Tiling the (musical) line with polynomials

Emmanuel Amiot (1) , Moreno Andreatta (1) , Carlos Agon (1)

1 Repmus - Représentations musicales

This paper aims at discussing the polynomial approach to the problem of tiling the (musical) time axis with translates of one tile. This mathematical construction naturally leads to a new family of rhythmic tiling canons having the property of being generated by cyclotomic polynomials (Tiling cyclotomic canons).

Mots clés: tiling; polynomials; canons; computer-aided composition

Mots clés: Informatique musicale

Domaines: Langage de programmation [cs.PL]; Son [cs.SD]; Traitement du signal et de l'image [eess.SP]; Machine Learning [stat.ML]; Intelligence artificielle [cs.AI]; Théorie et langage formel [cs.FL]; Musique, musicologie et arts de la scène

Emmanuel Amiot, Moreno Andreatta, Carlos Agon. Tiling the (musical) line with polynomials: Some theoretical and implementational aspects. ICMC 2005, Sep 2005, Barcelona, Spain. pp.227-230. ⟨hal-01161341⟩