There’s something quite strongly “neoclassical” about the whole historically-informed performance movement. Someone like Sir John Eliot Gardiner, who has championed the use of detailed historical knowledge of performance practice and instruments, has never actually been attempting to transport us all back to the 18th century. That would be futile, obviously. Part of the aim has surely always been to let us hear the past with fresh ears, to give new context to music otherwise familiar – to make something new from something very old. During Stravinsky’s long “neoclassical” compositional period, in which he flirted with traditional forms and styles in all manner of bizarre ways, he was out to do something similar.

So in a sense it’s no surprise that Gardiner should take to the neoclassical Stravinsky. What’s remarkable is how frighteningly good he is at it. At his 70th birthday concert at the Barbican, Gardiner, the London Symphony Orchestra, the Gentlemen of the Monteverdi Choir and some excellent soloists delivered delicious renditions of two of Stravinsky’s most contrasting neoclassical compositions: Apollon Musagète (1928) and Oedipus Rex (1927). It’s hard to imagine finer performances of either piece.

Oedipus Rex is problematic, usually. An “opera-oratorio” after Sophocles with libretto written by Jean Cocteau and then translated into Latin, it’s a piece which finds Stravinsky at his most deliberately obtuse. Not only does he choose to have the words in a language incomprehensible to most of the audience, but any sense of dramatic unfolding is also pre-empted by the (French-speaking) narrator, who explains precisely what’s going to happen just before it does. Out-Brechting Brecht, Oedipus Rex is almost obsessively focused on its own artificiality, and in Stravinsky and Cocteau’s hands the result is something often hard to love. Musical commentary on it, moreover, most often gets stuck on Stravinsky’s particularly flagrant polystylism: he flits capriciously from Handel to Verdi every couple of minutes, with shades of Mozart thrown in as well, and it can be difficult to take the whole thing seriously.

None of this, though, seemed to have much bearing on Gardiner’s vision. Beneath Oedipus Rex’s rather austere facade is a piece of music with all Stravinsky’s customary wit and vibrancy. Gardiner not only coaxed out this side of the piece, but he also found a dramatic thread throughout, which made Stravinsky’s odd mood shifts and unlikely musical decisions all fit rather well.

One key moment is the duet between Oedipus and Jocasta, shortly before their true identities become apparent. The dramatic tension is undercut by some of the lightest, frothiest music in the whole work, with graceful lines and elegant orchestral flourishes galore. Gardiner simply treated this as the fun orchestral showpiece it really is, allowing the music to go against the drama and hence work its perplexing effect. The frequently jarring relationship between words and music was described by Leonard Bernstein as a “black joke”. I get the impression Gardiner and Stravinsky might share a sense of humour.

Gardiner, his Monteverdi Choir and the LSO have teamed up for neoclassical Stravinsky before, in a recording of The Rake’s Progress. The collaboration here was no less successful than on that wonderful CD, with a sense of precision and a keen ear for details. The LSO were on typically fine form, but it was the men of the Monteverdi Choir, impeccable throughout, who were most striking (and not just because of the strange white face-paint they were sporting). Stravinsky isn’t kind to his soloists, often writing orchestral parts far more interesting than the vocal lines, but Stuart Skelton still managed to shine as Oedipus. Gidon Saks, a luxury piece of casting for the one-aria role of Creon, probably made as much of an impression as he could in the time available to him, though I was on the other side of the hall and couldn’t make him out as well as I would have liked. Mezzo Jennifer Johnson was a powerful, graceful Jocasta with gorgeous tone and marvellous diction. The three soloists drawn from the chorus – Alexander Ashworth, David Shipley, and one unfortunately not named in the programme – gave contrasting but highly effective contributions too. Fanny Ardant’s narration was also a great success.

What’s more, all of this was preceded by Apollon Musagète in the first half, which is among Stravinsky’s most straightforwardly beautiful compositions. The modestly-sized string orchestra, with violins and basses standing in a tight semicircle around the seated inner parts, produced an elegant, full sound for this mellifluous, often indulgent piece. From the deepest of pizzicato twangs to the lightest of trills, this picture-perfect rendition gave the impression that not a single detail in the score had gone unnoticed.

It speaks of a sense of adventure that Gardiner chose Oedipus Rex for his own birthday concert, having apparently never conducted it before. Here’s to more adventures such as this one, which turn the familiar into something vital and fresh.