72 Chapter 4
(1577), “ The arithmetician sees numbers in themselves, the musician and the algebraist
indeed know numbers, but in their relation to something else. ”^52 His implication is that
musicians were essential companions on the road that led from arithmetic to algebra in
that they reached beyond numbers to the “ something else ” manifest through music. If so,
the struggle to “ hear ” the mathematical irrational was indeed consequential on many
levels. Mediating between the realms of mathematics and felt experience, music evoked
and justified new concepts of number.Figure 4.8
Claudio Monteverdi, La favola d ’ Orfeo (first performed 1607), Act II, measures 274 – 279 (from the edition of
Venice, 1615). The messenger is recounting Euridice ’ s dying words: “ and calling on you, Orfeo, Orfeo, after a
deep sigh expired in these arms. ” Artusi objected to the “ irrational ” diminished seventh between voice (B ᅈ ) and
continuo (C ᅊ ) at the word grave (indicated by arrows), expressing the depth of her sigh ( ♪ sound example 4.5).