La La Land uses vivid primary colors in a way that mimics moments in Gene Kelly's masterpiece. Both films also feature romances set against the backdrop of the movie business.
La La Land directly draws on the final ballet of Vincente Minelli's Oscar winning classic. The George Gershwin score from this film, like La La Land, is inspired by jazz.
Jaques Demy's technicolor french musical has been mentioned as a direct inspiration by Chazelle himself. The gorgeous technicolor photography and the emotional mixture of joy and sadness are very much a part of both films. Demys The Young Girls of Rochefort is also clearly an inspiration.
While there are many forms of dance used throughout La La Land, there are two sequences where Emma Stone and Ryan Gosling are waltzing in a way that is inspired by the great work of Ginger Rogers and Fred Astaire in their greatest film, Swing Time.
If I had to pick a movie that La La Land reminds me of, the closest I think of is Woody Allen's Everyone Says I Love You. This film features actors who are not known for either singing and dancing doing both. It also features dancing in the air and in the city of Paris.
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