Alicia Keys has been working on “Hell’s Kitchen” for 13 years, so she found it serendipitous — in addition to thrilling — that on Tuesday morning her musical picked up 13 Tony nominations.

In an interview shortly after the nominations were announced, Keys was clearly heartened by the news. The show, featuring her songs and a book by Kristoffer Diaz, is personal for Keys. The show is about a 17-year-old girl whose life circumstances have enormous echoes of Keys’s own upbringing — the single mother, the hunger for independence, the passion for piano, even the same subsidized housing development.