He made his first appearance with the Orchestre de la Suisse Romande (OSR) in 1954, which led to several later commercial recordings for Decca.
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Argenta conducted the first commercial recording of Rodrigo's Concierto de Aranjuez, with Regino Sainz de la Maza as the soloist.
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He nonetheless continued to make recordings, such as Ernesto Hallfter's Sinfonietta, De Falla's Nights in the Gardens of Spain with Gonzalo Soriano, work with the OSR, and later in London, the stereo orchestral LP Espana, as well as the Tchaikovsky Violin Concerto with Alfredo Campoli and Liszt concertos with Julius Katchen.