Compendium of Music

Summary

The Compendium Musicae is Descartes’ first book. After meeting Isaac Beeckman, he conducted during the last two months of 1618 experiments on musical instruments (including resonance) and exchanged with his friend hypotheses about the nature of consonances and other problems concerning musical theory. The result is a brief treatise that Descartes offers to Beeckman on January 1, 1619, and that is copied, with two other contemporary pamphlets (one on hydrostatics and the other on falling bodies) in Beeckman's diary circa 1628. The Compendium was published shortly after Descartes’ death in Utrecht in 1650 from a manuscript submitted by an unidentified “disciple.” This edition served as the basis for subsequent editions. The original manuscript was lost but there are several copies prior to publication that served as the basis for current critical editions (see AT X 79–85 and Descartes 1987).

The structure of the work is similar to classical treatises of musical theory (Descartes mentions only Zarlino by name but indirectly refers to Salinas). Descartes defines the purpose of music and then sets out preliminary principles (Praenotanda) that he applies to the parameters of time and pitch, by treating consonances, scale, and dissonances. At the end he discusses, in a very short practical part, the manner of composing and the musical modes.

The purpose of musical theory is to identify the affections or properties of sound, as far as they may be known mathematically, which are capable of pleasing and of arousing the passions (Descartes thus resurrects two of the aims of classical rhetoric). These properties consist in differences in duration (rhythm and meter) and differences in pitch, which may be lower or higher (AT X 89). The qualitative properties of sound (e.g., timbre) are left to the physicist. The Praenotanda (AT X 91–92) form a system determining the measurable properties of the sound object from the requirements of the senses regarding proportionality. They clarify what is most pleasant from the search for understanding the object by the senses (which is done with the help of arithmetic proportions) and from the need for a certain variety: the pleasing object should not be too easy to understand, nor too difficult.