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The ballet had a very erratic style. Stravinsky was strongly influenced by Russian folk as well as several other popular forms of international music of the time. He was a classical traditionalist who had grown bored with the then-still-popular Romanticism going on in music. There was also a very odd choice to use the bassoon as the opening solo instrument to lead the ballet in. The instrument's tone, combined with the odd melodic structure, is known to cause unpleasantness in certain listeners.
Perhaps more famous than the work itself is the premiere it had. By the time the bassoon solo had kicked in, a riot was almost ensuing. Audience members were reportedly so loud that the music could not be heard. Infuriated audience members made cries of betrayal to classical music traditions. The clammoring only got worse as the show proceeded. Stravinsky would count it as an old shame until his older age, when the ballet started being vindicated.
What caused more of a riot than the music itself was the dancing. The choreography was very tribal and ritualistic; something that was almost unheard of in the realm of ballet. The dancers also made very sexually suggestive movements throughout the work, which proved to be quite controversial. The storyline also caused some harsh criticism, as it ended with one of the dancers (a "virgin") being sacrificed.
The sheet music still survives in full; what is missing is the original choreography program by Nijinsky. The original manuscript was missplaced and no other copies could be found. Though Joffrey Ballet made what is believed to be the most accurate reconstruction of the ballet's choreography in the 1980s, exactly how accurate it was is anyone's guess. The reconstruction was based off of descriptions of the dancers movements and some personal accounts of the dancers. This is not to undermine the reconstruction, as a lot of painstaking work was put into the detail, it is just impossible to know for sure exactly what Nijinsky intended without some sort of a manuscript.