About

Mathemusical Conversations: mathematics and computation in performance and composition is an international workshop jointly hosted by the Yong Siew Toh Conservatory of Music and the Institute for Mathematical Sciences, organised in collaboration with the Centre for Digital Music, Queen Mary University of London and theSciences and Technologies for Music and Sound Research Lab, Institut de Recherche et Coordination Acoustique/Musique, and in partnership with Raffles Institution.

Mathemusical Conversations celebrates the understanding of the essence of music through mathematics, with a special focus on performance and composition.

Ancient philosophers such as Pythagoras, Leibniz, and Diderot have long drawn profound connections between mathematics and music. In the liberal arts education of medieval universities, music was considered one of the quadrivium—four mathematical science subjects taught after the foundational trivium—alongside arithmetic, geometry, and astronomy. Today, the connections between mathematics and music have renewed relevance. The rise of computing devices and the ensuing digitization of music has led to new ways to represent, create and perform music, to study and understand it, and to make scientific discoveries as to how music is made and why. At the core of this digital music revolution are mathematical and computational techniques that drive scientific advances.

Many mathematicians and scientists are also fine musicians. For example, the young geometer Donald Coxeter composed music and wrote on the parallels between composition and mathematical proof; Albert Einstein was a talented and enthusiastic violinist. At the Massachusetts Institute of Technology, 60% of incoming freshmen declare advanced proficiency in music (usually performance), and 25% declare proficiency in other performing arts. Conversely, a number of prominent musical figures have publicly acknowledged their passion for mathematics, including the popular American classical composer Paul Schoenfield, who is a keen mathematician.

Almost every subfield of mathematics—including number theory, algebraic geometry, topology, geometric analysis, probability, statistics and mathematical physics—as well as every modeling technique—including optimization, stochastic systems, game theory, and network analysis—has contributed to these advances in digital music research. Every step of the music process, from composition (including improvisation, a form of real-time composition) to performance, from conceptualization to perception and cognition, can be modeled and studied using mathematical and computational means.

A landmark event in 1999, the Diderot Forum on Mathematics and Music organized by Assayag and colleagues spanned three countries (the cities of Paris, Lisbon, and Vienna) and led to a seminal book on the subject with an opening quote by Diderot: "c'est par les nombres et non par les sens qu'il faut estimer la sublimité de la musique" (It is through numbers, rather than through the senses, that music's sublimeness can be measured.) Likewise, the Mathemusical Conversations workshop celebrates, and stimulates debate about, the understanding and creating of music through mathematics.

It is with great enthusiasm and excitement, and not a little trepidation, that we accepted the honor of handpicking and inviting some of the world’s foremost thinkers and researchers on mathematics and music for the Mathemusical Conversations workshop. This would not have been possible without generous funding from the National University of Singapore (NUS) through the Institute for Mathematical Sciences and the Yong Siew Toh Conservatory of Music (YSTCM). Having the event hosted at YSTCM granted us access to internationally renowned musicians and visiting artists in the curation of the juxtaposing concerts, making this a truly integrated event from both the mathematical and musical perspectives.

The workshop's six thematic sessions and five concerts feature world-renowned speakers and performers, and are designed to appeal to the mathematically and musically curious. The lecture-conversations focus on mathemusical engagement, mathemusical creativity, canons, shaping performance, educating the mathemusical, and geometries. The concerts celebrate Paul Schoenfield’s music, human and machine intelligence, the prevalence of base 12 in music collections, musical canons, and musical creativity, and range in style from Classical to popular and jazz. The lecture-conversations will be published in a post-proceedings book to serve as a reference for the state of the art in mathematics and music thinking, and a foundation both for understanding human creativity and for enabling future music technologies.

It is especially fortuitous that the workshop coincides with NUS’ 110th anniversary, and Singapore’s 50th anniversary celebrations. We hope that you enjoy the programme as much as we did putting it together.

Prof Elaine Chew

Professor of Digital Media

Queen Mary University of London

Prof Gérard Assayag

Sciences and Technologies of Music and Sound Laboratory

Institut de Recherche et Coordination Acoustique/Musique, Centre National de la Recherche Scientifique, Université Pierre et Marie Curie