Abstract: Basic principles of the theory of harmony reflect physiological and anatomical properties of the auditory nervous system and related cognitive systems. This hypothesis is motivated by observations from several different disciplines, including ethnomusicology, developmental psychology, and animal behavior. Over the past several years, we and our colleagues have been investigating the vertical dimension of harmony from the perspective of neurobiology using physiological, psychoacoustic, and neurological methods. Properties of the auditory system that govern harmony perception include (1) the capacity of peripheral auditory neurons to encode temporal regularities in acoustic fine structure and (2) the differential tuning of many neurons throughout the auditory system to a narrow range of frequencies in the audible spectrum. Biologically determined limits on these properties constrain the range of notes used in music throughout the world and the way notes are combined to form intervals and chords in popular Western music. When a harmonic interval is played, neurons throughout the auditory system that are sensitive to one or more frequencies (partials) contained in the interval respond by firing action potentials. For consonant intervals, the fine timing of auditory nerve fiber responses contains strong representations of harmonically related pitches implied by the interval (e.g., Rameau's fundamental bass) in addition to the pitches of notes actually present in the interval. Moreover, all or most of the partials can be resolved by finely tuned neurons throughout the auditory system. By contrast, dissonant intervals evoke auditory nerve fiber activity that does not contain strong representations of constituent notes or related bass notes. Furthermore, many partials are too close together to be resolved. Consequently, they interfere with one another, cause coarse fluctuations in the firing of peripheral and central auditory neurons, and give rise to perception of roughness and dissonance. The effects of auditory cortex lesions on the perception of consonance, pitch, and roughness, combined with a critical reappraisal of published psychoacoustic data on the relationship between consonance and roughness, lead us to conclude that consonance is first and foremost a function of the pitch relationships among notes. Harmony in the vertical dimension is a positive phenomenon, not just a negative phenomenon that depends on the absence of roughness—a view currently held by many psychologists, musicologists, and physiologists.