He was born in Melbourne and joined the Melbourne Symphony Orchestra at 15, only a year after starting on the horn. He became a horn player because of a chance conversation he overheard at the age of 13 between his elder sister, Sir Charles Mackerras and a horn-playing colleague in the Sydney Symphony Orchestra. His sister was wondering out loud what to do with him. He was obviously musical; she assumed he must be able to play something. The horn player suggested the horn, and so he tried it. Recounting this anecdote, Tuckwell jokes "Piece of cake! Only one note at a time.

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