According the Donal O'Sullivan (Carolan - the life and times of an Irish harper, vol1, pp146), quoting Goldsmith - the musician in question played over on his fiddle the fifth concerto of Vivaldi. I assume this was the 5th Violin Concerto, RV253 La tempesta di mare. You can hear samples here: Naxos: Vivaldi Violin Concertos Op.8, 5-8 and 10-12, and you might hear a little similarity in the start of the 1st movement.

O'Sullivan also dismisses the story that he composed the concerto spontaneously after hearing the Vivaldi: "Presumably, the piece played by Carolan immediately after the test-piece is the one known as 'Carolan's Concerto'; but the title of this tune in Lee's 1780 Collection (the earliest we have) is not 'Carolan's Concerto' but 'Mrs. Poer'. Hence it is reasonably certain that 'Carolan's Concerto' was composed in honour of Mrs. Elizabeth Power, the wife of David Power, who lived at Coorheen, on the shore of Loughrea, County Galway. If so, it is unlikely that Carolan would have composed it extempore, as alleged, in the hall of Castle Bourke".


Mick