Sonification of Quantum Algorithms with Spline Models of Timbre, Melody, and Rhythm

In this paper we describe methods for mapping the information contained in a spline model of one cycle of an audio signal to the quantum information setting. We use this mapping to describe methods of sonification of quantum algorithms which use spline models to describe and generate timbre, melody, and rhythm. We show how a musical state vector given by n B-spline coefficients, which represent one cycle of a waveform, can produce these three musical elements simultaneously. We present two modes of correspondence between quantum and musical states. The first mode is derived from proposed signal processing of quantum audio, such as QPAM (Quantum Probability Amplitude Modulation), and the second mode works with superposition states achievable through quantum algorithms. Musical states are initialized using approximate timbres derived from instrument samples or synthesized timbres. Melodic contours are derived from spline models of these timbres, using continuous pitch and duration spaces. Musical examples are discussed, and larger compositional works are currently in production.