The lingering melodies from Super Bowl commercials—the ones that burrow into your brain and refuse to leave—aren’t accidental. Increasingly, the secret to a truly catchy tune lies in mathematical principles that composers have been leveraging for centuries, often intuitively. New research suggests that symmetry, a core concept in abstract algebra, plays a surprisingly powerful role in musical memorability.
Decoding Melodies with Group Theory
Researchers at the University of Waterloo in Ontario, Canada, have been applying group theory —a branch of mathematics focused on transformations and mirrored patterns—to analyze popular melodies. By assigning numerical values to each note on the chromatic scale, they transformed songs into algebraic notation, then mapped how techniques like inversion (flipping the tune), transposition (shifting it up or down scales), retrograding (reversal), and translation (movement over time) affect song structure.
The team discovered a clear separation between tonal structure (the core harmonic progression) and positional structure (how the melody unfolds over time). This duality allows them to systematically identify and even construct symmetric melodies. As study co-author Olga Ibragimova explains, “When we think of melodies as shapes we can transform, it becomes clear that composers have been using these kinds of symmetries intuitively for centuries.”
From Theory to Practice: The Composer’s Perspective
While the math behind earworms is becoming clearer, the creative process remains complex. Composer Nick Lutsko, who penned multiple jingles for this year’s Super Bowl, admits that his approach is far from analytical. “Whenever the goal is just to write something that’s very catchy and is going to get stuck in people’s heads, that’s, like, the least I think about,” he says. For Lutsko, catchy tunes often arise spontaneously, triggered by lyrics rather than calculated equations.
Yet, even Lutsko acknowledges the power of formal training: he himself holds a degree in commercial songwriting. This suggests that while intuition plays a key role, a structured understanding of musical principles can still sharpen a composer’s toolkit.
The Future of Songwriting
The emerging intersection between mathematics and music holds potential for both composers and researchers. The University of Waterloo’s work could lead to new methods for conceptualizing music, systematically constructing melodies, and predicting which tunes will become the next inescapable earworm. However, as Lutsko points out, sometimes the most effective approach is simply to “not overthink it” and let creativity flow.
Ultimately, whether through rigorous calculation or spontaneous inspiration, the goal remains the same: to create melodies that linger in the listener’s mind long after the music stops.
