ABSTRACT What makes a musical interval consonant? Since the early Greeks, there have been two contrasting views: an “objective” approach, focusing on the mathematical relationship of frequencies, and a “subjective” approach, emphasizing auditory perception. These approaches are reviewed, as are several proposed measures of consonance. The author then presents a composition that uses intervals that are rated highly by the measures of consonance but are outside the scales of Western music and so are subjectively unfamiliar. The goal is to see whether, via repetition and other devices for overcoming unfamiliarity, the consonance of these intervals can be conveyed.