A mathematical model for voice leading and its complexity - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2015

A mathematical model for voice leading and its complexity

Résumé

We give a formal de of the musical concept of voice leading in mathematical terms, based on the idea of partial permutations of certain ordered multisets. Then we associate a partial permutation matrix with a voice leading in a unique way and write an algorithm to easily transform any musical composition into a sequence of such matrices; we then generalise it in order to include in the model also rhythmic independence and rests. From that we extract a vector whose components return information about the movements of the voices in the piece and hence about the complexity of the voice leading. We provide some examples by analysing three compositions, also visualising complexity as a point cloud for each piece. Finally, we interpret the sequence of complexity vectors associated with each composition , thus considering the position of each observation with respect to time. The Dynamic Time Warping allows us to compute the distance between two pieces and to show that our approach distinguishes well the examples that we took into account, exhibiting a strong indication that the notion of complexity we propose is a good tool to identify and classify musical pieces.
Fichier principal
Vignette du fichier
1508.05833.pdf (1.07 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01218169 , version 1 (20-10-2015)

Identifiants

  • HAL Id : hal-01218169 , version 1

Citer

Mattia Giuseppe Bergomi, Riccardo Danilo Jadanza, Alessandro Portaluri. A mathematical model for voice leading and its complexity. 2015. ⟨hal-01218169⟩
210 Consultations
438 Téléchargements

Partager

Gmail Facebook X LinkedIn More