Musical Sympathy and Occult Knowledge

‘Is Music a science? Does it have evident, certain principles?’ These were questions Mersenne had in mind when he became fascinated by instruments, tuning and temperaments. Mersenne prized music as an art reflective of mathematical perfection and divine order. Unfortunately, the twelve-note octave as played on organ and harpsichord keyboards was (and is) not consistent with that ideal. No matter how it is tuned, it is impossible for more than a few of the degrees of the scale to act as the bass for harmonies that are pure and mathematically correct. For Mersenne this was not simply a musical problem, but also a philosophical one that required debate and research. One solution to the tuning problem, shown here, was to design keyboards with more than twelve notes per octave. By adding extra notes the number of playable keys and harmonies would be increased. Another way, known as ¼ meantone temperament, is described a few pages earlier. This was achieved by tempering (or adjusting) the intervals of the twelve-note scale so that the most used keys would sound (and be) almost perfectly in tune, with the imperfections distributed amongst less used keys.

Author: Marin Mersenne
Title: Cogitata physico-mathematica [Physico-mathematical thoughts] (Paris, 1644)
Shelfmark: C.14.3

C.14.3