Sensory dissonance (SD) quantifies the interference between partials in a mixture of simultaneously sounding tones and correlates with the perceived dissonance or unpleasantness of this mixture. While it is mainly studied in music perception, often using synthetic signals or symbolic inputs, in this paper, we focus on a practical application and investigate SD as a tool for analyzing the interactions between voices in multi-track music recordings. Using visualization and statistical analysis on an existing dataset of four-part chorales recorded with various wind instruments, we examine how timbre, tuning, and score influences SD. To do this, we introduce the notion of relative SD, which quantifies how individual voices in a multi-track recording contribute to overall SD of their polyphonic mixture. In addition to discussing practical aspects of measuring SD between and within real music signals, our case study shows potential benefits and limitations of using SD as an analysis tool in music production, for example, to inform or automate tasks like take selection or equalization.