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Ptolemy's Theory of Harmonics

Basic Astronomy of the Ptolemaic System

Islamic Reconstructions of the Ptolemaic System


Ptolemy's Theory of Harmonics

Claudius Ptolemy's Harmonics was one of the most sophisticated works of music theory to survive from the Hellenistic world. In it, Ptolemy related musical harmonies to the properties of mathematical proportions derived from the production of sounds themselves. Those harmonies he considered to be distributed in all aspects of the physical universe. In particular, they were there in the phenomena of the planets and the human soul.

Ptolemy argued that harmony was a kind of principle of activity, or form, reliant on the two highest senses, sight and hearing. Sight and hearing themselves generated two kinds of knowledge. Sight generated astronomy, since the heavenly bodies could be apprehended only through that sense. Hearing produced the discipline of harmonics. In each case, the point of the enterprise was to perceive and understand beauty. And as the most nearly divine of natural entities in their respective relams, the soul and the heavenly bodies manifested and appreciate beauty to unusual degrees. That, indeed, was one of the insights that made astrology credible. So astronomy and harmonics were twin sciences, and it should not be surprising to find complementary characteristics in them.

Ptolemy developed this argument into natural knowledge in a variety of ways. First, he imagined the musical scale extended along the zodiac, with an octave covering half of the ecliptic circle. So when two planets were in opposition, they formed an octave interval, and other aspects represented intervals correspondingly. He also advanced suggestions relating the motions of particular planets to changes in pitch, with lower pitches at rising and setting and higher at planets' moments of greatest altitude. Hints at a more detailed account of this correlation, based on a division of motions into those in "length," "depth," and "breadth," were to be supplemented by a chapter devoted to the topic, but the chapter was lost. And Ptolemy proposed that the sizes of the planetary spheres were subject to harmonic principles too. Finally, he related the astrological characteristics of the planets to their musical harmonies.

Ptolemy's harmonic theory of the heavens is thus probably irrecoverable today. It was irrecoverable, too, in Kepler's time. But Kepler became convinced that Ptolemy had envisaged at least a similar kind of argument to his own in the Harmonices Mundi - namely, that harmonic principles were manifested in music and the heavens because they reflected deeper archetypal elements common to both, and indeed to Creation itself.


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