The use of mechanical devices and numerical algorithms in the 18th century for the equal temperament of the musical scale
pp. 49-63
in: Gérard Assayag, Hans G. Feichtinger, José F. Rodrigues (eds), Mathematics and music, Berlin, Springer, 2002Abstract
An important subject in which music must reckon with mathematics is temperament of the musical scale. Let's briefly run through the terms of the problem so that any reader can grasp it. Every musical note has its own precise frequency; a musical instrument (especially one with a keyboard) can produce a finite set of discrete notes: what frequencies must an instrument maker choose so that the instrument can be both used and enjoyed by its player? The maker of the instrument runs into two incompatible facts.