Music entered deeply into the making of modern science because it was already a central

element of ancient philosophy. Greek concepts of number and cosmos were the founda-

tions to which their successors looked, even when they turned toward new directions. 1 The

ancient Greek word mousik denoted all the activities of the Muses, vocal and instrumental

art as well as the arts of poetry and dance, which the followers of Pythagoras then con-

nected with their teaching that all is number , thereby also implying that all is music . This

fundamental connection between music and mathematics had fateful consequences. Plato

developed what Pythagoreans first named philosophy into a new kind of education that

unified the study of arithmetic, geometry, music, and astronomy. Expressing the conso-

nance of the primordial musical intervals, integers were separated from irrational magni-

tudes, setting arithmetic apart from geometry. Yet mathematical ratios shaped the physical

world, as expressed in the mythical story of Pythagoras visiting a smithy: music was the

meeting ground where the first experiments interrogated the mathematical underpinnings

of experience. We retrace these deep connections by recapitulating their historical sequence.

Born on the island of Samos in the mid-sixth century b.c . e. , Pythagoras himself remains

so shadowy a figure that everything said about him is controversial. Even by the fourth

century, the brotherhood who deified him had dispersed; modern historians no longer

accept the traditional view that they founded Greek mathematics. 2 A century later, a few

fragments remain from the writings of those who came to be called Pythagoreans: Philo-

laus, a contemporary of Socrates, and his student Archytas, whom Plato knew and admired. 3

Philolaus held that all things, indeed, that are known have number: for it is not possible

for anything to be thought of or known without this, underlining the primal status of

number as the inescapable criterion of intelligibility. For him, music takes its place at the

very center of the treatment of number and the cosmos. In Homer, harmonia has the literal

sense of fastening together (the word is used to describe the fashioning of Odysseus s raft)

or a covenant or agreement (such as the compromise Hector proposes to Achilles during

their combat). 4 In Philolaus, harmonia has both the general sense of locking together

like and unlike in the cosmos, a unification of things multiply mixed, as well as specifi-

cally meaning an octave ( sound example 1.1). He lists more complex musical intervals

1 Music and the Origins of Ancient Science