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The concept of dissonance in music perception has been variously associated with the physical concepts of roughness, instability, and tension by appealing to a subjective cross-sensory analogy. For all the subjectivity around the term, it is noteworthy that non-musical test subjects in clinical experiments have produced remarkably consistent rank-orderings of musical sounds, according to the perceived dissonance of those sounds. Further studies in psychology, neuroscience, and mathematics show that consonance perception appears to be influenced not only by convention and culture but by the psychoacoustics of sound perception, likely by some combination of the Helmholtz theory of roughness and the theory of harmonicity originally contemplated by Galilei. In this work, we elaborate on Stolzenburg's relative periodicity, a harmonicity metric that can be computed in the time domain by neuronal systems. We aim to determine whether relative periodicity can be extended from pure sinusoids to empirical audio signals, and whether such extension would still yield dissonance rankings that comport with the known experimental perceptions of dissonance. By drawing on the theory of quasi-periodic signals, we show that the relative periodicities of many familiar dyads and triads agree with Stolzenburg's calculations and experimental dissonance rankings. However, we also observe substantial departures from Stolzenburg's work in the case of the most highly empirically dissonant dyads and the diminished triads. This discrepancy likely supports the work of Masina et al. that found periodicity unable to fully explain empirical studies of dyad dissonance.