The Mathematics of Mixing
Michael Terrell, Andrew Simpson, Mark B. Sandler · Journal of the Audio Engineering Society · 2014
Mixing is a quintessential optimization problem.Given control of several component tracks, a balance must be struck that reflects a trade-off between engineering methods, artistic objectives, and auditory perceptual constraints.Formally, this balance can be thought of as the optimal solution to a system of mathematical equations that describe the relationships between the component tracks within a mix.Hence, the nature of these equations defines the process by which solutions may be arrived at.As perception is strongly nonlinear, an analytical solution to this set of equations is not possible and so a search must be conducted.Here, taking loudness as an example, we develop an optimization theory treatment of the problem of mixing, complete with case studies to illustrate how auditory perception can complicate the process, not least due to masking-related interactions.