 Mersenne’s own general hypothesis was that consonance was due to the coincidence of the vibrations of the air, which itself depended on certain exact ratios in the mechanical properties of the instrument, e.g., the length, tension and breadth of the strings. However, as consonance was judged by the ear rather than directly by reason, discrepancies were found. For example, experiments showed that the ear hears an octave when the tensions of the strings are in a ratio of 1 to 4.25, whereas the physico-mathematical, Pythagorean, hypothesis prescribed 1 to 4. So here one would have to find ways to correct, or “discipline” experience through reason, in a move that is quite typical of Mersenne’s epistemology (see Dear 1988).