Descartes visuel musique et philosophie
Descartes visuel musique et philosophie

The compendium of music, presages of the Cartesian method

During summer 2016, France Musique gave a series of articles dedicated to philosophy in music and how philosophers perceive music. In this article, we will see how the writing of that very first essay introduces the "method" that would lead Descartes in all of his following works.

Major figure of the philosophical thinking of the 17th century, René Descartes especially distinguished himself by his thoughts on the edification of a universal science or on metaphysics. His contribution to the musical subject is unfortunately very little highlighted. Yet, his first work that he wrote at the age of 22 deals with music: an abbreviated called Compendium musicae dedicated to his friend Isaac Beekman.

Mathematician, physicist and philosopher, Beeckman is not a good enough musician to answer some questions of a technical aspect whereas he takes a big interest in musical theory. That is why René Descartes dedicated to him his Compendium, a book of about 60 pages written in only two months. At first sight, it looks like a summary of the young Descartes's knowledge, split is six distinct sections. To help his writing, the philosopher leans on the traditional discourse on music in use at the time: a explanation of the discourse on music based on the number theory of Pythagoras. Yet, Descartes gradually digresses from that discourse without clearly offering an alternative, making this text quite ambivalent.

The Pythagorean number theory and its posterity

Descartes is a young soldier in 1618 and widely rests on what he knows and what he has been taught: a musical theory extensively inherited from the writings of Gioseffo Zarlino, an Italien theorist and composer of the Renaissance. Zarlino's works are greatly influenced by the Pythagorean system.

This system assures that everything is number and that every object can be translated to a number to become comprehensible. It thus gives to music an important place. This theory saw the day with a legend. According to it, Pythagoras would have claimed that the main intervals of the Greek musical system (octave, quintum and quartum) refer to the four first prime numbers: what is immaterial - the interval - exist through a number.

This number theory had a lot of followers during the Antiquity. Thanks to music, Pythagoras thought he could demonstrate the numeric relations working in nature. The music then becomes the most perfect incarnation of the universal harmony, by analogy with the one prevailing the universe. The study of musical proportions allows to visualize the harmony that exists in the cosmos and therefore, that study can become a science. But Aristotle and Aristoxenus (his disciple) quickly contested this theory after finding many incoherences, like the hasty analogy with the numbers existing in nature.

Through this system, the theoretical music allows to contemplate the laws of the universe and completely distinguishes itself from the practice that finds itself depreciated and reduced to aesthetics. A musical work's beauty is evaluated by the perfection of the arithmetical proportions.

During the Renaissance, Zarlino turns the harmony prevailing nature into a precept of musical writing, leaning on the number theory and giving it a second youth. Despite the shortcomings emphasized by Aristotle and his disciple Aristoxenus, the theory didn't collapse before the musician and theorist Vincenzo Galilei came along.

Galilei explains in his Dialogo della musica antiqua e moderna that all sounds are natural and therefore, there is no way to copy nature in their layout. In the same idea, the beauty of consonances is evaluated thanks to the auditive experience and not according to arithmetical connections. By discarding the number theory, the musician restores the experience of music as a feeling, an idea that Descartes would use at the beginning of his Compendium: "[Music's] aim is to please, and move within us varied passions". 

The Compendium, a fracture in the traditional discourse and the premises of the Cartesian method

The Compendium musicae doesn't clearly establishes itself as a bill on music aesthetics but initiates the thoughts of Descartes on the subject. The Compendium stands as an important fracture in the discourse on music running at the time. Descartes starts with Zarlino's works to explain the calculation of the different intervals. He explains that we can divide a lute's string in six parts and sorts the consonant intervals in a chart.

Tableau des intervalles de Descartes
Tableau des intervalles de Descartes

By ranking those intervals, and leaning on the Pythagorean single chord, Descartes follows the tradition. Nevertheless, the way he proceeds is new: he starts from simple facts, obvious points and gradually, by deduction, offers answers. All his reasoning falls into place mechanically, every step that has to be proven validated by the previous one. The novelty of this reasoning is to logically articulate the philosopher's knowledge and to strengthen the place of experience in his process. The musical theory thus does not need anymore the analogy Zarlino used so much.

But, if the thought of "driving one's spirit" is innovative, the work nevertheless shows some incoherences that are probably due to Descartes's lack of experience in the music field. For example, he recommends that the string should be divided in six parts whereas it would have been easier to demonstrate the importance of some consonances towards the others, like the one of the tertium to the quartum. And looking at his method, it shows he progresses by feel since his process assumes layouts in order to stay coherent. 

The fuse of a music aesthetics

The Compendium musicae can easily be seen like the sum of the young man's theoretical knowledge. The work starts with the following sentence: music's aim is to please and spark off varied passions. The pleasure requires a certain proportion of the object - of the sound - and this proportion must be arithmetical, not geometrical. This object must also be varied, in order to keep the listener's ear interested.

Therefore, the beauty of music depends both on its capacity to provoke varied emotions and its proportionality that flatters reason. These two affirmations are yet irreconcilable, and we see here a weakness of the young Cartesian thought.

The novelty of Descartes's musical aesthetics is that he puts the Men at the center of his reflexion. It is the Man that receives the object, the sound, and that welcomes it through his senses. The beauty of music can be evaluated especially according to its capacity to provoke emotions within a person.

The publication of the text for the philosopher's death in 1650 opened the way for that Compendium to be published as well, even if it was supposed to be only for Isaac Beekman's eyes. Jean-Philippe Rameau could therefore use it as a basic material to define a new music theory. As a matter of fact, he thought good to take for him the rationalist method of Descartes but quickly betrayed him when he claimed the beauty of music was the result of a physical event when the philosopher had completely dissociated music aesthetics and science. 

The Compendium Musicae in innovative on many levels: it introduces the method that would guide Descartes's reflexion in all of his following writings. It also offers the introduction of a new music aesthetics in which Men practice ad receive, and has to ability to evaluate the beauty of a music piece.

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