PTOLEMY HARMONICS PDF

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He relied somewhat on the work of an earlier geographer, Marinos of Tyre , and on gazetteers of the Roman and ancient Persian Empire. As with the model of the Solar System in the Almagest, Ptolemy put all this information into a grand scheme. Following Marinos, he assigned coordinates to all the places and geographic features he knew, in a grid that spanned the globe. Latitude was measured from the equator , as it is today, but Ptolemy preferred [33] to express it as climata, the length of the longest day rather than degrees of arc : the length of the midsummer day increases from 12h to 24h as one goes from the equator to the polar circle.

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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. 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. 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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Ptolemy Harmonics

Institutes, academic libraries, public libraries, specialists, students, musicologists, classicists, philosophers, astronomers, historians of science. Equally influential was his treatise on harmonics, the ancient science which combined and brought to completion the study of philosophy and science. After discussing modulation, he expands his horizons by applying musical intervals to the human soul and celestial bodies, ultimately describing a cosmic harmony. The commentary offers a full exegesis of the text, loci paralleli, and citations of modern scholarly sources. Main Description Ptolemys comprehensive treatises on astronomy and geography were influential for nearly two millennia. 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.

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Ptolemy's intense diatonic scale

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.

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