This discipline seeks to understand aspects of music that are susceptible to reason

Can creativity be described in real time? Can beauty be joined with the truth? Mathematics respond: yes, mainly with the support of the tools of the mathematical theory of music (TMM), a discipline that seeks to understand those aspects of that art that are susceptible to reason, just as physics does it with natural phenomena.

This is explained by Emilio Esteban Lluis Puebla, researcher at the Faculty of Sciences of the National Autonomous University of Mexico (UNAM), who offered a brief panorama about these issues at a conference organized by the Institute of Mathematics of the Maximum House of Studies.

The specialist said that this field of study has its origin in Pythagoras, who addressed the relationship between mathematics and music. He was the first thinker who used the monocordium, an instrument that consists of a tensioned rope on a resonance box, which allowed him to analyze the musical intervals and the theory of harmony.

However, he added, from Pythagoras to the 80s of the last century, very little and not very sophisticated mathematics was on the music scene. It was until the first decade of the 21st century that TMM had a global boom.

For example, the mathematician and pianist Guerino Mazzola introduced the term TMM in 1980, to refer to a branch of musical theory that would use mathematical concepts and theorems instead of traditional musical theory, dominated by a mixture of philosophical, philological, psychological or cognitive perspectives.

The rise of the mathematical theory of music, the expert continued, “was driven by two factors: the progress of computer technology, which gave rise to sound synthesizers, as well as the development of software of musical annotation, designed to write, edit and reproduce scores. Also due to the failure of traditional approaches to solve fundamental problems in musical theory and musical execution.

“Mazzola (1947, Switzerland) is considered the world exponent of the TMM. Among his contributions, he introduced mathematical tools to analyze improvisation in jazz and algorithmic models to describe creativity in real time. It also applied algebraic geometry to study the relationships between chords and scales, allowing to visualize musical structures in higher dimensions.

“His work The moles of music: geometric logic of concepts, theory and interpretation (2002) is one of the most influential treaties in this discipline, with impact on research on artificial musical intelligence, algorithmic composition and computational musical theory. ”

Lluis Puebla explained that TMM consists of three fundamental elements: a precise language to define musical objects and relationships; mathematical models to describe harmonic, melodic, rhythmic, counterpoint processes, leading voices and musical execution; and experimentation with these theoretical models to validate and expand their applicability.

This discipline is based on various advanced branches of mathematics, such as categories theory, algebraic topology, group theory and graphics theory, which allow rigorously describing musical structures.

The scientist stated that the history of mathematics and music shows that these disciplines, although they differ in existential methodology, language and position, have an important creative interaction that has led to a synthesis of art and science that rewards the passionate already desperate efforts to gather beauty with the truthhe concluded.