Take the question of identity. French to the last shimmer of a Debussyan chord, raised under the heel of German occupation, Boulez chose to make his home among Germans in Baden-Baden. He spoke fluent German and English with a self-mocking ’Allo, ’Allo accent. He composed e e cummings ist der dichter as a kind of parody, a Frenchman setting an American poet’s words to a German title.

There is a wilful evasiveness in his titles. Le Marteau sans Maître, his 1955 breach with mathematical serialism, translates as “the masterless hammer” while exercising micro-control of a mezzo voice and six instruments. Éclat, literally “high style”, is substantive, altogether unshowy. Répons evokes the responsorium of his Catholic youth. Boulez rejected all religion; his memorial service was celebrated, nonetheless, in the church of Saint-Sulpice. This is a man who hid behind self-contradictions.

He could, of course, be clinically precise, devastatingly offensive. Composers who denied the historic necessity of Schoenberg-Webern serialism he declared to be “superfluous”. Britten was “bourgeois”, Shostakovich “conservative”. At the New York Philharmonic, he replaced Mozart with Haydn and refused to programme Tchaikovsky.

He called Paris “a provincial town” and said all opera houses should be “blown up”. He likened his rival Hans Werner Henzes to “an oily hairdresser” and dismissed Franco Zeffirelli as “the Henze of opera”. A Beatles record, he said, “is cleverer than an opera of Henze’s, and shorter, too”.

His credo was the inexorable march of progress, the rule that music advanced in a linear evolution from Bach, through Haydn and Beethoven, to Wagner, Mahler, Schoenberg, Webern and himself. All else was “superficial” or “useless”.

Upon this fundamentalist certainty, he was able to conduct the 1976 centenary Ring at Bayreuth, a cycle of bourgeois operas redeemed by the exactitude of his interpretation and the Spartan asceticism of his symbiotic director, Patrice Chéreau. Reactionary as it was, Boulez harnessed The Ring to his syncretic faith. Aired on BBC television as a 13-part weekly soap opera, the Boulez-Chéreau Ring was a landmark conversion of vicious past into possible future.

The essence of Boulez was an unshakeable self-confidence and an unerring ear that could pick out a false note in a huge orchestra in the thick of an atonal score. I have seen him at Abbey Road stop the London Symphony Orchestra in mid-bar and, with a forgiving wink, ask them to repeat a passage that, to my ears, sounded immaculate. The players called his sessions “a Boulez servicing”, a form of car maintenance. Cleveland and the Los Angeles Philharmonic signed up to similar work-outs.

Among musicians Boulez was a small boy in a playground, sharing in-jokes, revelling in low gossip. There was nothing austere or remote about him. On the contrary, he needed congenial company, craving it perhaps as a substitute for more intimate relationships. Glacially private where the personal was concerned, he shared his home with Hans Messmer, whom he referred to alternately as his “companion” or “valet”. When I once criticised his jacket as being a generation too old for him, he flushed and cried, “But Hans bought it for me!”

He disdained the vanities and vast entourages of regular maestros, getting by with a lone secretary and on public transport. He was always available for a chat, though he could be thin-skinned, taking prolonged offence at published criticisms a lot milder than the ones he hurled at the enemies of his imagined future. The charm, when he turned it on, was irresistible — and he knew it.