Preprint del Dipartimento di Matematica

Preprint n. 5/2003

A Mathematical Model to classify the musical patterns of listened melodic pieces

ANNA DAMIANI, PIETRO DI LORENZO, GIUSEPPE DI MAIO, MARIA OLIVETTI BELARDINELLI

This work is aimed at contributing to build up a mathematical model of musical similarity based on psychological experimental evidences. The model turns out a numerical rank value, usefully to classify the distance between musical pieces. The mathematical cores of the model are the cross-correlation function between two signals and the cluster analysis theory. The other mathematical instrument is the multivariate analysis: in fact, attention is paid to the numerical codification of all the significative parameters of each listened sequences. The planned tasks measure the capacity of expert listeners in abstracting salient features in relation to musical style differentiations. The subjects are asked to evaluate and to classify 40 musical sequences, chosen from the Sonatas repertoire for piano solo of Beethoven and Mozart, as belonging to two different categories on the basis of subjective specific and unspecific attributes, including global and local information referred to different musical patterns (like pitch, note durations, melodic and rhythmic contours, changes in the relational structure of the individual note). The subjects are also asked to clarify in writing on what basis (i.e. which significant parameters) they have built a mental representation of the two prototype categories. The results of the model are compared with the experimental psychological issues.