I don't think the attrubutes of a good tune are all that mysterious.
A typical melody will contain two statements, the first ending with a
feminine cadence, the second masculine--a question and answer or rise and
fall, so to speak.  Within this admittedly generalized framework the best
tunesmiths are able to use various devices which play on our emotions.
Someone mentioned the big tune in Brahms 1.  I think it would be quite
ordinary if Brahms had written the two statements of the theme and left
it at that.  But Brahms does two things: first, he puts an appogiatura
at the second cadence, delaying any sense of resolution.  Second, he goes
on with the theme, ragging the rhythm over the bar and crescendoing to
create tension.  He reaches a climax and slowly lets the whole affair
fall meanderingly back to the tonic.  Not only has Brahms come up with an
immensely satisfying utterance, he has also provided himself with a wealth
of material to develop.

I realize this is a pretty haphazard attempt at analysis; I don't have
score at hand.  My point is that you can analyze any piece of music or
extract from same exactly as you would a piece of prose or poetry.

Eric James