From Lemniscate to M. Pistoletto's Third Paradise Curve: Music as a Synthesis of the Relationship between Art and Geometry

Abstract

The research conducted herein is predicated upon the oeuvre of the Italian artist Michelangelo Pistoletto—a notable figure within the Arte Povera movement—with particular emphasis on his Third Paradise curve, a re-elaborated version of the lemniscate of Bernoulli, commonly recognized as the infinity symbol in mathematics. Following the elucidation of an equation for the Third Paradise curve—characterized by some properties different from those of the lemniscate—a compositional concept is developed by revisiting the forms of the aforementioned curves, further inspired by the cinematic art of Tarkovsky. This endeavor culminates in the creation of two interrelated pieces, the techniques of which are succinctly delineated, concentrating also on the generation of electronic sounds, the stages of their audio processing and the subsequent refinement. The work presented herein exemplifies the interplay between music, art, and algebraic curves; it further illustrates how music (free from market logic) can embody a synthesis among them—à la Pater, for whom in music the authentic measure of perfected art can be found—and serve as a conduit for delving into profound connections with spirituality while articulating themes of change and sustainability, as poignantly espoused in Pistoletto’s oeuvre.