Paris, spring 1778. The 22-year-old Wolfgang Amadeus Mozart is in the city with his mother. A performance of his Sinfonia Concertante has been - he claimed - sabotaged by an Italian composer, Giuseppe Cambini, and so to make amends, the director of the public concerts series Concert Spirituel, Joseph Legros, asks Mozart to write a new symphony. It's a chance for the young composer to make his mark as a newly mature musician with a public to whom he last performed as an infant prodigy on his family's lengthy tour of Europe's courts, when he and his sister were paraded in front of Europe's aristocrats

Father Leopold isn't with his son this time, having stayed at home in Salzburg to appease their employer, Count Colloredo. In Paris, Mozart's mother is very sick, and she will die shortly after the premiere of this new symphony, his 31st, still known as the "Paris".

This D major symphony, K297, is a unique document in Mozart's symphonic canon not just for what the three-movement work does musically, but for what it tells us about how Mozart played with his audience's expectations and reactions, how he consciously manipulated them to achieve the biggest possible effect on Paris's most prestigious stage for instrumental music.

He had no great opinion of Frenchman. He played through his new symphony in private to two friends before the premiere, and wrote to his father: "They both liked it very much. I too am very pleased with it. But whether other people will like it I do not know … I can vouch for the few intelligent French people who may be there; as for the stupid ones – I see no great harm if they don't like it. But I hope that even these idiots will find something in it to like; and I've taken care not to overlook the premier coup d'archet [A fancy term that simply means all the instruments playing together at the start of a symphony, one of the contemporary fashions of the Concert Spirituel.] … What a fuss these boors make of this! What the devil! – I can't see any difference – they all begin together – just as they do elsewhere. It's a joke."

And indeed, the opening movement of the Paris symphony is one of the grandest, most thrilling sounds Mozart ever made from an orchestra. He revelled in the fact that he could use clarinets for the first time in a symphony, having heard the new instrument for the first time in Mannheim, where he had toured before coming to Paris; there are horns, trumpets, and timpani, and a full compliment of woodwind – flutes, oboes, clarinets, and bassoons, the biggest orchestra Mozart had used in a symphonic context. The very opening is almost a parody of that coup d'archet, a unison, forte D in the first two bars that releases its tension in an orchestral firework of an excitably ascending scale in semiquavers in the third bar, and the whole movement is magnificently, swaggeringly confident.

In the first performance on 18 June (after a dress rehearsal that appalled Mozart with the (s)crappiness of the orchestra - "I've never heard worse playing in my life!" - and which made him unsure whether even to turn up for the concert) the Allegro impressed the public with more than its idiot- and crowd-pleasing opening. He wrote to Leopold, "In the middle of the opening Allegro there was a passage that I knew people would like; the whole audience was carried away by it, and there was tremendous applause. But I knew when I wrote it what sort of an effect it would make, and so I introduced it again at the end, with the result that it was encored." Now, that's fascinating testimony for what it reveals about this Parisian audience, who weren't only clapping between the movements to try and get them encored, but within them, as well. There's debate about exactly which passage Mozart means – Nikolaus Harnoncourt reckons it could be the beautifully scored few bars here, with a pizzicato bass line underpinning a subtly changing harmony in the strings and sustaining chords in the woodwinds, Mozart scholar Stanley Sadie thought it could be this place, from a little later in the movement, with its chromatic lyricism; I reckon it could have been this forcibly impressive music, which rejoices in all the glorious noise Mozart can make from his luxurious orchestral forces.

In fact, the whole symphony is a kind of negotiation and collaboration with ways of listening. The Andante exists in two versions, after Legros complained that the first one had too many ideas in it, so Mozart wrote another for when the symphony was repeated on 15 August. No-one's sure which is the first and which the second, but it seems likely the more elaborate movement in 6/8 is the original, and it's this that's usually played: you can listen to the alternate version, in 3/4 time, here.

The finale proves the point most of all. Here's Mozart again: "They liked the Andante, too, but most of all the final Allegro. I'd heard that all final Allegros, like all opening Allegros begin here with all the instruments playing together, generally in unison [another blessed coup d'archet, in other words], and so I began mine with just the 2 violin, piano for the first eight bars – immediately followed by a forte; the audience (as I expected) said 'Shh!' at the piano – then came the forte. The moment they heard the forte, they started to clap. I was so happy that as soon as the symphony was over I went off to the Palais Royal and had a large ice, said the rosary, as I'd vowed to do, and then went home." More audience intervention as part of the symphony's power, and even, its composition: Mozart says he "expected" the audience to say "Shh!". Mozart is also playing with rhythm as well as dynamic at the start of this movement: the first violins are syncopated above the burble of the seconds, which means that the forte seems to come in a beat early when you first hear it. That only amplifies the pleasure of surprise of this music, something Mozart absolutely calculated to achieve.

But the finale is also a miniature masterpiece because of how it layers some brilliantly worked counterpoint underneath the surface of its public spectacle. Mozart composes a fantastic fugato in the central section of the movement, music that must have tested the togetherness of the Parisian orchestra, and which would have gone over the heads of the "idiots" in his French audience. A contemporary review, almost certainly of the Paris symphony, remarked, "the composer obtained the commendation of lovers of the kind of music that interests the mind without touching the heart." That sort of thing would become a critical commonplace in contemporary accounts of Mozart's music - that it simply contained too many ideas, too much variety, too much content. No matter. Mozart had skillfully managed to win over the idiots and the savants of his Parisian audience, and written his grandest work of instrumental music so far.

Five key recordings

All of them grandly, virtuosically, and occasionally stentorian-ly magnificent!

Nikolaus Harnoncourt/Royal Concertgebouw Orchestra

Christopher Hogwood/Academy of Ancient Music

Charles Mackerras/Scottish Chamber Orchestra

Karl Böhm/Berlin Philharmonic Orchestra

Daniel Barenboim/English Chamber Orchestra