Symbols For Sound : Exploring Mathematical Music Theory April 04, 2012

Research Interest

Mathematical Music Theory. This research involves several mathematical areas used in scientific Musicology, such as Category Theory, Abstract Algebra, Algebraic Combinatorics on Words. It is cross disciplinary not only with Music, but with areas such as Computer Science and Cognitive Science.

Contact Information


Mailing Address

Department of Mathematics and Statistics
Georgia State University
COE 708
30 Pryor Street
Atlanta, GA 30303

Teaching Interests  
Bridge to higher Mathematics, Linear Algebra, Abstract Algebra,
Multivariate Calculus, Topology.

Selected Publications

(2013) Noll, T., Montiel, M. Glarean’s Dodecachordon Revisited. In Mathematics and Computation in Music J. Wild, J.Hust & J. A. Burgoyne (Eds.), pp. 151-166. Lecture Notes in Artificial Intelligence, Subseries of Lecture Notes in Computer Science, Springer Publishing Company. ISBN 978-3-642-39356-3

(2013) Norgaard, M., Spencer, J. & Montiel, M. Testing Cognitive Theories: a Probabilistic Based Algorithm for Melody and Rhythm in Jazz Improvisation. Psychomusicology: Music, Mind and Brain special edition on The Improvising Brain. Accepted for publication.

(2012) Aceff-Sánchez, F., Agustín, O., du Plessis, J., Lluis-Puebla, E. & Montiel, M. An Introduction to Group Theory with Applications to Mathematical Music Theory. Bookboon Ventus publishing Aps. ISBN: 978-87-403-0324-7. Online at:

(2009) Agustín, O., du Plessis, J., Lluis-Puebla, E. & Montiel, M. (2009). Una Introducción a la Teoría de Grupos con Aplicaciones en la Teoría Matemática de la Música. Online publications of the Mexican Mathematical Society. ISBN: 968-9161-37-7 (online version); 968-9161-38-5 (CD version); 968-9161-36-9 (hard copy version).(textbook)

(2004) Montiel, M. The Denotator: Its Structure, Construction, and Role in Mathematical Music Theory In Perspectives in Theoretical and Computational Music Theory, 89-105, Guerino Mazzola, Thomas Noll and Emilio Lluis-Puebla (Eds.), Epos, Universitat Osnabruck: Germany, ISBN:3-923486-57-x

(2002) Montiel, M. Contributor to The Topos of Music: Geometric Logic of Concepts, Theory and Performance by Guerino Mazzola, Birkhauser Publishing Company, Berlin: Germany. ISBN-13: 978-3764357313 (book)