The golden ratio: an ancient Greek formula could be responsible for most hit musicals

May 17, 2021 | Location Clayton Ladue

The golden ratio: an ancient Greek formula could be responsible for most hit musicals

John Gomez/Shutterstock

“What’s the secret to your success?” A simple question asked frequently of those who have achieved greatness in their field. Sometimes, that secret is so well disguised even the successful individual is unaware of its influence.

When it comes to sung-through musical theatre, it turns out, that is indeed the case. Since 1972, when Jesus Christ Superstar premiered on Broadway, the most popular sung-through musicals have almost unanimously employed a centuries-old formula known as “the golden ratio” – and surprisingly, they appear to have done so completely by accident.

The golden ratio is an irrational number approximately equal to 1.618. It exists when a line is divided into two parts, with one part longer than the other. The longer part (a) divided by the smaller part (b) is equal to the sum of (a) + (b) divided by (a), which both equal 1.618.

The ratio is found in nature, such as in the patterns of seeds within a sunflower, the shape of snail shells and, most recently suggested, in the human genome. Its connection with the aesthetic beauty of nature has attracted creatives throughout history to use the number to create art, music, and design.

When appropriately applied, the golden ratio is suggested to demonstrate an influence on human awareness of proportion and aesthetic beauty, resulting in artistic masterpieces including Da Vinci’s The Mona Lisa (1506), Bartok’s Music for Strings, Percussion and Celesta (1936) and Le Corbusier’s Unité d’Habitation (1920).

A surprising discovery

My area of expertise is musical theatre composition, and for my PhD research, I explored if the golden ratio would be a suitable tool for large musical composition. The 3D nature of musical design (plot, music, visual) allows for interesting elements to be integrated into a musicals structure at golden ratio points along its duration. These elements could include a dramatic moment such as a character death, a musical highlight such as a key change or a visual element such as choreography or a set change.

The crucial factor was to take the most important elements that bring a musical to life and place them at the golden ratio points. In theory, this replicates aesthetically pleasing patterns found in nature but recreated in a musical. The concept of my research was to use the results of analysis of the ten most successful sung-through commercial musicals.

This process helped to formulate a structure encompassing the golden ratio which I used to compose the musical The Green Door (with lyrics by Jane Robertson).

To analyse the musicals, I designed a model that sub-divided the duration of each into 16 golden ratio points. I then could identify if, what and where any interesting elements occurred.

You can imagine my astonishment when, early one morning, my calculations revealed that within Les Miserables, the principal characters of Fantine, Eponine, Gavrosche and Valjean all died on or very close to a golden ratio point. Further analysis revealed that major changes in the story line (matching to within less than 1%) coincided with all 16 golden ratio points.

The same process was applied to a further nine musicals, including Phantom of the Opera, Cats, Miss Saigon and Aspects of Love. The results displayed similar patterns but interestingly, a difference in accuracy became evident in musicals that had a shorter life-span at the box office. In essence, musicals that had the most box office success and longevity of run showed closer alignment to the golden ratio than those that had a shorter run, and less financial gain.

Unwitting followers of the ratio

The research highlighted another interesting phenomenon. There is no documentary evidence from the composers that imply any intention of aligning the musicals with the golden ratio.

Claude Michelle Schoenberg (composer of Les Miserables) kindly agreed to be interviewed concerning his method of composition. It was evident that no mathematical formula was included in that process. The discovered alignments are natural occurrences implemented by composers, writers and producers with years of experience, knowledge and talent in the musical theatre industry.

It would be wrong to assume a subconscious usage of the golden ratio is evident in the findings and I make no claim that it’s responsible for the success of the musicals analysed. But like in the works of Debussy, Bartok, Da Vinci and Le Corbusier, the ratio is there.

After seven years of research, I now believe, an aesthetic link to the ratio exists not just in the final work but primarily throughout the process of creation. The nurturing of ideas, the reflective process, the discovery of common elements, experience and self confidence in your own ability and skills combine to create an aesthetic process. This can only benefit the music and is seemingly influenced by that magic golden ratio.

So if you would like to put this to the test, I have created a spreadsheet that takes into account the theoretical and practical research and, with no guarantees, might help write the next blockbuster musical.

Locations near
ME
Ashburn 0.93 mi
43330 Junction Plaza
#160
Ashburn, VA 20147
Sterling 4.07 mi
44 Pidgeon Hill Drive
#100
Sterling, VA 20165
Leesburg 5.69 mi
521 E Market St
#B
Leesburg, VA 20176
Herndon 7.66 mi
2465 Centreville Road
#J2
Herndon, VA 20171
Stone Ridge 7.88 mi
42020 Village Center Plaza
#100
Stone Ridge, VA 20105
Reston 8.62 mi
1424 North Point Village Center
Reston, VA 20194
Purcellville 12.72 mi
1020 E Main St
Ste L
Purcellville, VA 20132
North Potomac 13.58 mi
12150 Darnestown Rd
Gaithersburg, MD 20878
Centreville 14.52 mi
5959 Centreville Crest Ln
Centreville, VA 20121
Fairfax 14.67 mi
11891 Grand Commons Ave
Fairfax, VA 22030
Potomac 14.98 mi
10232 River Road
#B
Potomac, MD 20854
Germantown MD 15.03 mi
12800 Middlebrook Road
Germantown, MD 20874
Tysons 15.45 mi
328 Maple Ave E
#A
Vienna, VA 22180
Haymarket 17.87 mi
15125 Washington St
Haymarket, VA 20169
Rockville 18.19 mi
20 Courthouse Square
#106
Rockville, MD 20850
Mclean 18.23 mi
1320 Old Chain Bridge Road
Suite #190
McLean, VA 22101
Gaithersburg 18.71 mi
9132 Rothbury Drive
Gaithersburg, MD 20886
North Bethesda 20.42 mi
5268 Nicholson Ln
#N
Kensington, MD 20895
Falls Church 20.59 mi
6674 Arlington Blvd
Falls Church, VA 22042
Manassas 20.65 mi
9722 Liberia Ave
Manassas, VA 20110
Bristow 20.71 mi
12705 Braemar Village Pz
Bristow, VA 20136
Burke 20.82 mi
9411 Old Burke Lake Rd
#C
Burke, VA 22015
Bethesda 21.3 mi
4918 Fairmont Ave
Bethesda, MD 20814
Annandale 21.64 mi
7000 Columbia Pike
Annandale, VA 22003
Damascus 22.77 mi
9815 Main St
Damascus, MD 20872
Arlington, VA 23.29 mi
4801 1st St N
Arlington, VA 22203
Cathedral Heights 23.51 mi
3706 Macomb St NW
Washington, D.C., DC 20016
Olney 23.96 mi
18157 Village Center Dr
Olney, MD 20832
Downtown Silver Spring 24.94 mi
1133 East West Highway
Silver Spring, MD 20910
Lorton 25.06 mi
9027 Silverbrook Rd
#A
Fairfax Station, VA 22039
West Washington 25.69 mi

Washington, DC 20009
Alexandria City 25.7 mi
4605 Duke Street
Alexandria, VA 22304
Lake Ridge 26.5 mi
12473 Dillingham Square
Lake Ridge, VA 22192
Frederick North 26.7 mi
905 W. 7th Street
Frederick, MD 21701
Northern Silver Spring 26.75 mi
732 Cloverly Street
Silver Spring, MD 20905
Alexandria 27.17 mi
6483 Old Beulah Street
Alexandria, VA 22315
Warrenton 27.42 mi
512 Fletcher Drive
Warrenton, VA 20186
Mount Airy 28.24 mi
411 E Ridgeville Blvd
Mt Airy, MD 21771
Capitol Hill DC 28.48 mi
621 Pennsylvania Ave SE
1st-floor unit
Washington, DC 20003
Dale City 28.99 mi
5512 Staples Mill Plaza
Dale City, VA 22193
Mount Vernon 29.66 mi
7696 H Richmond Hwy
Alexandria, VA 22306
Beltsville 30.89 mi
10914 Baltimore Ave
#B
Beltsville, MD 20705
Clarksville 31.56 mi
12250 Clarksville Pike
#D
Clarksville, MD 21029
Laurel 35.02 mi
10095 Washington Blvd N
#136
Laurel, MD 20723
Woodmore 35.27 mi
9101 Woodmore Centre Drive
Lanham, MD 20706
Glenn Dale 35.83 mi
10559 Greenbelt Rd
Lanham, MD 20706
Sykesville 36.57 mi
1207 Liberty Rd.
#D-104
Sykesville, MD 21784
Ellicott City 37.11 mi
3290 Pine Orchard Lane
#B
Ellicott City, MD 21042
Winchester 37.62 mi
2512 S Pleasant Valley Rd
Winchester, VA 22601
Columbia 38.19 mi
8827 Centre Park Drive
#F
Columbia, MD 21045
Stafford 39.58 mi
263 Garrisonville Road
#104
Stafford, VA 22554
Bowie 41.26 mi
15231 Hall Rd
Bowie, MD 20721
Waldorf 42.24 mi
3022 Festival Way
Waldorf, MD 20601
Crofton 42.6 mi
1153 Route 3 North
#120
Crofton, MD 21054
Owings Mills 44.15 mi
9433 Common Brook Rd #100
Owings Mills, MD 21117
Pikesville 46.84 mi
1433 Reisterstown Rd
Pikesville, MD 21208
Dunkirk 49.92 mi
10735 Town Center Blvd
#7
Dunkirk, MD 20754