The mathematical study of music had a history stretching from ancient Greece to seventeenth-century France and Italy, and had left a correspondingly plentiful written account of itself. But certain parts of that account loomed very much larger on the seventeenth-century horizon than others: notably the classical texts which had been edited and published over the preceding 150 years, and the early seventeenth-century works of René Descartes, Marin Mersenne and Athanasius Kircher. The earlier history of mathematical theories of music was one of increasingly complex elaborations upon a roughly stable basic idea – though that is not to say that ancient Greek ideas about the subject were simple. An essential difference between the aristoxenian and pythagorean approaches to music theory was the roles which they assigned to sense and to reason, and the relationship which they supposed to exist between them.