There are two different musicals based on The Great Gatsby, the production of The Great Gatsby A New Musical starring Jeremy Jordan and Eva Noblezada currently playing on Broadway, and Gatsby An American Myth currently playing at American Repertory Theater with music by Florence Welch from Florence and the Machine. Each are wildly different takes on the source material focusing on different characters, themes, and aspects of the novel to varying effects.
I saw Gatsby on May 25th in case anything has changed since then.
0:00 Intro
2:47 General Approach
7:08 Score
9:23 Casts
13:50 Physical Productions
18:52 Overall