ABSTRACT

The three letters presented here were addressed to Henry Oldenburg, the secretary of the Royal Society, during May 1664. They were prompted by a lost letter from Oldenburg of 4 May, reporting on the letter and personal appearance of John Birchensha received by the Royal Society during April, and by a second lost letter from Oldenburg informing Wallis that the first two letters presented here had been read to the society on 18 May. 1 The content of Wallis’s letters, and in particular his evasiveness about his dependence on earlier writings, are discussed in the Introduction (see pp. 2–8 above). The second letter, one of Wallis’s most substantial discussions of the theory of music, should be read in part as his response to the writings of his modern predecessors, acquaintance with which he would acknowledge in a postscript and in the third letter. At the same time, these three letters set out an agenda for the mathematical study of music that was distinctly Wallis’s own. As Wallis’s earliest surviving discussion of music theory and an important source for ‘The Harmonics of the Ancients compared with Today’s’ (Chapter 3 below), they therefore possess considerable interest.