How many times can you tell a good story? It depends on the teller, but that tends to suggest that the more a story is told the further it retreats from reality. Somebody once said that if everyone who claimed to have been at the first performance of Stravinsky’s The Rite of Spring had actually been there, you’d have needed Wembley stadium to fit them all in. Conversely, the famous riot has been so anthologised that it has now become chic in academic circles to question whether it actually happened.

Gillian Moore is not chic in this sense, but simply offers a stylish and concise account of the event, complete with the fisticuffs and catcalls, the cries of “dentist” (because of Nijinsky’s quaint choreography of the head resting sideways in the hand), the insults and general racket, the supposed arrival of the police, the terrified dancers desperately counting the sevens and elevens of complex music they could barely hear. Recent events in Paris have reminded us of the peculiar genius of the French for semi-organised violent demonstrations, and there’s not much doubt that something of the kind took place that May night of 1913 in the new, open-plan Théâtre des Champs-Élysées, though without the tear gas or the blazing cars. In art as in politics, France has always had its underground, and the Rite disturbance was almost certainly pre-planned, perhaps deliberately provoked by the publicity-conscious Sergei Diaghilev, but then, as happens with évènements, got somewhat out of hand.

Whatever it was exactly, the riot was what made The Rite of Spring famous, long before anyone had heard and seen it apart from a few thousand Parisians and Londoners (the two early Russian performances were concerts). But it wasn’t what made it great. Rowdy first performances do not a masterpiece make. Victor Hugo’s play Hernani is supposed to have ignited the 1830 July revolution in Paris, but who ever stages it now, except in the form of Verdi’s opera? The Rite has had a very different posterity, and it’s one of the strengths of Moore’s finely illustrated monograph that it supplies chapter and verse, not only on the score’s background and artistic context – material available, if less handily, elsewhere – but also, more originally, on the amazing subsequent reach of music whose ancestry was so esoteric that Stravinsky could plausibly claim it had virtually no tradition behind it and had come to him out of the blue.

Thanks mainly to the work of the US scholar Richard Taruskin (briefly acknowledged by Moore), we now understand that Stravinsky’s early ballets, The Firebird, Petrushka and The Rite of Spring itself, were a perfectly logical development of 19th-century Russian folklore nationalism. The composers of the Mighty Handful (Moguchaya Kuchka), who included Stravinsky’s teacher Nikolai Rimsky-Korsakov, had been brilliant amateurs, but Rimsky-Korsakov himself had turned professional as a conservatoire teacher, and in so doing provided a model of how a slightly crazy, off-the-wall Russianism might discipline itself into a large international force. I think Moore is mistaken in claiming that Stravinsky didn’t know how to write his music down before studying with Rimsky (privately – he was never a conservatoire student); but it’s true that, like the kuchka, he lacked, and continued to lack, proper theoretical training. What he seems to have got from Rimsky was a powerful work ethic, and a realisation that his music must always be painstakingly structured, never thrown to the four winds. In a sense, he never learnt to write “well” academically. His Paris success baffled his ex-fellow R-K pupils, who understood his limitations but not his genius. But then they stayed in St Petersburg and for the most part slotted comfortably into Soviet pedagogy; Stravinsky went west, and sped away from the inhibitions of a too-demanding academy.

Much of this Moore charts lucidly and readably. Her prehistory harks all the way back to the Decembrists of 1825, then takes in Tolstoy, the realist (Peredvizhniki) painters, the neonationalist arts-and-crafts movement of Abramtsevo and Talashkino, the World of Art (Mir Iskusstva), and the neoprimitivism of Nikolay Roerich, the scenarist and designer of the Ballets Russes Rite. This is elegant, useful contextual history, though Stravinsky did not - as she suggests - meet Roerich in 1904, and had no connection with the World of Art until commissioned by Diaghilev in 1909. No more than any other writer is she able to explain the astounding rapidity of his evolution in three or four years from the sparky Russianism of orchestral pieces such as Fireworks to the harsh brutalism of The Rite, even with the recently rediscovered Funeral Song to help. But she is right to emphasise the ritual, processional character of this latter piece as a key property of the ballet and (she might have added) a great deal of Stravinsky’s later work. Ritual isn’t just the subject matter of the Rite; it’s the essence of its musical thinking and, one could say, the crucial discovery from the more relaxed processional form of Petrushka.

Moore, director of music at the Southbank Centre in London, would be well able to write a musical study of the Rite. But this book, deliberately, is not that. Instead, she offers good summaries of the music’s essential innovations – its montage-like architecture (of which Stravinsky was rightly proud), its harmony built up vertically out of standard chords that happen not (according to the rule book) to belong together, its jagged rhythms that emerge from the changing lengths of the melodic phrases. But I could do without her blow-by-blow account of the score, a sort of musical Rough Guide for the faint-hearted; some will find it helpful, but it’s an odd thought that more than a century after its first performance and after 150 stage productions and thousands of concert performances, such a narrative should still be thought necessary.

More riveting is her account of what she calls the aftershocks: the increasingly fantastic ballet productions; the contradictory interviews with conductors – some saying no interpretation is required, others insisting, with Mirga Gražinytė-Tyla, that The Rite of Spring “must never be normal”; the composers, from Prokofiev to Andriessen and beyond, who have (let’s be honest) stolen from The Rite; and not least the jazz and pop musicians who have incorporated fragments, even whole chunks, of it in their work. There’s something curiously pleasing about Charlie Parker quoting the opening bassoon melody in “Salt Peanuts”, or jazz trio the Bad Plus making a complete version of the ballet (among other Stravinsky arrangements, not mentioned here). Frank Zappa’s obsession with Stravinsky is well known, but I had no idea how much of it found its way into his music. “I feel like taking my clothes off, dancing to The Rite of Spring,” Neil Tennant sings on the Pet Shop Boys single “I Wouldn’t Normally Do This Kind of Thing”, though the song itself, perhaps reassuringly, shows no traces of Stravinsky.

• Stephen Walsh’s Debussy: A Painter in Sound is published by Faber. The Rite of Spring: The Music of Modernity is published by Apollo. To order a copy for £16.71 (RRP £18.99) go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £15, online orders only. Phone orders min p&p of £1.99.