Music and the Making of Modern Science

Hearing the Irrational 67

with the sides of another square built on that diagonal).^38 If indeed Aristoxenus built tone

and semitone on the diesis as an arbitrary unit, that would ignore the inherent incommen-

surability of tone and semitone or quarter tone, as discussed above. At the very least, by

abandoning the idealized fiction of a pure ratio underlying every note Aristoxenus was

able to bring forward the practical “ commensurability ” of every pitch sung or played on

real strings: because we can hear those intervals, he implies, they must de facto be

commensurable.

At the beginning of his book, Vicentino embraces Aristoxenus and “ experience as the

mistress of things, ” paradoxically outstripping the “ modern ” practice of music by reviving

the “ ancient, ” specifically through the retrieval of the lost enharmonic genus he considers

Figure 4.6

Young man playing a pair of auloi while a courtesan dances with castanets. Red-figured cup painted by Epiktetos,

ca. 500 b.c.e.