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Background: Human melodies are generally thought of as sequences of discrete pitches: discrete categories, and also discrete / level pitches. Western musical theory does have terms for deviations from discreteness (vibrato, glissandi, scoops), but melodies, when recorded in symbolic notation, are typically defined as a sequence of discrete pitches. Here we ask, is this an appropriate description of music? Are pitches really discrete? Does the degree of discreteness vary across cultures? Is there something special about the perception of human music, or is discreteness common to other domains (bird song, human speech)? These questions are hindered by the fact that pitch-discreteness lacks a rigorous quantitative definition. Aims: To establish a rigorous, information-theoretic framework in which we can quantify the degree of discreteness. To validate this framework using human perceptual data, and to use the framework to study the above questions.