Somewhere deep within the working heart of the National Gallery of Australia in Canberra, in a part of the building visitors never get to see, is an area made up of rows and rows of broad timber cabinets, each shallow drawer numbered and each containing a Ballets Russes costume. One, architectural in inspiration, is by de Chirico; another, boldly geometric and made up of black-out material, is by Matisse. Yet another shows Natalia Goncharova’s modernist take on the Russian peasant.

In one, like all the others in a padded bed-like arrangement with pale green satin sheets covering it, is Petrouchka’s costume: a cotton tunic with red and blue satin ribbons around the zigzag hem; pink satin cuffs; a tightly gathered circular collar; and a pair of trousers, made up of large squares of pink and yellow satin. The little blue boots that go with it are somewhere else.

Most of the costumes were bought at auction in London in 1973 by James Mollison, the gallery’s founding director, as a way of looking at how the performing arts relate to the bigger picture of contemporary art. Since then, the gallery has built up the collection, expanding it to include artists’ drawings of...