We know that Igor Stravinsky became practically an overnight success in Paris after the first performance of Michel Fokine's Firebird by Sergei Diaghilev's Ballets Russes at the Théâtre National de l'Opéra on June 25, 1910. He was befriended by not only the height of Parisian society but also its leading composers of the day, including Claude Debussy, Maurice Ravel, and Erik Satie. Those who have analyzed Stravinsky's scores scrupulously have come up with any number of instances of "cross-fertilization" between him and Debussy going in both directions. However, less has been written about the influence of Satie; and this may deserve further attention.
For example, the timing of events is such that it is very likely that Stravinsky would have been exposed to (if not performed) Satie's four-hand suite, Aperçus Désagréables, whose three movements are a pastorale, a chorale, and a fugue. It is not out of the question that Satie's evocation of these "ancient" forms may have planted the first seed of neo-classicism in Stravinsky's consciousness. Indeed, Satie's outrageously "anti-harmonic" approach to chorale writing may have provided an incentive for Stravinsky's own take on that form after he had to give up the high life of Paris for exile in Switzerland. This would predate what Stephen Walsh, author of the Grove Music Online entry for Stravinsky, sets as the beginning of Stravinsky's neo-classical period in 1920; but the chorale was a great bastion of classical thinking. Stravinsky probably could not resist the temptation to deliver it a raspberry that would outdo Satie's earlier efforts. (There are two more of these chorales in Satie's En Habit de Cheval.) The pastorale and fugue would surface in somewhat more distinguished form after 1920, but it seems reasonable to assume that Stravinsky started his wheels rolling with the chorale in his music for Charles Ferdinand Ramuz' The Soldier's Tale. Besides, I find it hard to believe that Stravinsky could have covered all of the ground he did without acknowledging Satie's influence!