Musical behavior predates the emergence of Homo sapiens and primitive song could have evolved in primates 65 MYA, convergent with and independent of its emergence in Aves and Cetaceans. The avian literature uses quantitative metrics such as trill rate, consistency, repertoire size, song bout length, and complexity to evaluate song quality. There have been few analogous efforts to quantify the aesthetic qualities of primate vocalizations. We developed a novel method to quantify the elaborateness of acoustic displays using published spectrograms of primate vocalizations (n=832 calls). These spectrograms (plots of acoustic energy across both frequency and time) were visually scored along the following ethnomusicologically universal acoustic parameters: tone, interval, transposition, repetition, rhythm, and syllabic diversity. Principal components analysis was used to reduce the scores to a single univariate measure of musical elaborateness. The resulting index is mathematically defined as the expected number of syllables reappearing within a call. Specifically it is the count of unique syllables multiplied by the probability that any given unit reoccurs over time or at different frequencies. This “reappearance diversity” correlated well with vocal display contexts. To test the general utility of the index we explored popular co-evolutionary theories on the function of song such as group and pair level signaling as well as the acoustic [habitat] adaptation hypothesis. Species that live in monogamous family units (2-5 individuals) had higher index values. Reappearance diversity was not related to habitat as would have been consistent with the acoustic adaptation hypothesis.