La matematica armonia dei suoni naturali. Ovvero, l'armonica matematica dei suoni naturali

Talamucci, Federico

Matematica, cultura e società, Série 1, Tome 7 (2022) no. 2, pp. 135-158

Résumé

The collaboration of mathematics in the two musical systems of Pythagorean sounds and of equal sounds is evident and opportune for generating the elements and managing their relationships. The only essential notion for a rational intervention in the two sound worlds is that of distance between sounds. The scale of natural sounds does not seem to dialogue directly with a purely mathematical module that articulates its definition and is generally presented as a manual adjustment of the ancient Pythagorean sounds. The overturning of the words harmony-mathematics in the two parts of the title summarizes the main themes proposed: in the first sections of the article the role of proportion in the arrangement of sound systems ascertained by the theory and practice of music over the centuries is highlighted, in particular focusing on the relevance of the harmonic proportion for the natural sound system. The tangible juxtaposition between numbers linked to sounds and architectural modules theorized in the Renaissance is recalled to celebrate the mathematical harmony of a certainly unitary aesthetic and artistic thought. If this first part develops the presentation of the most important sound systems in Western music and traces their proportions according to arguments defendants and applicants, in a second phase of the work (Section 4) the starting point is confined to mathematics, to ask whether the latter is able, by means of an exhaustive algorithm, to produce a harmonic complex with musical sense, to starting from a basic nucleus, which draws inspiration from the reasons for the good proportion of the Renaissance construction elements. The object therefore is not only to illustrate the harmonic device of the already formed natural scale, but to implement the formation of sound elements that respond to the unitary principle of proportion and combine harmoniously.