January 2013 is turning out to be a pretty major month for 20th-and 21st-century classical music in London’s cultural mainstream, with Harrison Birtwistle’s The Minotaur roaring loudly at the Royal Opera House and the Southbank Centre’s The Rest Is Noise series, a year-long celebration of 20th-century music, launching currently. But the London Symphony Orchestra showed on Thursday night that it is perfectly possible to tell eloquent, provocative stories about the 20th century through classical music with nothing more than a single, conventional orchestral programme.

This was the first of several LSO concerts this month featuring John Adams on the podium, shining a spotlight on his own music as well as his conducting talents, and it involved three different but complementary works spanning a total of around a hundred years – Bartók’s Dance Suite (1923), four of Debussy’s Cinq poèmes de Baudelaire (1890) in an orchestration by Adams, and Adams’ own Harmonielehre (1985). Only three pieces, but a veritable rainbow of influences, styles and ideas.

Bartók’s Dance Suite doesn’t show its composer at his most distinctive, despite its heavy folk leanings. Rather, it provides particularly compelling evidence for the pervasiveness of the influence of Stravinsky’s The Rite of Spring on European composition in the decade or so following its infamous première. Prominent bassoon solos, dark, stabbing string chords, and skewed neo-folk melodies all combine to make a suite which is a bracing listen on its own terms, but not particularly revelatory in the light of the rest of the century. Where Bartók sounds least like Stravinsky, though, he shows himself more open to Debussy than the astringent Russian ever was, and the Dance Suite also contains its fair share of richly Impressionistic swirls and colours. The fourth movement in particular, marked “Molto tranquillo”, sounds almost like a conversation between Debussy and Stravinsky, with full, harp-rich orchestral chords alternating with mousey woodwind melodies. The LSO’s soloists were uniformly impressive in this performance, and Adams’ spirited and driven interpretation had much to commend it as well.

If the Bartók piece spoke of a compositional face-off between Debussy and Stravinsky, the piece which followed was Debussy pitched against that senior influence of his, Richard Wagner. Debussy’s settings of poetry by Baudelaire – himself quite the Wagnerite – show their young composer part but not all of the way towards finding his distinctive compositional voice amidst the sea of Wagnerism which was French music of the later 19th century.

Adams’ sincere and sometimes rather romantic orchestration has the effect of drawing the songs a little closer to the world of Wagner, even despite the modestly proportioned, almost brass-free ensemble. It’s a discreet arrangement, never drowning out the original, but it makes a good case for its own survival, Darwinistically speaking, by doing an awful lot of things that a solo piano simply can’t – majestic horn solos, slow crescendos on held chords – but which are perfectly attuned to the original material. The LSO seemed to relish this delightful indulgence, and were themselves perfectly attuned to the night’s soloist, soprano Dawn Upshaw, whose spotless French, beautiful tone and perfect projection were a model for anyone trying to sing in the Barbican Hall.

Bartók, Stravinsky, Debussy and Wagner were all brushed to one side for the evening’s second half, which saw Adams himself pitched rather directly against Arnold Schoenberg. Although none of Schoenberg’s music was actually played, the title of Adams’ work, Harmonielehre, ensured the continued presence of Schoenberg, since this word is also the name of Schoenberg’s treatise on tonal harmony (written 1910–11, published 1922). Given the emphatically tonal nature of Adams’ music and Schoenberg’s reputation, this nod to the Austrian is generally interpreted as flatly ironic – but I don’t think it’s quite as simple as that. At any rate, it’s worth remembering that Schoenberg’s Harmonielehre is actually devoted fully to the teaching of “conventional” tonal composition of a Bach-to-Brahms type nature, despite being written during Schoenberg’s most daring atonal years. Schoenberg, as ever, is far more ambiguous a figure in music history than tends to be remembered.

Musically, though, Adams’ Harmonielehre certainly does seem to eschew the influence of Schoenberg as thoroughly as it can – though in the eerie, changeable second movement, “The Anfortas Wound”, he does declare himself open to the rest of the Austro-German canon. Mahler is explicitly recalled, the movement’s huge, dissonant climactic chords referencing the Tenth Symphony, and the presence of “Anfortas” in the title inevitably hints at Wagner’s Parsifal. But while it’s a work full of historical puzzlements, it’s also a thrilling orchestral showpiece, dynamic, accessible and provocative in a way that a lot of people don’t expect of new orchestral music.

In this piece, John Adams had an animated LSO completely in his thrall, responding in a flash to his commands and together fashioning a memorable account of this contemporary classic. For all the historical ghosts this concert summoned up, the hero of the evening was very much alive.