‘The Harmonics of the Ancients compared with Today’s’: Appendix to Ptolemy’s Harmonics, 1682

The appendix which Wallis provided for his 1682 edition of Ptolemy’s Harmonics was his longest account of the mathematical theory of music. As discussed in the Introduction, ¹ it seems to have been intended to perform more than one function, illustrating not just the relationship of ancient musical theory to modern but also John Wallis’s technical mastery of the contents of the Harmonics and providing a forum for Wallis to publish his own ideas about modern musical theory. In the final sections he in fact re-worked, sometimes quite closely, material from his letters to Oldenburg of 18 years previously.