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The mathematics of music

Jônatas Manzolli creates computer programming models to produce a multisensory spectacle

At the Barcelona laboratory, Manzolli takes command of the computer to create sounds and images

Public domain imageAt the Barcelona laboratory, Manzolli takes command of the computer to create sounds and imagesPublic domain image

Brazilian composer and mathematician Jônatas Manzolli has spent much of his time immersed in activities at the Center for Autonomous Systems and Neuro-Robotics of Barcelona’s Pompeu Fabra University. Through the manipulation of computer keyboards, he creates an integrated  profusion of colors, shapes and sounds—a spectacle for the senses that covers the walls in images and fills the room with eight channels of audio.  But Manzolli is no neuroscientist or engineer; he does music and math. “For my students, I am someone who translates back-and-forth, like a pendulum,  between two dimensions,” explains Manzolli, a professor at the University of Campinas (Unicamp) Institute of the Arts, where he coordinated the Interdisciplinary Center for Sonic Communication (Nics).

In Barcelona, Manzolli developed the CromaCronos system (from croma for color and cronos signifying time or music) through which his multisensory compositions are created. Having resolved the technical aspects of his work through precise mathematical representations and algorithmic systems, “the creative part” has become Manzolli’s main focus. “I can program the computer and put together a sort of sound installation, or go up on the stage and interact with the machine in real time as a musical instrument,” Manzolli explains. He will do just that this year in a performance entitled Descobertas (Discoveries), “an interactive multimodal concert with the Unicamp Symphony Orchestra” during ceremonies commemorating the university’s 50th anniversary.

In his role as musician, Manzolli’s laboratory work encourages, in his words, “a contemporary approach to complex systems” (in this case, the mechanisms of the human brain). “Rather than doing graphic simulations through the computer, our actual surroundings become a simulator where we enter and appear,” he explains. Neuroscientists working in the laboratory use this system to understand, through images and sound, not only the impulses that the computer operator creates, but also those that we produce unconsciously, by breathing or through our skin’s electrical conductivity, for example.  Manzolli avails himself of these resources as he explores artistic possibilities. “The system,” he explains, “rests above an entire layer of mathematical representation which, when translated into images and the sounds that I play, responds to my stimuli, thereby initiating a dialogue.”

Colors and shapes emerge from the musician’s conscious and unconscious impulses...

Public domain imageColors and shapes emerge from the musician’s conscious and unconscious impulses…Public domain image

Circuits of the brain
Manzolli’s research at the institute, in Spain, with support from FAPESP and the National Council for Scientific and Technological Development (CNPq), also involves collaboration on a project that uses games and virtual reality to help stroke victims and others who suffer from brain injuries. “The system produces visual and sound stimuli and encourages patients to interact in virtual reality through corporeal representation,” explains Manzolli. “In this way, the patient’s damaged brain circuitry can be reconnected or rechanneled,” he adds. Among the project’s successes is a book that Manzolli is co-writing with Spanish neurologist Anna Mura and Swiss neuroscientist Paul Verschure, with whom he has worked since 1998.

Manzolli’s taste for music and math has a long history, at least since he began playing piano at age seven. When the time came to sit for his university entrance examinations, he chose mathematics as his course of study. Halfway through his studies at Unicamp and feeling the boredom of tedious, theoretical calculations, he was introduced to the work of Greek musician and architect Lannis Xenakis (1922-2001), who developed a unique system for composing his instrumental and electronic works. “For Xenakis,” says Manzolli, “music was a cloud of complex notes and textures, and therefore must be created according to stochastic models” (i.e., indeterminately, by means of random variables). With great enthusiasm, the young math student sat for the entrance examination and was admitted to the music program of the Institute of the Arts at Unicamp, which at the time allowed students to enroll simultaneously in two separate programs.

Manzolli chose to study composition and conducting and associated himself with professors who specialized in experimental electroacoustics and contemporary music. At the time, during the mid-1980s, high-quality computers were hard to find in Brazil.  Manzolli used an analogical synthesizer (“a dream,” he recalls) to create his works, and jokes that he produced “neck compositions” by attaching strips of 4-track magnetic recording tape to the nape of his neck and then edited and mixed the sounds.

...such as breathing and the electrical activity on the surface of his skin

Public domain image…such as breathing and the electrical activity on the surface of his skinPublic domain image

After graduating with a master’s degree in mathematics and a doctorate in musical composition, Manzolli returned to Unicamp as a professor in 1994 where he immediately joined Nics, which he sees as “the only reason everything I’m doing now is working out.”  Manzolli attributes the group’s creative ability to its interdisciplinary structure, which brings together students of various backgrounds, including music, engineering, mathematics, and dance (important to Manzolli’s work, in which the interface of gestures is used to compose music).

Contrary to what we might assume, the most conventional and popular use of the computer for music—composing scores—is just one of many sound-creating possibilities that the machine offers. The technology enables a musician to program at the very moment of execution. “I often say that the process of composition is always an improvisation,” Manzolli explains. “Since music is a phenomenon that occurs in time, there is always the aspect of the ‘here and now’ at play,” he adds. “With the computer, the musician can expand or contract this aspect as he wishes.”