Ptolemaic astronomy [after Ptolemy (Claudius Ptolemaeus) b. c.75 AD]

This is a geocentric (Earth-centered) system of astronomy, assuming the sun to be the center of the Solar system. The planets were assumed to move in paths based on perfect circles. 

Ptolemy's system was heavily indebted to Hipparchus (BC c.190 - c.120).

The system prevailed for approximately 14 centuries, during which time it became progressively "refined" and more and more complicated, in order to explain the actual, observed motions of the planets.

In actuality, the planets move in ellipses, not in circles (Kepler, 1571 - 1630). Even by Kepler, discoverer of the elliptical motion, circles were thought to be Divine, and to symbolize perfection. Only after Copernicus (1473 - 1543) and Galileo (1564 - 1642) did the heliocentric (Sun-centered) Solar system start to become accepted as the physical fact (contrary to the idealised teaching of the Church, at the time). 

In other words, the Ptolemaic model of the universe was idealised. It fitted the facts approximately well, but only up to a point. The same is true today, of temperament theory, which itself is not disconnected from the great "tradition" of "Pythagoreanism".[1]  

As part of the same thrust of work, and drawing on the Pythagorean tradition, Ptolemy developed a complex science of "harmonics", largely derived from previous thought, and especially with ideas connected with the Pythagorean tradition. "Harmonics" is a science of whole number ratios, and, basically, so is temperament theory. Both spring from the same philosophical soil, and have their roots in observations on vibrating strings and musical pitch. 

One scholar has described Ptolemy as a ‘number cruncher’,[2] because he went to such lengths to make the construction of the universe fit the principles of "harmonics" and whole number ratios, but this was not merely an exercise in mathematics or science. Ptolemy accepted Plato’s conception of the arithmetically proportioned soul, and that the effects of music on Man were due to the kinship between the "harmonics" of the soul, and the harmonic structure of musical phenomena.[3]

Ptolemy developed an extensive astrological correlation between the heavens, music, and the human soul.[4]  ‘Harmonics’ was for Ptolemy, not merely a quantitative science, but a manifestation of a predictable, divinely ordained order.[5] Knowledge of this ‘divine’ order he believed to be both subjective and theoretical and to be a function of nature that allows subjective perception of the divine order.[6]

‘The power of attunement is present in all things’, states Ptolemy, ‘but is revealed most fully through human souls and through the movements in the heavens’, and thus ‘The power of harmonia is a form of the cause corresponding to reason’.[7]