Mathematics and Computation in Music 2026 (MCM 2026)

23 Jun 2026, 08:30 → 26 Jun 2026, 15:45 US/Eastern

Bard College, Annandale-on-Hudson, New York, USA

ScheduleFinal_MCM2026_BardCollege_NewYork.pdf

Tuesday 23 June

09:15 → 09:45 Arrival, Registration Pickup, or Registration

09:50 → 09:55 Welcome and Opening Remarks

Speakers: Mariana Montiel, Charles Doran

10:00 → 12:05 Voice Leading and Rhythm

Convener: Jason Yust

10:00 The Note at Infinity

Speaker: Dmitri Tymoczko

10:35 Counting Rhythms Using Combinatorics on Words

Speaker: Gonzalo Romero-Garcia

11:05 Coffee Break, Registration Pickup, or Registration

11:35 On Perfectly Balanced Sets: a Computational Investigation

Speaker: Paul Lascabettes

12:15 → 12:45 Poster Session

12:15 Poster: Tonnetz-Based Mathematical Invariants for the Analysis of Unequal-Tempered Tuning Systems

Speaker: Kateri Doran

12:20 Poster: Musical Perspectives

Speaker: Dmitri Tymoczko

12:20 Poster: Towards a Formalization of Fretboards and Gestural Effort

Speaker: Matt Chiu

12:50 → 13:50 Lunch Break: On Own at Cafeteria or Restaurants

14:00 → 15:40 Applications of Mathematics to Music Theory Analysis of Composers and Styles: Part 1

Convener: Gonzalo Romero-Garcia

14:00 Note Spelling Without Scales in Morton Feldman’s String Quartet No. 2

Speaker: Noah Kahrs

14:35 Persistent Homology on Pointed Chord Spaces

Speaker: Alessandro Casali

15:10 Modeling End-Weighted and Goal-Directed Conceptions in Gamelan Gong Kebyar

Speaker: Qiuwan Zhao

15:40 → 15:50 Break

16:00 → 16:35 MatheMusical Virtual Museum & Planet Voices by Gilles Baroin

16:00 MatheMusical Virtual Museum & Planet Voices by Gilles Baroin

Speaker: Gilles Baroin

16:35 → 18:45 Dinner Break: On Own at Cafeteria or Restaurants

19:00 → 20:00 Keynote Address: Thomas Noll

Convener: Mariana Montiel

19:00 Keynote by Thomas Noll: The Algebra of the 'Tongesellschaft': Towards a Mathematical Conceptualization of Tonal Interaction

The concept of the well-formed scale has been a classic paradigm within mathematical music theory for more than three decades. This keynote address traces its subsequent structural and theoretical developments since our inaugural conference in 2007.
By indexing the seven pitches of the diatonic scale both by fifths and by step intervals, one obtains a permutation of the integers from 0 to 6. The fundamental impetus for this entire line of inquiry lies in the fact that this permutation constitutes a multiplication by 4 modulo 7, which is an automorphism of the cyclic group Z7. From this structural kernel, a comprehensive network of mathematical models has evolved, illuminating how pitches organize themselves and give rise to musical meaning.
Drawing upon Jacques Handschin's evocative concept of the "Tongesellschaft" (tone-society), this lecture invites us to re-evaluate historical frameworks of tonal organization through the lens of algebraic models. The trajectory spans from the medieval gamut and the interpretive conventions governing sixteenth-century partbooks to the ultimate consolidation of common-practice harmonic tonality.

Speaker: Thomas Noll

20:10 → 21:30 Concert

20:10 Concert: The Music of Tom Johnson

Deep Rhythms VIII (Wood Block Music) by Tom Johnson
Performed by Michael Jones

Tilework for Solo Violin by Tom Johnson
Performed by Wendy Case

Alexandrins pour Guitare by Tom Johnson
Performed by Matt Sargent

Selections from The Chord Catalogue by Tom Johnson
Performed by Juan Diego Mora Rubio

Wednesday 24 June

09:00 → 11:15 Algebraic and Topological Perspectives on Scale Theory, Harmony, and Neo-Riemannian Transformations: Part 1

Convener: Mariana Montiel

09:00 All-Interval Series in Cyclic Spaces

Speaker: Ethan Bonnell

09:35 Alternative Symmetries and Systems

Speaker: Luis R. A. Finotti

10:10 A Matrix Representation of Lewin Duality, and Dualizing Operators for Dual Groups of Triadic Transformations

Speakers: Thomas M. Fiore, Thomas Noll

10:45 A Theory of Scales and Orbit Covers

Speaker: Drew Flieder

11:15 → 11:30 Coffee Break, Registration Pickup, or Registration

11:35 → 12:40 Algebraic and Topological Perspectives on Scale Theory, Harmony, and Neo-Riemannian Transformations: Part 2

Convener: Mariana Montiel

11:35 Symmetries of the Modal Color Theory Hyperplane Arrangements

Speaker: Paul M. Sherrill

12:10 Wick-Rotated Fibonacci Polynomials from the Scale-Step Interval Patterns of the Pentatonic and Diatonic Collections

Speaker: M. A. Coury-Hall

12:40 → 13:40 Lunch Break: On Own at Cafeteria or Restaurants

13:50 → 15:30 Algebraic and Topological Perspectives on Scale Theory, Harmony, and Neo-Riemannian Transformations: Part 3

Convener: Mariana Montiel

13:50 Harmonic Qualities of Generic Sets

Speaker: Jason Yust

14:25 Modeling the Harmonic Syntax of Rock Music with Hidden Markov Models

Speaker: Matthew Anthony Ludwig

15:00 Planar Projections of Tone Systems and Faithful Keyboards

Speaker: Marek Zabka

15:40 → 17:05 Communication Performance

15:40 Functional Harmony After Tonality: Composing with Orbit Covers

Speaker: Drew Flieder

16:25 An Application of Alternative Symmetries and Systems

Speaker: Luis R. A. Finotti

17:10 → 17:40 MatheMusical Virtual Museum & Planet Voices by Gilles Baroin

17:10 MatheMusical Virtual Museum & Planet Voices by Gilles Baroin, Wednesday

Speaker: Gilles Baroin

17:40 → 18:45 Dinner Break: On Own at Cafeteria or Restaurants

18:45 → 19:00 Walk 15 Minutes to László Z. Bitó ’60 Conservatory Building

19:00 → 20:00 Keynote Address: Noam Elkies

Convener: Charles Doran

19:00 Keynote by Noam Elkies: Canonical Forms and Transformations

We review the problem of constructing musical canons, and the standard recursive technique for constructing them given a criterion of harmonic consonance. We then illustrate how symmetries and near-symmetries of the consonance relation help composers create canons that go beyond counterpoint exercises to serve as structural and expressive tools.

Speaker: Noam Elkies

20:10 → 21:30 Concert

20:10 Concert: Participant Compositions and Performances

I.
Composer: Kateri Doran
Performers: Kateri Doran (flute) and Saoirse Doran (clarinet, piano)

Quantum Loops — solo flute (ca. 6 minutes)

Mirror Loops — flute and clarinet (ca. 3 minutes)

Euler’s Toccata — solo piano (ca. 3 minutes)

II.
Composer: Clifton Callender
Performer: Jingwen Tu (piano)

Meditations on a Warming Planet, No. 1 & 3 (ca. 7 minutes in total)

III.
Composer: Octavio Agustín-Aquino
Performer: Trevor Babb (guitar)

Gabriela
La Toninera
Camila
Ximena
(ca. 8:30 minutes in total)

IV.
Composer: Brian Martínez Rodríguez
Performer: Trevor Babb (guitar)

Preludios de Bitácora: I. Bitácora de la Vista sobre el Mar (ca. 4 minutes)

V.
Composer: Noam Elkies
Performer: Noam Elkies (piano)

No Clapping 'til the Music Ends: A Study in Canons for Solo Piano Suggested by Reich's Clapping Music (2008) (ca. 5 minutes)

VI.
Composer: Jason Yust
Performers: Steve Bonacci (saxophone), Matt Sargent (guitar), Michael Jones (percussion), and Taylor Long (percussion)

Prime Meridian (ca. 6 minutes)

Thursday 25 June

09:30 → 12:10 Mathematical Approaches to Music Cognition, Pitch Perception, Consonance-Dissonance, and Performance

Convener: Clifton Callender

09:30 Transformational Analysis of Geometric Nets under Isotonicity Constraints

Speaker: Kristina Hurajova

10:05 Consonance Ratings of Most Even Tetrachords Obtained by Variation of Phases

Speaker: Luis Nuno

10:35 Coffee Break, Registration, and MatheMusical Virtual Museum & Planet Voices by Gilles Baroin

11:05 Sound and Visual Objects in N Dimensions in the Labyrinth of Time

Speakers: Gilles Baroin, Stephane de Gerando

Link to Stéphane de Gérando's Video "Sound and Visual Objects in N Dimensions in the Labyrinth of Time"

11:40 Perceptual Signal Analysis and Eigenvalue-Weighted Metrics for Musical Audio Quality Assessment

Speaker: Sanjay Majumder

12:15 → 12:45 Applications of Mathematics to Music Theory Analysis of Composers and Styles: Part 2

Convener: Gonzalo Romero-Garcia

12:15 Quantifying Costere’s Polarization of Pitch-Class Collections via Jensen–Shannon Divergence

Speaker: Fernando Gualda

12:45 → 14:20 Lunch Break: On Own at Cafeteria or Restaurants

14:30 → 15:35 Quantum Theory and Music

Convener: Sara Sabag-Sabja

14:30 Entangled Function Leading

Speaker: Thomas Noll

15:05 Density Matrix RNN (DM-RNN): A Quantum Information Theoretic Framework for Modeling Musical Context and Polyphony

Speaker: Mariana Montiel

15:45 → 16:30 Electronic Music Demonstrations by Bard Preparatory Students

16:35 → 17:10 Communication Performance

16:35 The QuArtet: Embodying Quantum Theory as an Ensemble

Speaker: Thomas Noll

17:10 → 17:50 Walk 15 Minutes to Blithewood Manor for Banquet IF Pre-registered for Banquet, Otherwise On Own for Dinner at Cafeteria or Restaurants

18:00 → 20:00 Banquet in Blithewood Manor IF Pre-registered, Otherwise Dinner at Cafeteria or Restaurants

Friday 26 June

09:30 → 11:30 Algorithms and Modeling for Music and Music Related Phenomena

Convener: Marek Zabka

09:30 The Predictive Benefit of Order Increases in Melodic N-Gram Models

Speaker: David Temperley

10:05 The Operatic Voice (I): Survey of Mathematical and Computational Models

Speaker: Sara Sabag-Sabja

10:35 Coffee Break, Registration, and MatheMusical Virtual Museum & Planet Voices by Gilles Baroin

11:00 The Operatic Voice (II): Characterization of Squillo: Acoustic Parameters and Perceptual Validation

Speaker: Sara Sabag-Sabja

11:35 → 12:35 All Invited: Meeting of the Society for Mathematics and Computation in Music

i. General synthesis of activities over the last 2 years (Mariana Montiel)
ii. Website (Gonzalo Romero-Garcia, Thomas Noll)
iii. Publications Committee Report (Clifton Callender, Marek Zabka)
iv. Financial Report (Thomas Fiore)
v. Elections (Gonzalo Romero-Garcia, Thomas Noll)
vi. Presentation of MCM 2028 in Warsaw (pre-recorded by Pawel Dlotko) (Thomas Fiore, Mariana Montiel)

Speakers: Mariana Montiel, Gonzalo Romero-Garcia, Thomas Noll, Clifton Callender, Marek Zabka, Thomas Fiore, Pawel Dlotko

12:35 → 13:35 Lunch Break: On Own at Cafeteria or Restaurants

13:40 → 14:45 Computational Approaches to Music

Convener: Thomas Noll

13:40 Automated Harp Pedaling: A Graph-Theoretic Approach to Pitch Spelling and Pedal Settings

Speaker: Clifton Callender

14:15 A New Version of OMM for Melodies and Rhythms

Speaker: Carlos Agon

14:55 → 15:35 Communication Performance

14:55 Rotation: An Algorithmic Musical Work Based on Temporal Translations, Pattern Variations, and Musical Tilings

Speaker: Paul Lascabettes

15:35 → 15:45 Closing

Speakers: Mariana Montiel, Charles Doran