Boffin finds ‘golden’ Ancient Greek maths formula proving why we love musicals

A researcher has discovered the hidden link between an ancient Greek mathematical formula and hit musicals like Cats and Grease.

Maybe the next time you're singing along to 'My shot' from Hamilton, you'll wonder if there's some secret mathematics hidden in there too.

According to Stephen Langston, programme leader for performance at the University of the West of Scotland, there’s actually an ancient Greek formula behind these hit musicals called the golden ratio.

While they may be accidental, Langston firmly believes that the golden ratio is very much present in hit musicals like Jesus Christ Superstar.

Not sure what the golden ratio is? Let us explain in fairly simple terms.

It’s basically an ‘irrational number’ (1 +√5)/2) which is approximately equal to 1.618. It exists when a line is divided into two parts where one part is longer than the other.

The longer part, which in this case is (a), divided by the smaller part (b) is equal to the some of (a) + (b) + divided by (a) – which both equal 1.618.

So, it turns out that actually ended up being pretty confusing. But how on earth is this equation behind key musicals like Jesus Christ Superstar? Well, it seems that the musical design (visual, music, plot) has some interesting elements at golden ratio points throughout.

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Stephen was always interested in how the golden ratio had been used in music since studying it at Liverpool University. His fascination with musicals and popular songs made him realise that a lot of 'interesting things' seem to happen in songs about two-thirds of the way through.

He said: "I started a PhD at UWS, and it was aspects of this research that uncovered the close relationship to the golden ratio and sung through musical form. The entire PhD took six years to complete (part-time) but this also involved testing my theories out via writing a full scale sung through musical ( The Green Door) .

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"It was discovered that it is very difficult to create a musical in a golden ratio format without exceptional planning, so a guide, structure format and template was created directly from the PhD research to help other composers try the process. This system is now being tested (nicknamed the Marley System, as it was created when my first son was born)."

The eureka moment was at about three in the morning after Stephen had spent months analysing and calculating various golden ratio patterns. When the calculations were programmed into his spreadsheet it all clicked.

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He added: "I was astonished to discover, not that the main synopsis points occurred at golden ratio points, but how accurately they occurred, and continued to occur.

"What became even more interesting was then analysing a further ten west end musicals to discover they all shared the same characteristics and matched the golden ratio – some with greater accuracy than others, however, the match was there."

Major changes throughout the plot matched with all 16 golden ratio points that were originally divided by Stephen. Examples of these key elements could be a dramatic moment, a character death, a key change or visual change like a set change, or change in choreography.

It’s not just Jesus Christ Superstar that shows elements of the golden ratio though. Have you ever heard of a little musical called ‘Les Misérables’? Well, key main characters Fantine, Eponine, Gavrosche and Valjean all died very close to, or on a golden ratio point.

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After analysing it even further, Stephen discovered that the further a musical was away from the golden ratio, the less successful the musical was in box office duration. For instance, Les Miserables and Phantom of the Opera have a 99% accuracy match.

"The musical Chess was additionally analysed and demonstrated one of the least matches to the GR (however, there was still a match). Tim Rice has famously said on several occasions he got the story wrong, and the Marley system backs that up. Who knows, if Tim utilised the system, you never know, he might get a Les Miserables type box office run which obviously translates into box office success."

Don't be put off if there is no evidence of a golden ratio in a musical though, Stephen said: "Musicals do not need the golden ratio to be a hit. Musicals are hits because of the genius composers, writers and producers who team together to create wonderful pieces of art.

However, the research is demonstrating that the Marley System can be used as a guide to create sung-through musicals which gives the structure a solid form that can be associated with our most successful musicals. To get a hit, you need to marry your story with appropriate melodies, lyrics, harmonies, dance, costume, set, lighting etc – and a lot of luck."

Stephen is now utilising the Marley System to compose a new 2-hour concert piece of music for orchestra and choir, The Scottish Fantasia. The story structure has been mapped out and soon to be divided into time durations to create a perfect match to the golden ratio.

"When I composed The Green Door as part of my research the process was utilised to try ideas out – ‘let’s see what would happen’. The results led to the creation of the Marley system which can now be utilised to create an exact match of the golden ratio in durational form. It’s up to the composer, lyricists, and story writers to get the rest right.

"The next stage of the research is to analyse concert music and non-sung through musicals. Who knows what we will find there, but I would not be surprised to find a golden ratio match!"

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