Did Stravinsky sleep with men? Does it matter?

Those questions have been percolating through the worlds of music and dance since the publication of a quietly inflammatory essay by the writer and musician Robert Craft in the June 21 issue of The Times Literary Supplement.

Mr. Craft, 89, was Stravinsky’s confidant and literary collaborator in his final decades and has for many years written his own accounts of the composer’s life and work. His essay appeared on the heels of his latest book, “Stravinsky: Discoveries and Memories” (Naxos), which repeats its most provocative assertions, blending the artistic, historical and personal.

Mr. Craft contends first that Stravinsky’s creative influence over the epochal 1913 ballet “The Rite of Spring,” particularly its choreography, was far greater than has been assumed. And then there’s the gay thing.

“It will come as a surprise to most people,” Mr. Craft writes in the book, “that in the early Diaghilev period” — the years following 1909, when Stravinsky began collaborating with Sergei Diaghilev’s Ballets Russes — “Stravinsky was exclusively in an ambisexual phase while writing ‘Petrushka’ and ‘The Rite of Spring.’ ”