Melody: a line you can follow
A melody is a sequence of single notes that your ear hears as one continuous line, the way your eye reads a drawn curve rather than a scatter of dots. What turns notes into a line is shape: how far each note moves from the last one, where the line rises, where it peaks, where it comes down to rest. Shape is also what you remember. You can whistle a melody you heard once; you cannot whistle a chord chart.
Three shapes
Same key, same rhythm, three completely different lines. Play all three and watch the grid as much as you listen:
Steps sing, leaps speak
The working unit of melody is the move from one note to the next, and every move is an interval with a cost. Steps (one or two rows) are cheap: the ear glides over them, voices sing them easily, and a line built from them flows. Leaps are expensive: they grab attention, they are harder to sing, and a line built only from them sounds like the "Big leaps" button, angular and restless. Most good melodies spend steps freely and leaps deliberately, and after a big leap they tend to step back the other way, paying the ear back for the jump.
The power of one peak
Play "The arch" again and notice where your attention goes: to the single highest note, and to the fall after it. A phrase with one clear peak reads as one gesture; a phrase with three competing peaks reads as noise. Where you place the peak, early, late, high, barely above the rest, is one of the strongest decisions in a line, and the contour, the overall shape of rise and fall, is what survives in memory after the actual notes blur.
In your music
Draw your lead into the piano roll and zoom out until the notes blur: the shape you see is the shape your listener hears. One arch or two? Peaks fighting each other? All leaps and no glue? The grid makes contour visible the way no instrument does. And a bassline is a melody too, judged by the same moves; what happens when two of these lines play at once is where this trail is headed.