Quadratic difference tones belong to a family of perceptual phenomena that arise from the neuromechanics of the auditory system in response to particular physical properties of sound. Long deployed as “ghost” or “phantom” tones by sound artists, improvisers, and computer musicians, in this article we address an entirely new topic: How to create a quadratic difference tone spectrum (QDTS) in which a target fundamental and harmonic overtone series are specified and in which the complex tone necessary to evoke it is synthesized. We propose a numerical algorithm that solves the problem of how to synthesize a QDTS for a target distribution of amplitudes. The algorithm aims to find a solution that matches the desired spectrum as closely as possible for an arbitrary number of target harmonics. Results from experiments using different parameter settings and target distributions show that the algorithm is effective in the majority of cases, with at least 99% of the cases being solvable in real time. An external object for the visual programming language Max is described. We discuss musical and perceptual considerations for using the external, and we describe a range of audio examples that demonstrate the synthesis of QDTSs across different cases. As we show, the method makes possible the matching of QDTSs to particular instrumental timbres with surprising efficiency. Also included is a discussion of a musical work by composer Marcin Pietruszewski that makes use of QDTS synthesis.

This article describes a set of “textual” technological practices that have been emerging over the past decade in the work of underground electroacoustic and computer music composers, focusing particularly on Florian Hecker and Russell Haswell. Guided by methodological insights from the field of software studies, the article zooms in on two computer programs, PulsarGenerator and GENDYN, presenting a genealogical analysis of them as cultural objects and outlining how these lines of descent are aestheticized in their works. In the hands of these artists, sound synthesis procedures carry an author function, and this transgresses both their legal status as technological “inventions” rather than texts, as well as their ontological status in the electroacoustic music genre. Combined with a compositional focus on “sounding” the materiality of these technologies—the particular affordances, limitations, and quirks of their operative functioning—this textual practice contributes to a new aesthetic, one that challenges the prevailing logic of secrecy, alchemy, and semblance in this music. Using the notion of “ontological politics” inherited from science and technology studies, I show how these practices highlight zones of contestation over electroacoustic music’s ontology.

This article describes methods of sound synthesis based on auditory distortion products, often called combination tones. In 1856, Helmholtz was the first to identify sum and difference tones as products of auditory distortion. Today this phenomenon is well studied in the context of otoacoustic emissions, and the “distortion” is understood as a product of what is termed the cochlear amplifier. These tones have had a rich history in the music of improvisers and drone artists. Until now, the use of distortion tones in technological music has largely been rudimentary and dependent on very high amplitudes in order for the distortion products to be heard by audiences. Discussed here are synthesis methods to render these tones more easily audible and lend them the dynamic properties of traditional acoustic sound, thus making auditory distortion a practical domain for sound synthesis. An adaptation of single-sideband synthesis is particularly effective for capturing the dynamic properties of audio inputs in real time. Also presented is an analytic solution for matching up to four harmonics of a target spectrum. Most interestingly, the spatial imagery produced by these techniques is very distinctive, and over loudspeakers the normal assumptions of spatial hearing do not apply. Audio examples are provided that illustrate the discussion.