Mathematics and Computation in Music

(Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2009)

This book constitutes the refereed proceedings of the Second International Conference on Mathematics and Computation in Music, MCM 2009, held in New Haven, CT, USA, in June 2009.


The 26 revised full papers presented were carefully reviewed and selected from 38 submissions. The MCM conference is the flagship conference of the Society for Mathematics and Computation in Music. The papers deal with topics within applied mathematics, computational models, mathematical modelling and various further aspects of the theory of music.


This year’s conference is dedicated to the honor of John Clough whose research modeled the virtues of collaborative work across the disciplines.

MCM 2009: Paper Abstract


Compatibility of the Different Tuning Systems in an Orchestra


Alfonso del Corral, Taller de Música Jove
Teresa León, Universidad de Valencia
Vicente Liern, Universidad de Valencia


Focusing on the daily practice of musicians, we give flexibility to the mathematical treatment of musical notes, tuning systems and the relations between them. This allows us to connect the theory and the practice of music. Using the techniques of fuzzy logic, we describe the concepts with fuzzy sets and introduce the a-compatibility as a degree of interchangeability between tuning systems. To show how our proposal works, we use a fragment of Haydn and analyze the compatibility of the notes taken from 48 recordings for the tuning systems of Pythagoras, Zarlino and Equal Temperament of 12 notes.