PTOLEMY HARMONICS PDF

See all videos for this article Ptolemy, Latin in full Claudius Ptolemaeus, born c. In several fields his writings represent the culminating achievement of Greco-Roman science , particularly his geocentric Earth-centred model of the universe now known as the Ptolemaic system. Top Questions What is Ptolemy best known for? How did Ptolemy impact the world? While distorted, his work influenced Byzantine and Renaissance cartographers.

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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. Prima Europe tabula. In the second part of the Geography, he provided the necessary topographic lists, and captions for the maps. It seems likely that the topographical tables in books 2—7 are cumulative texts — texts which were altered and added to as new knowledge became available in the centuries after Ptolemy.

Maps based on scientific principles had been made since the time of Eratosthenes , in the 3rd century BC, but Ptolemy improved map projections. It is known from a speech by Eumenius that a world map, an orbis pictus, doubtless based on the Geography, was on display in a school in Augustodunum , Gaul in the 3rd century. An edition printed at Ulm in , including woodcut maps, was the first one printed north of the Alps.

One reason is that Ptolemy estimated the size of the Earth as too small: while Eratosthenes found stadia for a great circle degree on the globe, Ptolemy uses stadia in the Geography. It is highly probable that these were the same stadion, since Ptolemy switched from the former scale to the latter between the Syntaxis and the Geography, and severely readjusted longitude degrees accordingly.

See also Ancient Greek units of measurement and History of geodesy. Because Ptolemy derived many of his key latitudes from crude longest day values, his latitudes are erroneous on average by roughly a degree 2 degrees for Byzantium, 4 degrees for Carthage , though capable ancient astronomers knew their latitudes to more like a minute. He agreed Geography 1. When switching from stadia per degree to , he or Marinos expanded longitude differences between cities accordingly a point first realized by P.

It must be added that his original topographic list cannot be reconstructed: the long tables with numbers were transmitted to posterity through copies containing many scribal errors, and people have always been adding or improving the topographic data: this is a testimony to the persistent popularity of this influential work in the history of cartography.

That it did not quite attain the unrivaled status of the Almagest was, perhaps, because it did not cover some popular areas of the subject, particularly electional astrology interpreting astrological charts for a particular moment to determine the outcome of a course of action to be initiated at that time , and medical astrology , which were later adoptions. The great popularity that the Tetrabiblos did possess might be attributed to its nature as an exposition of the art of astrology, and as a compendium of astrological lore, rather than as a manual.

It speaks in general terms, avoiding illustrations and details of practice. Ptolemy was concerned to defend astrology by defining its limits, compiling astronomical data that he believed was reliable and dismissing practices such as considering the numerological significance of names that he believed to be without sound basis. It is, indeed, presented as the second part of the study of astronomy of which the Almagest was the first, concerned with the influences of the celestial bodies in the sublunary sphere.

Thus explanations of a sort are provided for the astrological effects of the planets , based upon their combined effects of heating, cooling, moistening, and drying. A collection of one hundred aphorisms about astrology called the Centiloquium , ascribed to Ptolemy, was widely reproduced and commented on by Arabic, Latin and Hebrew scholars, and often bound together in medieval manuscripts after the Tetrabiblos as a kind of summation.

It is now believed to be a much later pseudepigraphical composition. The identity and date of the actual author of the work, referred to now as Pseudo-Ptolemy , remains the subject of conjecture. Ptolemy wrote about how musical notes could be translated into mathematical equations and vice versa in Harmonics.

This is called Pythagorean tuning because it was first discovered by Pythagoras. However, Pythagoras believed that the mathematics of music should be based on the specific ratio of , whereas Ptolemy merely believed that it should just generally involve tetrachords and octaves.

He presented his own divisions of the tetrachord and the octave, which he derived with the help of a monochord. Main article: Optics Ptolemy His Optics is a work that survives only in a poor Arabic translation and in about twenty manuscripts of a Latin version of the Arabic, which was translated by Eugene of Palermo c.

In it, Ptolemy writes about properties of light , including reflection , refraction , and colour. The work is a significant part of the early history of optics [44] and influenced the more famous 11th-century Book of Optics by Alhazen Ibn al-Haytham. Ptolemy combined the mathematical, philosophical and physiological traditions. He held an extramission-intromission theory of vision: the rays or flux from the eye formed a cone, the vertex being within the eye, and the base defining the visual field.

Size and shape were determined by the visual angle subtended at the eye combined with perceived distance and orientation. This was one of the early statements of size-distance invariance as a cause of perceptual size and shape constancy, a view supported by the Stoics. He also divided illusions into those caused by physical or optical factors and those caused by judgmental factors.

He offered an obscure explanation of the sun or moon illusion the enlarged apparent size on the horizon based on the difficulty of looking upwards.

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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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Notable Features of the Ptolemaic System

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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Ptolemy's intense diatonic scale

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