Dublinese highlights of Tinney's solo career include two major recital series in the at the Irish Museum of Modern Art (1991, 1995) and six recitals on Beethoven's piano sonatas at the Royal Dublin Society (2000–02).
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As a young musician, in 1983 he won the first prize of the International Ettore Pozzoli Piano Competition that takes place in Seregno, Italy.
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