Generating Quadratic Difference Tone Spectra for Auditory Distortion Synthesis

Quadratic difference tones are one of a family of perceptual phenomena that arise from the neuromechanics of the auditory system in response to particular properties of physical sound. Long deployed as ’ghost tones’ by improvisers, computer musicians and sound artists, in this paper we address the problem of creating quadratic difference tone spectra, where a QDT fundamental and harmonic overtone series is specified and the necessary acoustic components needed to evoke it are synthesised. A numerical algorithm for solving target distributions of amplitudes for the synthesis of quadratic distortion tone spectra is proposed. The algorithm aims to find a solution for a target distribution of amplitudes that matches the desired spectrum as closely as possible. The experiments were conducted using different parameter settings and target distributions. The results show that the algorithm is effective in solving the problem in the majority of cases, with at least 99% of the cases being solvable in real-time. The article also discusses the convergence of the algorithm and its potential mathematical properties. Additionally, audio examples implemented in Max are provided to demonstrate the synthesis of different quadratic distortion tone spectra using this approach.