I participated in June to the Mathematics and Computation in Music (MCM) 2019 conference, of which this post is a very short summary.
The conference took place in Madrid, shared between the Universidad Politécnica de Madrid (Technical University of Madrid) and the Conservatory of Madrid. It was wonderfully organized by Mariana Montiel, from Georgia State University, and Francisco (Paco) Gómez, from the Technical University of Madrid.
As the first talk of the conference, Moreno Andreatta and myself presented our joint work with Andrée Ehresmann (who unfortunately could not come): “Groupoids and Wreath Products of Musical Transformations: A Categorical Approach from poly-Klumpenhouwer Networks“. The slides can be accessed here: MCM2019_final_slides_popoff_andreatta_ehresmann.
Jason Yust, from Boston University, then presented his work on Fourier space and music theory/music analysis. This is an important and recurrent topic in mathematical music theory, with various contributors such as Jason, Dmitri Tymoczko, Emmanuel Amiot (who wrote a book about it recently). Note that we are considering here the Fourier transform of various symbolic structures, such as chords, and not the Fourier transform of audio signals.
Another recurrent topic is combinatorics on words in music, in which Thomas Noll is a main contributor. An entire issue of the Journal of Mathematics and Music has been devoted to this subject recently.
More specifically, Noll considers words on an alphabet of two letters, which is linked to the free group of rank 2. Substitutions of letters correspond to positive automorphisms of this free group, and allows one to progressively ‘fill’ a scale starting from the definition of the octave as a stacked fifth and fourth. Ultimately this is linked to Sturmian morphisms, Christoffel words, and even the special linear group , although I’m not familiar enough with the subject to give details here.
On the subject of rhythmic canons, Jeremy Kastine from Georgia State University, Atlanta/ Georgia Highlands College, Rome has presented original research in which he combines ideas from rhythmic canons and maximally even sets.
In essence, this amounts to creating a rhythmic canon almost as usual (i.e. one beat corresponds to one voice only) but in which the condition that every beat is covered by one voice is relaxed. Instead, we assume that the beats on which one voice is present form a maximally even set. Jeremy exposed different types of such tilings, namely regular and irregular maximally even tilings, and ways to enumerate them, at least partially. The question remains open whether the techniques and algorithms he introduced are sufficient to enumerate them in general, and it certainly opens new topics of research.
During the coffee breaks, various demos had been setup. Below is Moreno Andreatta and Corentin Guichaoua demonstrating a web-based visualization of a Tonnetz (developed by Corentin) which can be played in real-time on a MIDI keyboard.
Corentin has made the code available on GitLab for those interested.
Speaking of visualizations and demos, a large part of the conference was devoted to the question of reaching out to various audiences with mathematics and music, whether it is a general audience, mathematics students, or composers / students in composition. Brent Milam, from Georgia State University, gave a fantastic talk (‘A Collaborational Concert: Mathematics Club-Composition Seminar and their Interdisciplinary endeavor‘) in which he summarized his experience in a project he led, where music students were asked to compose pieces based on various mathematical music theory findings and results (for example, maximally even sets, tonnetzes, neo-Riemannian transformations, etc.). Although these students had been paired with mathematics students for help, this did not go smoothly, mainly because of communication issues related to mathematics and music, and Brent is hoping to build on this experience for the next semester. Emmanuel Amiot also talked about his experience in ‘Concerferences‘, i.e. a blend of a concert and a conference for general audiences and how to organize them.
In the afternoon, plenary talks took place in Madrid’s Conservatory. As a tradition in MCM conferences, this was followed each evening by a concert.
The first day, Gilles Baroin presented his latest music video on temperaments and their visualization in various spaces, from 1D to 4D.
Gilles has developed for many years now various systems for visualizing pitches and chords and their transformations, to the point that he practically lives in 4D space :) Don’t hesitate to check his YouTube channel !
The concert of the first evening was given by Moreno Andreatta, a ‘Math’n Pop‘ concert that he is used to perform. This included various songs built from math/music results such as Hamiltonian cycles in the Tonnetz, i.e. going smoothly through all 24 major and minor chords (check out this song from his concert for an example of three hamiltonian cycles).
Overall, this was a fantastic conference, with many new contributors in various domains (algebra, scale theory, canons, etc.) and we hope the next one in 2021 will be as good as this one.