The Fifth Hammer

The Fifth Hammer

Pythagoras and the Disharmony of the World

By Daniel Heller-Roazen

How the ordering of the sensible world continues to suggest a reality that no notes or letters can fully transcribe.

Distributed for Zone Books

Hardcover $27.95 T £22.50





How the ordering of the sensible world continues to suggest a reality that no notes or letters can fully transcribe.

An ancient tradition holds that Pythagoras discovered the secrets of harmony within a forge when he came across five men hammering with five hammers, producing a wondrous sound. Four of the five hammers stood in a marvelous set of proportions, harmonizing; but there was also a fifth hammer. Pythagoras saw and heard it, but he could not measure it; nor could he understand its discordant sound. Pythagoras therefore discarded it. What was this hammer, such that Pythagoras chose so decidedly to reject it?Since antiquity, “harmony” has been a name for more than a theory of musical sounds; it has offered a paradigm for the scientific understanding of the natural world. Nature, through harmony, has been transcribed in the ideal signs of mathematics. But, time and again, the transcription has run up against one fundamental limit: something in nature resists being written down, transcribed in a stable set of ideal elements. A fifth hammer, obstinately, continues to sound. In eight chapters, linked together as are the tones of a single scale, The Fifth Hammer explores the sounds and echoes of that troubling percussion as they make themselves felt on the most varied of attempts to understand and represent the natural world. From music to metaphysics, aesthetics to astronomy, and from Plato and Boethius to Kepler, Leibniz, and Kant, this book explores the ways in which the ordering of the sensible world has continued to suggest a reality that no notes or letters can fully transcribe.


$27.95 T | £22.50 ISBN: 9781935408161 192 pp. | 6 in x 9 in 5 b&w illus.


  • Heller-Roazen brings remarkable gifts and skills to his inquiry. Formidably learned and versed in many languages, he has also steeped himself in the original texts and in the manifold and difficult interpretative directions that have struggled with this archetypal narrative....I thoroughly admired Heller-Roazen's thoughtful and beautiful writing in The Fifth Hammer.


  • This tightly reasoned book rewards close study, and will be of interest to astronomers, mathematicians, and students of musical history.

    The Sun News


  • The Fifth Hammer is a dauntingly learned, conceptually demanding, exceedingly complex, and—at the same time—gripping book. Opening with a vivid account of Pythagoras's discovery of harmony, Heller-Roazen burrows ever deeper into the haunting disturbance of the incommensurable, a disturbance that called forth some of the most remarkable efforts of mind in the history of the human race. 'It is my pleasure,' Heller-Roazen quotes Kepler, exalting in his own musical account of the universe, 'to yield to the inspired frenzy.' The fortunate readers of The Fifth Hammer will experience something of the same frenzy.

    Stephen Greenblatt

    Cogan University Professor of the Humanities, Harvard University