Is math the secret to musicals? A formula known to the ancient Greeks could help explain why West End shows succeed or fail, a British academic has found.
Commercial successes such as Les Misérables, The Phantom of the Opera and Cats correspond to the “golden ratio” of balance and harmony, also found in artifacts such as the Mona Lisa and Notre-Dame.
Shows that suffered at the box office, including Chess and Martin Guerre, do not come close, suggesting a link between the ratio and commercial success.
“It was a eureka moment,” said Stephen Langston, a lecturer at West of Scotland University, who made the discovery during studies for his PhD.
The golden ratio, or divine proportion, of one to 1.618, was first identified by Euclid more than 2,300 years ago and is associated with beauty, such as the proportions of the Mona Lisa’s face and nature. The numbers of petals on flowers, shapes of shells and way trees divide into branches appear to follow a sequence named after the Italian mathematician Fibonacci. As the sequence continues the ratio between successive numbers comes closer and closer to the golden ratio.
The golden ratio is also linked to architectural masterpieces including the Eiffel Tower, paintings such as The Last Supper and musical compositions by Mozart. But its existence in musical theater was previously undiscovered.
The golden ratio, or divine proportion, of one to 1.618, was first identified by Euclid more than 2,300 years ago and is associated with beauty, such as the proportions of the Mona Lisa’s face and nature.
Langston analyzed the structure of several musicals. He divided the duration of each work by 1.618 to establish a first golden ratio point. Langston then subdivided each of the resulting two sections again to establish further golden-ratio points.
The lecturer mapped the timings that resulted against major moments in the musical, such as a dramatic change of key or death of a character.
Les Misérables and Phantom of the Opera, two of the highest-grossing musicals of all time, had major plot points within 1% of where they should be according to the golden-ratio structure.
In Les Misérables, for example, the music dramatically shifts about 62% of the way through, as the barricades are revealed to mark the beginning of the 1832 Paris Uprising. At the same point in Phantom of the Opera, the Phantom returns after everyone thought he had gone for good.
Claude-Michel Schönberg, who composed the music for Les Misérables, denies using any mathematical formula. When Langston interviewed him, he said: “I always write from scratch. As each story is completely different, I will never use the same kind of melody … when I am starting to write a musical, I am starting from the first note.” The research suggests the ratio may be applied subconsciously.
Stuart MacRae, a senior lecturer in composition at the Royal Conservatoire of Scotland, said: “Arguably, any work of art is most effective when it’s well-proportioned, and when it’s a dramatic work it’s important that the audience’s attention span and interest is carefully managed and guided through the story.
“It’s quite probable that we might feel especially satisfied by a musical theater work in which the second part feels slightly shorter than the first part.”
Chess closed after a box office slump. Critics described the plot as unfocused with no shifts in energy level. Martin Guerre also failed.
The plot points of both are not where they should be, according to Langston’s calculations.
He says the golden ratio is “one tiny element in the musical construction” along with the score, lyrics, story, costume, set and lighting.
“It doesn’t mean your musical will be successful, but it does mean you are modeling your musical on things that we know have worked,” Langston said.