psychoacoustic theories of dissonance often follow Helmholtz and attribute it to partials (fundamental frequencies or overtones) near enough in frequency to affect the same region of the basilar membrane and therefore to cause roughness, i.e., rapid beating. In contrast, tonal theories attribute dissonance to violations of harmonic principles embodied in Western music. We propose a dual-process theory that embeds roughness within tonal principles. The theory predicts the robust increasing trend in the dissonance of triads: major < minor < diminished < augmented. Previous experiments used too few chords for a comprehensive test of the theory, and so Experiment 1 examined the rated dissonance of all 55 possible three-note chords, and Experiment 2 examined a representative sample of 48 of the possible four-note chords. The participants' ratings concurred reliably and corroborated the dual-process theory. Experiment 3 showed that, as the theory predicts, consonant chords are rated as less dissonant when they occur in a tonal sequence (the cycle of fifths) than in a random sequence, whereas this manipulation has no reliable effect on dissonant chords outside common musical practice.