QDTS

Rodrigo Cádiz^1,2, Esteban Gutiérrez³, and Christopher Haworth⁴

¹ Music Institute, Pontificia Universidad Católica de Chile
² Department of Electrical Enginering, Pontificia Universidad Católica de Chile
³ Department of Information and Communications Technologies, Universitat Pompeu Fabra
⁴ Department of Music, University of Birmingham

Introduction

Cuadratic and cubic difference tones (QDT and CDT respectively) are particular kinds of auditory distortion products (ADP) where two pure tones are used to generate the perceptual illusion of a third pure tone. This ADPs have been thoroughly studied and compared in the last decades (see e.g. [1], [2] and [3]), and the necessary conditions to generate them are well known. Quadratic Difference Tone Spectra (QDTS) on the other side, is a new kind of ADP where several pure tones are combined to generate a full spectra made out of QDT.

The theory behind the construction of a QDTS was first introduced in [4], and a real-time algorithm that solves the computations needed to generate any given QDTS was first introduced in [5].

This repository contains an implementation as a MAX external of the algorithm built in [5] to generate QDTS presented at the International Computer Music Conference 2023 hosted in the Chinese University of Hong Kong.

Contents

The three main folders of the repository contain the implementation in MAX, some example patches recorded in video and the experiments that supported the contruction of the algorithm itself respectively.

1. MAX external

In this folder everything related to the MAX external can be found.

• The subfolder Builds contains current builds for the external for the Windows and MAC operative systems. A little tutorial on how to run the external can also be found in this subfolder.

• The subfolder Code contains the necessary code to build the MAX external in case that the current builds stopped working. A little tutorial on how to build the MAX external can also be found in this subfolder.

• The subfolder Patches contains several MAX files that can be used to easily manipulate the MAX external.

2. Demos

In this folder, several video demos of the MAX external. Each demo contains a brief readme file containing a description of it, an uncompressed audio file of the demo and a series of patches to recreate the video demo locally.

3. Experiments

The algorithm implemented uses several standard mathematical tools, however due to its heuristic nature, several experiments were made prior to its construction in order to fully understand the problem.

In each subfolder, a python project containing the experiment can be found together with a brief readme file containing a description of the experiment itself.

References

[1] J. B. Dewey, “Cubic and quadratic distortion products in vibrations of the mouse cochlear apex,” JASA Express Letters 2, vol. 11, no. 114402, 2022.
[2] E. Zwicker, “Different behaviour of quadratic and cubic difference tones,” Hearing Research, vol. 1, no. 4, pp. 283–292, 1979.
[3] R. Plomp, “Detectability threshold for combination tones,” The Journal of the Acoustical Society of America, vol. 37, no. 1110, 1965.
[4] G. Kendall, C. Haworth, and R. F. Cádiz, “Sound synthesis with auditory distortion products,” Computer Music Journal, vol. 38, no. 4, 2014.
[5] C. Haworth, E. Gutiérrez and R. F. Cádiz, “Generating Quadratic Difference Tone Spectra for Auditory Distortion Synthesis,” (to be published).