between music and mathematics had fateful consequences. Plato developed what Pythagoreans...

  5. 2 The Dream of Oresme
    (pp. 21-34)

    For two centuries after he wrote it, Boethius’s treatise on music was unavailable, seemingly lost in the “dark ages.” Beginning in the ninth century, manuscript copies began appearing in ever-increasing numbers; Boethius became the principal source of music theory (and of arithmetic) long before Latin translations made Aristotle’s writings directly accessible. In this intermediate period during which Aristotelian science remained relatively unknown, ancient musical theory continued to be taught.¹ In that sense, musical science maintained a continuity that other branches of natural philosophy generally had lost, in the absence of available ancient sources. After the renaissance of the twelfth century,...

  6. 3 Moving the Immovable
    (pp. 35-54)

    In the century after Oresme’s imaginary debate between Arithmetic and Geometry, their sisters Music and Astronomy returned to the question whether a seemingly immovable center could somehow move. That center could be the Earth or the mode of a musical composition, both generally assumed to be unchanging. Because each celestial sphere was associated with a mode, a change of mode suggests motion between spheres. As innovative musical compositions used unprecedented changes of mode, the immovable musical center began to move. In the following decades, the new astronomy put forward the theory of a moving Earth. Other musical considerations moved Vincenzo...

  7. 4 Hearing the Irrational
    (pp. 55-72)

    A century after the immovable center began to move, another seeming impossibility began to seem necessary: a new concept of number that encompassed both integers and irrational quantities. The transformation of the ancient concept of number underlies modern mathematics, and hence also much of modern science. Though a number of social, economic, cryptographic, and even legal perspectives have shed light on this mysterious shift, music (both theoretical and practical) helps illuminate the hesitation about the nascent concept of irrational number in the work of three close contemporaries: Michael Stifel, Girolamo Cardano, and Nicola Vicentino. All three worked at the frontier...

  8. 5 Kepler and the Song of the Earth
    (pp. 73-88)

    For Johannes Kepler, music was crucial to the emergence of a new astronomy. Kepler’sHarmonices mundi libri V(Harmony of the World, 1619) culminates in his so-called third law of planetary motion: the square of the orbital period of any planet is proportional to the cube of its mean distance from the sun.¹ This surprising connection emerged from Kepler’s search for harmonic relations between planetary data and became a touchstone for Newtonian celestial mechanics. As important as this result is, Kepler presents it without fanfare, certainly not as the “law” it was later called. For him, it was only a...

  9. 6 Descartes’s Musical Apprenticeship
    (pp. 89-102)

    René Descartes pioneered the “new philosophy” through his achievements in mathematics, natural science, and metaphysics, yet his work in music has remained relatively unknown. He himself was diffident about his musical knowledge and accomplishments, though he first found his voice addressing musical questions. His work on music has many connections with his new physics and his view of the cosmos as a fluid continuum, whose vortices and motions explain light and celestial mechanics.

    At age twenty-one, Descartes wrote his earliest essay,Compendium musicae(Compendium of Music, 1618), when he had just begun his career as a gentleman-soldier, supporting the Netherlands...

  10. 7 Mersenne’s Universal Harmony
    (pp. 103-120)

    Advances in mathematics and natural philosophy owe a great deal to conversation, whether in person or via correspondence, contrary to the misapprehension that such work emerges in isolation. Descartes’s interest in music could have remained undeveloped, had not his dialogue with Beeckman initially stimulated him to assemble his thoughts on the subject. During the critical years from 1629 to 1634 and thereafter, Mersenne’s questioning sustained Descartes’s continuing response.

    So far, Mersenne himself has remained in the background, as if he were merely a sounding board for Descartes. To some extent, this reflects the disparity in what remains of their correspondence:...

  11. 8 Newton and the Mystery of the Major Sixth
    (pp. 121-132)

    Though Isaac Newton considered poetry “ingenious nonsense,” music had a significant if limited place in his intellectual world.¹ His youthful manuscripts demonstrate the scope of his knowledge and interest. Later, at a critical point in his optical writings, he relied on a musical analogy to compare the seven notes of the diatonic scale and the seven colors he likewise attributed to the spectrum. A close examination of his use of this analogy discloses its power and implicit limitations. Newton’s case may be read as a cautionary tale about the way musical analogies can open possibilities but leave important matters provocatively...

  12. 9 Euler: The Mathematics of Musical Sadness
    (pp. 133-150)

    Among Continental scholars who advanced and reconsidered Newtonian physics, Leon-hard Euler was probably the greatest and surely the most prolific. Of his thirty thousand published pages, only a few hundred are devoted to music, but these have a special significance among his works. Music was one of the first topics he addressed at length, and he returned to it several times throughout his life. Moreover, musical questions led Euler to consider new mathematical topics and devise new approaches that then characterized several of his most important initiatives in mathematics and physics. Indeed, Euler’s individual mathematical discoveries, great as they are,...

  13. 10 Euler: From Sound to Light
    (pp. 151-160)

    Besides his enormous achievements in mathematics, Euler was deeply involved in many areas of physics. His early work on music had a direct bearing on his study of sound, which in due course contributed to his studies of the mechanics of continuous bodies, the transmitters of sound vibrations. These important advances in continuum and fluid mechanics also moved Euler to advocate a wave theory of light, as against Newton’s emission (particle) theory. Throughout, Euler used the examples of sound and music as exemplars for a new understanding of light and color.

    In the century after his seminal work on optics,...

  14. 11 Young’s Musical Optics
    (pp. 161-180)

    The crucial evidence for the wave theory of light was the work of an amazingly multitalented individual, who, though surely unique in his constellation of abilities, manifests the fruitful breadth of scope so important in the advances made by other contemporary natural philosophers. Thomas Young used studies of sound and music to advance the theory of wave motion, especially the concept of interference, which he learned from sound and then applied to light. Sir John Herschel singled out Young’s insight into sound interference as “the key to all the more abstruse and puzzling properties of light, which would alone have...

  15. 12 Electric Sounds
    (pp. 181-194)

    Thomas Young’s translation of sound into light provided a crucial example for parallel work connecting sound with electricity and magnetism that emerged in the decades just before and after him. The early connection that Georg Christoph Lichtenberg made between electricity and its visual trace led directly to Ernst Chladni’s vibrating plates, which gave visual form to sound. Félix Savart continued the exploration of the electricity–sound connection, as did Hans Christian Ørsted and Johann Wilhelm Ritter in their own ways. In all these cases, sound represented a parallel venue for ideas and experimental approaches that contributed to the Biot–Savart...

  16. 13 Hearing the Field
    (pp. 195-216)

    In the wake of Ørsted’s discovery, the entwined stories of Charles Wheatstone and Michael Faraday likewise interwove sound and electromagnetism. Starting out as an apprentice bookbinder, Faraday altogether lacked mathematical education; he said he could not understand a single equation. From his earliest work as a laboratory assistant to Humphrey Davy, Faraday thought in terms of experiments, in the felt reality of observation and manipulation, his visual turn of mind manifested in the constant sketches he put in his diaries, essential adjuncts to his hands-on experiences. His cultural awareness was far more sonic; he never mentions paintings or the visual...

  17. 14 Helmholtz and the Sirens
    (pp. 217-230)

    In the decades after 1850, Hermann von Helmholtz undertook extensive investigations into the nature of vision and hearing that rested on his deep interest in music and visual art. His unfolding conception of the “manifolds” or “spaces” of sensory experience radically reconfigured and extended Newton’s connection between the musical scale and visual perception via Young’s theory of color vision. In the process, Helmholtz’s studies of hearing and seeing led him to compare them as differently structured geometric manifolds.

    Helmholtz’s life trajectory, spanning activity and mastery in many fields, was legendary in his own time. Though deeply interested in physics from...

  18. 15 Riemann and the Sound of Space
    (pp. 231-244)

    Already in 1862, in the midst of his detailed investigations of vision and hearing, Helmholtz became interested in the more general question of the problem of space itself.¹ At first, he was unaware of the seminal work done decades before by Carl Friedrich Gauss and Bernhard Riemann. Beginning with practical problems in geodesy that originated partly in his work surveying the duchy of Brunswick, in 1827 Gauss had formulated a mathematical criterion that calculated the degree of curvature of a two-dimensional surface (itsintrinsic or Gaussian curvature) only from surveying data collected within that surface.² Gauss proved the “remarkable theorem”...

  19. 16 Tuning the Atoms
    (pp. 245-254)

    By the end of the nineteenth century, the Pythagorean quest might have seemed played out. With Newtonian and Maxwellian physics securely in place, the metaphorical language of harmony, not to mention the details of music theory, might appear to be only a historical vestige, a transitional scaffolding that by then could be left behind. But facing the puzzles and paradoxes of the nature of matter first raised by the study of spectra, physicists again resorted to the precise kinds of numerological-musical theorizing that had many precedents in the Pythagorean episodes discussed above. At such moments of trial and disorientation, it...

  20. 17 Planck’s Cosmic Harmonium
    (pp. 255-270)

    Though Balmer and Rayleigh did not comment on the disappearance of music as part of the foundations of their work, other scientists indicated awareness and even intentionality about the process that Husserl summarized by saying that “sedimentation is always somehow forgetfulness.”¹ In part, this reflected a widespread decision of scientists to reach past the “all-too-human,” including music and sensation in general. Thus, in 1909 Max Planck argued that

    the characteristic feature of the actual development of the system of theoretical physics is an ever extending emancipation from the anthropomorphic elements, which has for its object the most complete separation possible...

  21. 18 Unheard Harmonies
    (pp. 271-284)

    Many of the physicists in the generation after Planck continued to be enthusiasticKulturträger, devoted especially to music. Einstein was famously loyal to his violin and to Mozart, yet wrote that “music does not influence research work, but both are nourished by the same sort of longing, and they complement each other in the satisfaction they offer.”¹ Indeed, there is no evidence of direct involvement of music in his work such as we have considered earlier in this book. This was not because music was insignificant for him as an intellectual or a scientist; as his sister noted,

    music served...

  22. Notes
    (pp. 285-310)
  23. References
    (pp. 311-334)
  24. Sources and Illustration Credits
    (pp. 335-336)
  25. Acknowledgments
    (pp. 337-338)
  26. Index
    (pp. 339-348)