Q.E.D.

As the sounds have relations with the numbers, they could be also related to points, lines and angles. In other words, we could imagine to have a “geometrical” interpretation of the basic musical elements and of their relationships. The figural approach of geometry, that is the perception of reality by means of an intuitive and synthetic concept of that, has a strong creative connotation. I was especially inspired by the idea of conceiving a similarity between the creative dimension in the music and the logical one in the geometry. For that, I strive to conceive different ways of combination, development and evolution of the own musical parameters, exactly like the ways of representation effected by the geometrical thought. It is a sort of “translation” between two different types of approach, both connoted by the contribution of the intuition, the imagination, the creativity and the rationality. Specifically, I was inspired by Euclid's Elements, the synthesis of geometrical knowledge in ancient times, valid even now.

The piece is articulated in several sections, differentiated in the musical writing, in relation to some musical images suggested by the postulates included in the 1st book of the Elements, where Euclid enunciates the properties of the basic geometrical elements (points, straight lines, circumferences, angles). Trying to imagine the geometrical properties of these elements in a musical way, I found a facilitation in the pragmatic approach of the graphic representation utilized in this field and, particularly, in the various practical procedures as illustrated by Niccolò Tartaglia with his annotations to the euclidean text. The detailed sequences of the actions, to give a graphic demonstration of the postulates, inspired to me some images of sequences of the musical gestures. The last section is developed according to two opposite aptitudes: one is based on the euclidean sentence; the other is founded on the conception of known as “not-euclidean geometries” (hyperbolic or elliptical), that entail an enunciation of a contrary form of the 5th postulate (that related to the parallel lines).

This kind of approach offered me the opportunity to think and to “draw” in a new way the conception of my musical thought.

Piece commissioned by the FontanaMIX Ensemble for the 60ème International Festival of contemporary music « La Biennale Musica » of Venice.
World premiere : 11th October 2016 – Ca' Giustinian, « Sala delle colonne », Venice
Ensemble FontanaMIX
Francesco La Licata, conductor