PROGRAMME
BOOK OF ABSTRACTS
The study of the relationship between music and mathematics has a thousand-year-long history which predates Pythagoras. Mathematics and music share a common basis of language and creativity. From the theory of tuning systems and temperament to physical acoustics, from harmonic analysis to spectrograms, from the structures of rhythms and pulses to the continuous stretching of the laws of harmony and the exploration of the musical forms carried out by contemporary composers, all elements of music lead to an immediate connection to mathematics. Established and recent research has witnessed the use of set theory to describe how musical objects are related and organised, the use of group theory in the context of transformational analysis of tonal and atonal compositions, the application of Grassmannians to the study of temperaments, and the investigation of category theory, topology and differential geometry to provide a basis of music theory.
The Institute of Mathematics and its Applications is glad to announce the launch of the first IMA conference on “Mathematics in Music”, to take place on 13-15 July 2022 at the Royal College of Music, London. The conference focusses onto the exploration of the connections between mathematics and music, in particular current developments of music theory, music performance, music perception and music technology based on or inspired by mathematical applications and concepts, including (but not limited to) category theory, group theory, topology, differential geometry, combinatorics, analysis, acoustic theory, as well as artificial intelligence, deep learning, language processing and coding.
The conference is aimed at mathematical researchers working at the frontier between mathematics or computation with music theory, musicology, music performance, sound engineering and composition, as well as at musicologists or computational musicologists, performers and composers using quantitative tools and formal methods from mathematics in their investigation and professional practice of music.
We are very keen that student researchers are a core part of this event and would very much like to encourage anyone studying music and mathematics to submit an abstract to join us for this conference. The event will include a student prize for the best submission, with the winning student being awarded a book voucher from the IMA and a free RMA membership from the RMA.
In the framework of the 1st IMA Conference on Maths in Music at the Royal College of Music, London, 13-15 July 2022, Prof Robin Wilson (Open University) and Dr Rob Sturman (University of Leeds) will give a joint public talk on “Numbers and Notes; Patterns and Progressions”, on Thursday, the 14th of July, at 14:20, introducing the audience to the amazing connections between music and mathematics.
Invited Speakers
Prof Emily Howard, Royal Northern College of Music
Prof Guerino Mazzola, University of Minnesota
Prof Geraint Wiggins, Vrije Universiteit Brussel & Queen Mary University of London
Prof Moreno Andreatta, CNRS Director of Research at IRMA, University of Strasburg
Prof Robin Wilson, Open University
Orchestral Geometries: Torus, sphere, Antisphere , Emily Howard
The transformation of mathematical notions into musical ideas has become an important research methodology within my compositional practice. Whilst never a direct translation, it is precisely by attempting to carry out this impossible task that something is gained. I find that this approach often reveals new questions from unusual vantage points that result in unexpected ways to organise sound. Over the past seven years, the development of a series of geometry-inspired orchestral works has been a central preoccupation. For each of these Orchestral Geometries, an abstract mathematical shape was the imaginative cornerstone for the creative process. Each work is titled after the shape in question, and it is as though this foregrounded shape was a filter through which myriad decisions about the piece were made. The series is ongoing and the three existing works explore different curvatures: Euclidean geometry (Torus, 2016), elliptic geometry (sphere, 2017) and hyperbolic geometry (Antisphere, 2019). Torus is concerned with musical implications that arise from considering the significant mathematical result that there are two ways around a torus (a mathematical doughnut) that do not intersect; musical parameters are torus-shaped by design. When writing sphere, I was influenced by the consideration of local ‘musical’ space informing notions of higher dimensional global ‘mathematical’ space. Musical responses to two different models of hyperbolic space (the Poincaré disc and pseudosphere or antisphere) occur simultaneously in Antisphere; notions of negative curvature and shrinkage (for the angles in a triangle add up to less than 180° in hyperbolic space) have led to musical parameters being transformed as though through a saddle-shaped lens. In this lecture I will introduce this research by presenting musical examples alongside a commentary illuminating thought processes and transformational methodologies. Scores and recordings of Torus, sphere and Antisphere can be found here: http://www.emilyhoward.com/works.php
Mathematics and music: the perspective of the listener, Michelle Phillips
There are many ways in which we may find mathematics in music – by analysing a musical score, by a songwriter or composer talking about the techniques that they use to write music, by the notation itself having a mathematical title or mathematical annotations throughout, etc. However, this paper is concerned with another way in which we encounter music – as we hear it unfold in real time. Research regarding the perception of music has blossomed over the last 30-40 years, and has revealed aural perception to be a complex, multi-faceted, and flexible process. How we hear music depends on many factors, including not only the features in the music itself, but also our own personal tastes and characteristics, and how we respond to the music. Moreover, the environment in which we listen to music (and how our attention is divided), and the particular performance we are hearing (no two live performances are ever completely the same) contribute to this complicated web of factors which influence our sense of how we hear music as it happens. This notion that our sense of how long sections of music are may vary according to multiple aspects, for example, music perception research has shown very convincingly that our sense of musical duration changes according to how much we are enjoying the music, or how familiar it is, gives us a useful critical lens through which to view discussions of whether we can hear mathematical relationships in music. For example, Howat’s (1983) statement that “[Debussy’ proportional systems] they show ways in which the forms are used to project the music’s dramatic and expressive qualities with maximum precision” ([1], page 1) could be interpreted as suggesting that Debussy’s structures are available to perception in some way. This paper will discuss how music perception research can help us to examine such scholarship, and provide us with tools to explore mathematics and music which necessarily take account of the latest research regarding music perception.
Mathematics and the Source of Music, Geraint A. Wiggins
Sometimes, we mistake mathematical models of physical phenomena for rules that define those phenomena. For example, we sometimes talk about formulae that describe the relationships between physical quantities as though they themselves were the “Laws of Physics”. I think this arises partly from a desire (which is probably a Western world-view) to quantify and understand our world in direct, straightforward and incontrovertible terms: a sort of Ockham’s Razor of expression.
This desire extends beyond physical phenomena into cultural ones. Over the past few hundred years, Western music theory has attempted to codify what does and does not happen in (Western) music. In many cases, it does so by naming common phenomena, and placing constraints on what may occur in a performance. For example, certain chord progressions “should” be used to end a piece of music. Even when transformational creators, such as Arnold Schoenberg, set out to change the world, they have tended to do so in terms of adapting or denying existing accepted rules, and often replacing them with new ones. More incremental transformers, such as Beethoven, gently and steadily changed the rules by example, over an extended period. But throughout this evolution, indeed since the Ancient Greeks, Western philosophers of music have attempted to describe music as it appeared in their world in quasi-formal, quasi-mathematical terms. And in more recent years, some music theorists have begun to study the relationship between musical structures and mathematical structures such as groups, directly.
Our desire to understand external phenomena, in terms of rules with which we can calculate, is an important part of our modern world, without which scientific progress could not happen. But it can sometimes be misleading. In particular, to describe music as it currently exists in terms of rules begs the question of why the rules now are different from the rules that existed 800 years ago. Why, for example, did chromatic harmony not arise in Mediaeval Italy (except in the music of Gesualdo, who is generally dismissed as an insane outlier), and why is the English cadence beloved of Thomas Tallis no longer in use? An adequate theory of music should not only be able to describe such musical structures, but also to explain how and, ideally, why they may become more or less important over time and also how and why they can change.
However, the vast majority of music theory does not address these questions, except perhaps via the lineage of ideas passed from teacher to pupil. In particular, the vast majority of music theory focuses on the surface form of the music: what are the notes, what rules do they follow or break and so on. Only rarely does one read about the effect of music-theoretic structures on the listener, and then often only in terms of semiotic connotation: Romantic notions of musical “semantics” conveying figurative ideas (for example, “hunting the stag”). Structural theories of this kind, therefore, run a scientific risk: without a clear idea of how change in music can happen, a theory that adequately describes, say, all the music from Pérotin to Maxwell Davies, risks being so general that it distinguishes nothing from anything, and thus becomes meaningless.
The reason that attempts to describe music based on its surface are doomed to failure, or at least incompleteness, is that the surface of music is an effect, and not a cause, of the phenomenon. To see this, consider what happens in a room containing musical scores, recordings and musical instruments, but no people, and ask, “is there music in this room?” The answer is definitively, “No.” There are representations of the surface of music (in the form of notes on scores, perhaps, and of digital representations of sound waves on CDs). But in the absence of a listener (who might also be player), these representations mean little: it is the interpretation of listener and/or player that turn the information into music. Furthermore, it is the ability of the listener to hear sound (or imagine it from reading a score) and to understand musical structures – which are not explicitly present in the musical surface – that actually creates music itself.
Thus, music is fundamentally a psychological phenomenon, entirely dependent on the ability of the human mind to perceive and process sound. It is, of course, also a cultural, artistic, social, sociological, economic, and wonderful phenomenon, and many more things, too. But it is psychological first. Without the involvement of a living brain (usually, but not always, human), there is no musical activity, by definition. A complete music theory, that is capable of describing not just the surface of music but also its source in the mind, must therefore include psychology and psychological phenomena, for it is these which ultimately delimit what is musically possible.
Mathematics has its place in this psychological study too. Mathematical and computational models of perceptual and cognitive process can help us understand the mechanisms that underlie musical hearing and understanding, by permitting rigorous experimentation. With such models we can perhaps explain the general tendency towards complexity in music, for example, or why it is easy for a Greek child to clap in complex rhythms that a British professional musician might have to think twice about. In this talk, I will describe a series of models based in the mathematics of information theory, which seem to capture particular aspects of human musical experience, at levels beyond, and syntactically independent of, the surface, particularly well.
Without such a deep view of music, we attempt to study the movement of an iceberg by looking only above the waterline. It is the deep currents of mind, not the superficial glistening of notes and chords, that ultimately determine the nature of music and musical culture. To understand the iceberg of music, then, we must dive down, beyond the surface, into the musical mind.
The Music of Maths: a ‘mathemusical’ journey, Moreno Andreatta
In this presentation, I will provide an overview of some of the most active research axes of the SMIR (Structural Music Information Research) Project I’m leading at the University of Strasbourg. The project, hosted by IRMA (Institut de recherche mathématique avancée), is carried out since 2017 in deep collaboration with computer science researchers from the Music Representation Team at IRCAM in Paris. Ongoing research axes include the use of Mathematical Morphology, Formal Concept Analysis and Persistent Homology in the automatic classification of musical styles; the categorical formalisation of transformational music analysis; the interplay between algebraic and geometrical approaches in the construction of tiling rhythmic canons and their connection to Homometry theory and Fuglede Spectral Conjecture. After discussing the “mathemusical” dynamics underlying all these research axes, I will offer several music‐theoretical examples showing how to creatively use some formal and computational tools in mathematically‐based popular music compositions. I will end by shortly discussing some recent research directions in music cognition and perception we have explored in the last two years within a subproject supported by CNRS and entitled ProAppMaMu (Processes and Learning Techniques of Mathemusical Knowledge).
Some useful links
- The SMIR Project: http://repmus.ircam.fr/moreno/smir
- The Tonnetz web environment: https://morenoandreatta.com/software/
Biography
Moreno Andreatta holds diplomas in mathematics from the University of Pavia, piano performance from the Novara Conservatory and computational musicology from the EHESS (Ecole des hautes études en sciences sociales) in Paris. A founding member of the Journal of Mathematics and Music (Taylor & Francis), he is the co‐editor of the two series “Computational Music Sciences” (Springer) and “Musique/Sciences” (IRCAM/Delatour). CNRS Director of research on mathematics and music at IRMA (Institut de Recherche Mathématique Avancée) in Strasbourg, Moreno Andreatta is also associate researcher within the Music Representation Team at IRCAM in Paris. He is currently the principal investigator the SMIR Project on Structural Music Information Research, aiming at investigating the power of algebraic, topological and categorical formalization in the field of computational musicology.
Robin Wilson and Rob Sturman – PUBLIC LECTURE – Numbers and notes
Accomodation Options
1. Prince Consort Village
2. Citadines South Kensington London Park International
3. Millennium Gloucester Hotel London Kensington
4. Hotel Xenia, Autograph Collection
5. Premier Inn London Kensington
Registration
Registration for this Conference is currently open.
If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in.
If you are attending the conference please use the hashtag #IMAMathsMusic2022 and tag the IMA on socials!
Conference Fees
Non Member – £300
IMA/RCM/RMA Member – £150
IMA/RCM /RMA Student Member – £100
Non Member Student – £120
*Conference fees do not include lunch.
Conference Dinner – £50 for a 3 course meal and wine.
Important Dates
Extended Call for Abstract deadline – 24 April 2022
Abstract acceptance notification – 6 May 2022
Final registration date – 1 July 2022
Conference Dates – 13-15 July 2022
Organising Committee
Matteo Sommacal, Northumbria University
Michelle Phillips, Royal Northern College of Music
Dimitri Scarlato, Royal College of Music
Rob Sturman, Leeds University
Further information
E-mail: conferences@ima.org.uk Tel: +44 (0) 1702 354 020
Institute of Mathematics and its Applications, Catherine Richards House, 16 Nelson Street, Southend-on-Sea, Essex, SS1 1EF, UK.
In cooperation with the Royal College of Music
Supported by the Royal Music Association
This combination of Music n Maths subjects is a base of life ,since rhythem in breathing n in yoga pranayam helps to understand and live a most useful life to any individual.Not only to mankind but all species on the earth.
Presenting at this conference was a blast something I’d never have experienced at school, the people there were truly passionate about the beautiful connection between maths and music and I was inspired to continue my paper and research this in the future.