“Science describes things as they are; art, how they are felt, how one feels they are,” wrote Fernando Pessoa. The poet’s certainty was the same idea that fuelled debate and a profusion of philosophical treatises in the late sixteenth century, with its Platonic-Pythagorean belief in mathematics as the foundation of science and art, and the early seventeenth century, when people realized that not everything could be reduced to numbers – especially the things one felt.
A pioneer of this critical view was the musician Vincenzo Galilei (1520-1590), the father of Galileo Galilei, who before the scientific revolution had already noticed the limits of “mathematization,” which was capable of generating positive changes in the classification of some sciences, but was ineffectual in others. “Not only because the search for the nature of the objects of some sciences was being questioned, but because different forms of interaction between practical and theoretical knowledge and the knowledge of craftsmen happened in different ways,” says the historian Carla Bromberg, who is working with the various theoretical treatises of Vincenzo, most of them unpublished, in her research for her post-doctoral research, From numbers to sound: the transformation of the sixteenth century concept of music, as advocated by Vincenzo Galilei.
“He showed that music was a natural sound phenomenon, contradicting the tradition that was prevalent at the time that saw it as merely numbers and proportions,” she explains. “In his writings, the result of practical experimentation and mathematical observations, Vincenzo clarified just how out of step music theory and music practice were in his day and proposed ideas that became the fundamentals of acoustics, baroque music and the tonal system that lasted for more than 150 years,” observes the researcher. Although better known as the father of Galileo, Vincenzo influenced the natural philosophers who were his contemporaries and came after him, like Marin Mersenne, Simon Stevin and his own astronomer son.
If today it is a mere source of pleasure, since the Middle Ages music had been considered a science whose foundation was arithmetic; consequently its object was not the sound but the number. In universities it was only accepted that one theorized about the world of sound. Few of the authors of these treatises played music. “It was the clash between the forms of practical and technical knowledge with the theoreticians that showed the need for change and for method. Advocating ideas that contradicted authorities and the structures of Western thinking was something that Vincenzo was already doing before Galileo.”
In his musical treatises, the lute player and musical theoretician outlined an innovative investigative method. “Going against the trends of his time, Vincenzo advocated the supremacy of observation and experiment,” notes the researcher. Vincenzo did not hesitate to question traditional doctrines. “As no one had explained the problems in a way to satisfy the intellect, it was necessary to check and argue about the theoretical facts,” he wrote. He said that regardless of who the author might be, whether ancient of modern, it was necessary to challenge false allegations, because an idea should not be propagated merely because of the authority of its creator.
Vincenzo’s target was precisely those who followed Pythagorean concepts, such as Gioseffo Zarlino (1517-1590), chapel master of St. Mark’s Cathedral in Venice. Although he had been Galileo’s teacher for some time, Zarlino had a traditional interpretation of the mathematical nature of music and tried to make the old Pythagorean-Platonic framework legitimized in a textual tradition fit in with the “new sounds” coming from the excesses of polyphony. From his experiments, Galilei concluded that many of the reasons put forward theoretically did not exist in practice. Vincenzo also realized that many of the musical intervals denied by the system that was then in effect actually existed and could be represented mathematically.
According to the researcher, in trying out in practice variations in the behavior of bodies, in other words, of matter, and perceiving that this generated sound differences, Vincenzo saw that there were factors that mathematical sciences were unable to explain. It was this evidence of the incompatibility between the mathematical world with its abstract objects, and the physical world with its real objects that led Galilei to conclude that if the nature of the material studied, sound, was sensory, the evidence derived from experimentation was the best way to investigate it. The study of speculative music should not be favored over the study of sounds, the field of things “as one feels they are.”
However, just as his son would do, the father’s arguments upset the concepts that had been established for a very long time. Zarlino’s argument was based on the theory of integer ratios, which had been transmitted by the philosopher Sevério N. Boécio and was based on the Greeks. It was historically illustrated through the legend of the invention of consonance, attributed to Pythagoras and his monochord, an instrument supposedly comprised of a single string stretched between two fixed points. It was believed that the philosopher had investigated the relationship between the length of a vibrating string and the musical tone it produced. Pythagoras observed that by pressing on a point located at the 3/4 mark on the string, which was the equivalent of reducing it to 3/4 of its original length, and then playing it, a sound was heard that was a quarter above the tone emitted by the entire string. With 2/3rds of the original length of the string a fifth higher was heard and with half the length an eighth above was heard. Music, like the entire Universe, was mathematical.
For Vincenzo, however, numbers were not sonorous, but had to be applied to some sonorous body; in other words, numbers merely represented the sounds of the music. Mathematics began to instrumentalize music and not form its foundation. Therefore, music was not a perfect numeric system that existed in celestial realms, as Pythagoreans insisted, but comprised sounds emitted by bodies whose different compositions affected the auditory perception of given theoretical ratios.
With his lute, he showed that the pitch of a note could vary not only as a function of the length of a string or the tension in it, but also when the thickness or the material of which it was made was altered. According to the theory, the legitimization of musical intervals presupposed also that the intervals excluded from the system were not natural. However, for Galilei, one sound was as natural as any other: if it pleased the ear or not could not be explained by a numerical system, but by the particular and individual hearing itself. Mathematics had no power over the senses. Vincenzo released music from the domination of numbers when he showed that empirical reality did not necessarily match the ancient ratios that were thought to organize the Universe.
Galilei’s great act of daring was to work directly on bodies of sound, experimenting with sound using metal vessels and other objects that were of different sizes, widths and volumes, as well as strings made from a variety of materials, observing that sounds changed according to the behavior of each material. “Vincenzo thus showed for the first time the relevance of matter and its behavior,” states the researcher.
The science of acoustics
Through musical instruments, Vincenzo introduced the principles that would be studied in the future by the science of acoustics, developed by Joseph Saveur in the seventeenth century, notes Carla. By “denumbering” music, Vincenzo made a bold attack. “The theoreticians of the sixteenth century emphasized Pythagorean ratios because they formed part of a way of grasping the world. According to Pythagorean thinking, everything that existed was represented by numbers and their relationships by mathematical ratios,” the author reminds us. “By invalidating the concept of Pythagorean ratios in music, Galilei shook up the major order. But perhaps because he didn’t belong to any court, religious entity or university, his work did not achieve the impact it should have had.”
Vincenzo treated music as a physical and cultural phenomenon simultaneously. It was a human creation based on physical laws that governed the production of sound, as well as a sound phenomenon subject to certain cultural rules. “For him, the combination of sounds, described as consonance or dissonance, depended both on natural causes as well as on convention, which is what explained why the music that pleased the Italians did not have the same effect on other nations,” remembers the researcher. For many, these views directly influenced his son, Galileo.
“The father’s studies pointed to what would become acoustics and those of the son to mechanics. Both attacked pillars of Aristotelian wisdom, such as the mathematical foundation of music and the perfection of the heavenly world, and embraced another pillar, that of the relevance of the behavior of materials to the study of movement and mechanics,” in Carla’s analysis.
From numbers to sound (nº 2009/52252-8); Modality Post-doctoral studies grant; Coordinator Carla Bromberg – Cesima/PUC-SP; Investment R$ 144,869.89 (FAPESP)