Music Math: Does Music Follow a Zipfian Distribution?

Presenter: Brian Best

Research Category: Interdisciplinary Topics, Centers and Institutes
PI: Brian Best

Zipf’s law is a mathematical distribution based on the proportions of different data points. Based on the development of language in early human history, the Zipfian distribution is followed by several human biological and sociological processes, including word frequency in many languages, gene expression levels, and neuron firing rates. In this project, note distribution in music was studied with the theory that if it followed a Zipfian distribution, it might explain why humans like music, as it would match the natural math of our bodies and brains. Twenty-two songs from a variety of genres, time periods, composers, and cultures were analyzed for note frequency distributions. These frequencies were graphed and compared to the ideal Zipfian distribution for each song. Rather than following a Zipfian distribution, it was found that the music followed a different pattern, and this pattern followed a similar shape for every song studied. This indicates that there is an innate neurological pattern followed cross-culturally and through time when writing music. We may like music as a species, not because it follows the natural pattern of our brains, but because it deviates from what we are used to. This result opens doors to finding exactly what makes music so appealing, and it extends to the realms of music therapy and music experimentation using mathematics.