FORT WORTH — It would be hard to convince most entrants in the Cliburn competition of the fact, but studies have shown that it really doesn’t matter much to his or her career where a competitor finishes, as long as it’s not too far from the top.Take Barry Douglas, who played a Cliburn at the Bass program Tuesday night. Douglas came in third in the 1985 Cliburn, yet he has gone on to become one of today’s most prominent pianists (helped, it has to be admitted, by a later gold medal at the Tchaikovsky competition).There are other examples, some of them spectacular.At any rate, Douglas gave a convincing demonstration of his artistry and skill Tuesday with a recital devoted to the music of two Viennese giants, Brahms and Schubert.First on the program were the four Klavierst ü cke of Brahms’ Opus 119. These works are from late in the composer’s career; they came after a long hiatus in Brahms’ writing for the solo piano.The first three are gentle pieces that are a far cry from the piano works of early Brahms. Douglas gave them subtle and lyrical performances, keeping the dynamics understated though working up some power for the playful third Intermezzo.Only with the final piece, a Rhapsody, does Brahms look back to his old heroic style; this was given a forceful interpretation.One of Schubert’s most powerful and tuneful works, the popular Wanderer Fantasy, came next. It is a varied composition, with virtuosic power required in the opening movement, depth of interpretation mandatory in the funereal slow movement, a sense of playfulness needed in the third movement, and a sense of drive required in the final movement, when Schubert switches into his most heroic mode.Douglas brought it off on all counts; the highlight, in a performance with plenty of highs, being the deeply moving slow movement.Back to Brahms, Douglas turned to a set of pieces highly popular in the composer’s lifetime, though not much heard in our time. This was the 16 Waltzes of Opus 39. These are miniatures, highly varied, with some of them cheerful, some melancholy, and most of them lovely. No. 15 of the group is probably the one that most music lovers would recognize.Douglas gave subtle, idiomatic performances of these charming works. Made you long for the old times.The final work on the program was Brahms’ massive Piano Sonata No. 3, his final work in the form. This started well and was continuing in fine form when a deadline pushed me to the exit.