Music and the Making of Modern Science

Music and the Origins of Ancient Science 13

the great Alexandrian astronomer and music theorist Claudius Ptolemy (second century

c.e .), who rejects the evidence given by reed pipes and flutes “ or weights suspended from

strings, ” as well as by “ spheres or discs of unequal weight, ” and never mentions hammers,

judging instead that the monochord (presumably at constant tension) “ will show us the

ratios of the concords more accurately and readily. ”^11 Following Ptolemy, we may specu-

late that the smithy story dramatized original findings with strings. No one may have

thought to check whether hammers really behaved that way because it all seemed reason-

able: how could hammers not obey the proportions already established for strings

and pipes?

Here emerges another recurrent peril of experiment: taking a certain pattern, observed

in one context, to dictate what “ must ” happen in another, seemingly analogous situation.

None of these problems figured in Pythagorean lore, which presented the story as a

miracle; number triumphs even in a smithy. The real wonder may be that numerical ratios

can be clear for a simple string, however complex elsewhere. This underlying thread

emerges more clearly if we return from Boethius ’ s late Roman summary (written almost

a thousand years after the earliest relevant texts) to consider what survives of the earliest

Greek evidence.

The Pythagoreans called pythmenes ( “ base ” or “ foundation ” ) two, three, and four the

“ first numbers ” because they “ produce the ratios of the concords, ” the primal conso-

nances of octave, fifth, and fourth.^12 One, never considered a “ number ” in Greek math-

ematics, is both even and odd, the primal monad ( monos , “ solitary, ” “ unique ” ) out of

Figure 1.2

A monochord from John Tyndall, Sound (1871).