Igor Stravinsky died 40 years ago today. I find this astonishing – partly because Stravinsky seems to belong to another era: a century ago, he was conceiving and composing The Rite of Spring, and yet we are only separated by him by just over a generation, and yet his influence and his legacy still seems so contemporary.

Stravinsky is the only common influence that composers from Steve Reich to Thomas Adès, from Judith Weir to John Adams, from Elliott Carter to Louis Andriessen, can all agree on. Without Stravinsky, there would be no minimalism, not much neo-classicism, not enough rhythmic energy, and not nearly enough compositional freedom in the 20th and 21st centuries. Four decades on, the Stravinsky that's proved most popular with audiences, orchestras and concert halls is the colouristic brilliance of the three early ballets, Firebird, Petrushka, and the Rite.

Nothing wrong with that, but to commemorate this anniversary, treat yourself to the less familiar Stravinsky, especially those crystalline pieces of the late, serial period, including my favourite, the Variations: Aldous Huxley in Memoriam, a work that packs more drama, punch, and density into its six minutes than some composers manage in a lifetime. (And while you're at it, explore much of the rest of Stravinsky's late music, including The Flood and Movements for Piano and Orchestra, on NewMusicXX's brilliant channel, on which you could all too easily lose weeks of your life.)

And from the other end of his life, and another world of expression, astonish yourself – if you don't know it! – by the joyous tune-fest of the first movement of Stravinsky's Op 1, his Symphony in E Flat. Stravinsky was a pupil of Rimsky-Korsakov, and the piece is dedicated to his teacher, who sat next to the 25-year-old Igor at the first run-through, and told him to be careful when writing for trombones in their middle register. The journey between the 1907 Symphony and the 1964 Huxley Variations is one of the most astonishing creative odysseys in the history of the 20th century. Find some time this week to marvel anew at Stravinsky's ceaselessly contemporary brilliance.