Ptolemys comprehensive treatises on astronomy and geography were influential for nearly two millennia. Equally influential was his treatise on harmonics, the ancient science which combined and brought to completion the study of philosophy and science. This volume offers a comprehensive English translation and commentary of Ptolemys Harmonics. The treatise begins with Ptolemys study of pitches and intervals, for which he extracts both an idealized musical scale and a new acoustical tool. After discussing modulation, he expands his horizons by applying musical intervals to the human soul and celestial bodies, ultimately describing a cosmic harmony. The English translation faithfully reproduces Ptolemys style and includes all the charts surviving in the manuscript tradition. The commentary offers a full exegesis of the text, loci paralleli, and citations of modern scholarly sources.


It is the fortunate modern who dusts off this classic introduction to harmonics, for harmonics is a fascinating science that germinated among our stone age ancestors, took root in ancient Egypt and Mesopotamia, and blossomed here during the Greco-Roman epoch with Ptolemy as its greatest proponent. Far from abandoned today in anything but name, harmonics has now divided and reproduced itself amidst a very large array of scientists ranging from astro-physicists examining our universe, all billions of light years of it, to geneticists examining a phenomenon as microscopic as the nuclear structure of human DNA. It is the study of the harmony that can be found in mathematics, music, the human soul, and the cosmos which contains it all.

In a word or two, harmonics is the science of cosmic and psychic harmony. It starts with numbers and the relationship between numbers (mathematics). When applied to a taut string, such numerical relationships produce musical sounds, and these mathematical-musical relationships can be felt within ourselves. Certain musical sounds make us feel certain ways, and so music and our souls are harmonically related. Similarly, as the planets circle the heavens they stand in similar mathematical-musical proportions. Understanding all this, attempting to reduce it to a mathematical description, that is the domain of harmonics. Even more so than their widely heralded gifts to rational civilization—philosophy, tragedy, and politics—harmonics was ancient Greece’s greatest attempt at rationalizing our existence.

And yet, harmonics was also ancient Greece’s most beautifully proportioned and well-crafted creation, as intellectually stimulating to the mind as then ewly completed Parthenon must have been to the eye. No Greek science was ever more exacting, but none of their arts was ever more ambitious. Harmonics was ancient Greece’s most profound, comprehensive logos, for it stood on the shoulders of philosophy and mathematics and physics to tune in to the cosmic harmonies of the celestial spheres, and it organized and analyzed human habit and ethics and probed the psychic realms of the human soul.

I will tell you from the outset that the pages of this volume will hardly seem to hum any divinely inspired music as you page through them. Much of the text is mathematical proportion and geometrical proofs, and just when the author was about to detail the relationships between mathematical-musical proportion, the human soul, and the heavens, he… well, we cannot be certain, but Byzantine rumor has it that he died. Nonetheless, what the following pages do offer is the finest presentation of this cumulative science one of the most influential scientists the Western world has ever known was able to pen some indeterminate interval before his death a mere 1850 years ago.

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