Drawing inspiration from the notion of cognitive incongruence associated with Stroop's famous experiment, from musical principles, and from the observation that music consumption on an individual basis is becoming increasingly ubiquitous, we present the SoundSignaling system -- a software platform designed to make real-time, stylistically relevant modifications to a personal corpus of music as a means of conveying information or notifications. In this work, we discuss in detail the system's technical implementation and its motivation from a musical perspective, and validate these design choices through a crowd-sourced signal identification experiment consisting of 200 independent tasks performed by 50 online participants. We then qualitatively discuss the potential implications of such a system from the standpoint of switch cost, cognitive load, and listening behavior by considering the anecdotal outcomes of a small-scale, in-the-wild experiment consisting of over 180 hours of usage from 6 participants. Through this work, we suggest a re-evaluation of the age-old paradigm of binary audio notifications in favor of a system designed to operate upon the relatively unexplored medium of a user's musical preferences.