Broadway’s Greatest Hits: A Love Affair with The Golden Ratio

Posted Jun 16, 2021

The Golden Ratio is one of the traditional topics that teachers highlight when trying to convince students that “math is everywhere.” From ancient Greek architecture to the modern design of ukuleles, that eponymous irrational number of phi can be found in the human engineering of aesthetically-pleasing products. 

We know that artists, builders, composers, and choreographers intentionally and purposively have used (approximately) 1.618 as a metric for designing that mimics the underlying natural patterns established through the Fibonacci sequence. What may be more surprising is that, even unbeknownst to their creators, the most successful theatrical performances have the Golden Ratio in the show’s bones.

Recent research (Langston, 2021) has uncovered that Cats, Miss Saigon, Phantom of the Opera, and even (arguably) the most successful contemporary musical — Les Misérables — contain pivotal composition moments occurring in intervals that can be sub-divided into 16 golden ratio points. Although these key pivots cannot be declared the reason for the critical accolades and their long-running stature, it is difficult to dismiss that a strong correlation exists between the prevalence of phi and the popularity of a show. Furthermore, according to Langston, “There is no documentary evidence from the composers that imply any intention of aligning the musicals with the golden ratio.” 

To learn more about his research and The Green Door, Lagston and Robertson’s original musical based on the Golden Ratio, visit The Conversation (The golden ratio: an ancient Greek formula could be responsible for most hit musicals). And let’s give mathematics a round of applause for keeping the footlights of Broadway afire.

Jeff Smith
MAEM Graduate Director

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