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M. Terrell, A. Simpson, and M. Sandler, "The Mathematics of Mixing," J. Audio Eng. Soc., vol. 62, no. 1/2, pp. 4-13, (2014 January.). doi: https://doi.org/10.17743/jaes.2014.0002 M. Terrell, A. Simpson, and M. Sandler, "The Mathematics of Mixing," J. Audio Eng. Soc., vol. 62 Issue 1/2 pp. 4-13, (2014 January.). doi: https://doi.org/10.17743/jaes.2014.0002
Abstract: Although audio mixing has always been viewed as the artistic task of either a conductor balancing the musicians in a live performance or a mixing engineer combining multiple tracks in a sound studio, this research considers mixing as a mathematical optimization problem. Using an auditory model, the authors demonstrated how numerical optimization can be used to pose and solve a mix problem. There is interplay between artistic objectives, perceptual constraints, and engineering methods. Taking loudness as an example, it is shown that the nonlinearity in the perceptual model leads to complex behavior, which can be overcome by careful choice of optimization strategies and parameters.

@article{terrell2014the,
author={terrell, michael and simpson, andrew and sandler, mark},
journal={journal of the audio engineering society},
title={the mathematics of mixing},
year={2014},
volume={62},
number={1/2},
pages={4-13},
doi={https://doi.org/10.17743/jaes.2014.0002},
month={january},} @article{terrell2014the,
author={terrell, michael and simpson, andrew and sandler, mark},
journal={journal of the audio engineering society},
title={the mathematics of mixing},
year={2014},
volume={62},
number={1/2},
pages={4-13},
doi={https://doi.org/10.17743/jaes.2014.0002},
month={january},
abstract={although audio mixing has always been viewed as the artistic task of either a conductor balancing the musicians in a live performance or a mixing engineer combining multiple tracks in a sound studio, this research considers mixing as a mathematical optimization problem. using an auditory model, the authors demonstrated how numerical optimization can be used to pose and solve a mix problem. there is interplay between artistic objectives, perceptual constraints, and engineering methods. taking loudness as an example, it is shown that the nonlinearity in the perceptual model leads to complex behavior, which can be overcome by careful choice of optimization strategies and parameters.},}

TY - paper
TI - The Mathematics of Mixing
SP - 4 EP - 13
AU - Terrell, Michael
AU - Simpson, Andrew
AU - Sandler, Mark
PY - 2014
JO - Journal of the Audio Engineering Society
IS - 1/2
VO - 62
VL - 62
Y1 - January 2014 TY - paper
TI - The Mathematics of Mixing
SP - 4 EP - 13
AU - Terrell, Michael
AU - Simpson, Andrew
AU - Sandler, Mark
PY - 2014
JO - Journal of the Audio Engineering Society
IS - 1/2
VO - 62
VL - 62
Y1 - January 2014
AB - Although audio mixing has always been viewed as the artistic task of either a conductor balancing the musicians in a live performance or a mixing engineer combining multiple tracks in a sound studio, this research considers mixing as a mathematical optimization problem. Using an auditory model, the authors demonstrated how numerical optimization can be used to pose and solve a mix problem. There is interplay between artistic objectives, perceptual constraints, and engineering methods. Taking loudness as an example, it is shown that the nonlinearity in the perceptual model leads to complex behavior, which can be overcome by careful choice of optimization strategies and parameters.