"Kinky Boots" is based on the 2005 British movie about a real-life shoe factory that struggles until it finds new life in fetish footwear. Lauper's songs and a story by Harvey Fierstein have made it a crowd-pleaser.
The haul did not match the record number of nominations for a musical, which is 15, set by "The Producers" in 2001 and "Billy Elliot" in 2009. "The Book of Mormon" nabbed 14 Tony nods in 2011.
"Matilda: The Musical" is a witty musical adaptation of the novel by Roald Dahl and is true to his bleak vision of childhood as a savage battleground.
Both will compete for the best musical prize with the acrobatic "Bring It On: The Musical" and "A Christmas Story, The Musical," adapted from the beloved holiday movie.
Among the flurry of nominations, "Kinky Boots" also earned Fierstein a nod for best book, David Rockwell got one for sets, Jerry Mitchell for directing and for choreography, and its two leading men -- for Billy Porter and Stark Sands. Annaleigh Ashford earned a featured role nomination.
"Matilda" earned nominations for choreography, Matthew Warchus' directing, Chris Nightingale's orchestrations, best book by Dennis Kelly, Tim Minchin for lyrics and songs, and Bertie Carvel for best leading role in a musical.
The best play nominees are Richard Greenberg's "The Assembled Parties," Nora Ephron's "Lucky Guy," Colm Toibfn's "The Testament of Mary" and Christopher Durang's "Vanya and Sonia and Masha and Spike."
The nominations were announced Tuesday in a televised event co-hosted by Tony winner Sutton Foster and "Modern Family" star Jesse Tyler Ferguson. The awards will be broadcast on CBS from Radio City Music Hall on June 9.
The Tony committee also said playwright Larry Kramer, author of "The Normal Heart" and co-founder of the Gay Men's Health Crisis, will receive the Isabelle Stevenson Award for a "substantial contribution" on behalf of a charity or social service organization.
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