Music and the Origins of Ancient Science 19
Greatest ” ), synthesized the observational data of Babylonian, Egyptian, and Greek observ-
ers over centuries and presented a theoretical model that predicted the motion of the planets
with an accuracy exceeding anything that had come before, which stood unchallenged for
a millennium. At the same time, Ptolemy ’ s Harmonics synthesized musical learning on a
scale comparable to his astronomical work. Andrew Barker has emphasized the scientific
accomplishment of this work, which bridges observational practice with theory in ways
comparable with Ptolemy ’ s Almagest. 34 Though the Almagest had been transmitted via the
Arabs and received in the West by the twelfth century, the Harmonics only reentered the
stream of Western music theory in the sixteenth century. Parts of this work were translated
then, though its extant corpus was fully available only in the early seventeenth century.
As we shall see, its reentry was consequential not just for the study of music.
Unlike his Almagest , Ptolemy ’ s Harmonics was not transmitted in its entirety. Its final
Book III is an intriguing torso that integrates certain astronomical topics, showing the
explicit connection between these matters in his mind. In particular, Ptolemy connects the
motions of the planets in his geocentric system with changes of musical modes, for which
we use the modern term “ modulation ” to translate his term metabol ē , whose primary con-
notations are both the transformations of metabolism (in which ingested foodstuffs are
digested and changed into living flesh) and its political sense of revolution , change of
regime. Ptolemy notes ways in which the “ proper motions ” of planets (moving closer or
farther from their center) parallel musical change of mode.^35 This reflects ancient practices,
especially the Athenian “ New Music ” of the late fifth century b.c.e. ; Ptolemy ’ s discussion
shows the astronomical correlates of musical modulation.^36 Though the surviving text of
his Harmonics breaks off at this point, enough survives to give a clear sense of the depth
and range of the correlations between music and astronomy in his work. This connection
will return in the controversies over heliocentric astronomy.
Plato ’ s “ fourfold way ” of philosophical preparation set out arithmetic, geometry, music,
and astronomy as higher studies to follow the initial “ threefold way ” of grammar, rhetoric,
and logic, the linguistic basis on which all discourse rests. His Republic proposed the first
utopia, the idealized “ no-place ” that, even if unrealizable in practice, could set a standard
and pattern to which to aspire. His advocacy of the education of women and his critique
of slavery remained controversial for millennia.
His radical educational proposals shaped the immediate future. Traditional Greek
paideia had consisted of memorizing Homer and learning rudimentary arithmetic; Plato
created “ liberal education, ” worthy of the free born ( liberi ), as opposed to the rote training
of slaves to perform their assigned tasks.^37 His vision everywhere haunts the modern uni-
versity, even when it turns against the liberal arts to prefer utilitarian vocational training.
Beginning with the Academy that Plato founded, his three- and fourfold ways became
standard as education of the elite. This pattern was transmitted to the Romans and, via
Boethius, to the West as the trivium and quadrivium ; the church then used this plan of
liberal education to form its clerics, gradually including rulers and nobility.