Music and Euclid's Algorithm

Benjamin Wardhaugh explains the connection between mathematics and music by way of Leibniz and Euclid in the September issue of Plus magazine: "A little while ago I was reading some letters written by the 17th century German mathematician Gottfried Leibniz to an obscure contemporary of his, Conrad Henfling. The letters were about music theory and the details of how to tune musical instruments. I was surprised to find that at one point Henfling started to use Euclid's algorithm to justify his musical reasoning. How useful could a mathematical technique from the third century BC be to a 17th-century musician? Very useful indeed, it turns out. Euclid's algorithm provides a way of dealing with equations of musical pitch, potentially helping musicians and instrument makers to tune musical instruments." Read on here.