What makes a winning melody? What makes a melody winning?
It seems that how it is harmonized and accompanied is absolutely critical. But to consider the melody per se does not enable us to answer the question in the fullest possible fashion. We need to ask what came before, and what is about to happen. Two case studies...
Georges Enescu, Symphony No. 1 in E flat, Op.13, 3rd movement, second theme
About 2 minutes into this movement (and again at 6 minutes), we hear a long version of the second theme in a minor mode. It's basically a rising scale starting on the tonic, preceded by the dominant falling to the leading note, in one way outlining a perfect cadence, some sort of closure, in another way launching the yearning scale which culminates in a compression of the three-note opening motif. After this it winds its way down again. The building blocks of the theme have all appeared before so it feels familiar yet new. Its harmonization includes some surprising jumps, and the orchestration involves strings melting into winds and back. Its balance of pausing and moving on again is calculated to move one's internal organs very effectively. Each time it subsides into thematically-related material. These brackets of the quasi-familiar and the overall major tonality of the movement make this minor theme stand out in performance.
Xaver Scharwenka, Piano Trio No. 2 in A minor, Op.45, 1st movement, main theme
This theme is announced in skeletal form by the piano, and the whole opening is quiet, though once the strings get going on the melody proper this is the quiet of an extremely powerful engine operating well below its true strength. At this point the piano turns to a rippling accompaniment the strings are well-supported and the harmony moves tonic-relative major-tonic, which if it were not part of such a serious melody could almost be described as lilting or folksy. This theme is always looking forward, its internal repetitions drive it on rather than backward, and Scharwenka knows how good it is so is not afraid to use it a lot! Each time it comes back, we are left wanting more, and he does not disappoint!