Get the Popular Science daily newsletter💡 Breakthroughs, discoveries, and DIY tips sent six days a week. It’s not your fault if a 30-second advertisement spot’s melodic hook continues to keep you up at night, however. “Our goal was to build a clear mathematical bridge between abstract algebra and the experience of listening to music,” said study co-author Olga Ibragimova. “What surprised us is how cleanly the mathematics separates tonal structure from positional structure,” explained systems design engineer and study co-author Chrystopher Nehaniv. “I know [people] talk about algebraic equations and the math or science behind songwriting, but to me it’s almost supernatural.