A melody doesn't need to be long, or even especially memorable in isolation, to become the backbone of a full-length piece of music. What matters is what a composer does with it afterward. Melodic development is the general term for the techniques composers use to take a short musical idea, often no more than a handful of notes, and grow it — through repetition, variation, and transformation — into material substantial enough to sustain a movement lasting many minutes.
A motif is a starting point, not a finished melody
A motif is the smallest musically meaningful unit a composer works with — often just a short rhythmic and melodic fragment, sometimes only three or four notes. The opening of Beethoven's Fifth Symphony is one of the most widely cited examples: a four-note rhythmic-melodic cell, short-short-short-long, that on its own is almost too brief to register as a "melody" in the way a singable tune usually is. What makes it structurally significant is that Beethoven returns to that same four-note cell constantly throughout the movement, in different keys, at different pitches, passed between different instruments, compressed and stretched — developing an idea simple enough to state in under a second into the connective tissue holding a movement together that runs for several minutes.
The toolkit: repetition, sequence, inversion, augmentation
Composers have a standard toolkit of techniques for developing a motif once it's introduced. Repetition simply restates it, often building familiarity and anticipation. Sequence repeats the motif at a different pitch level, preserving its shape while shifting where it sits. Inversion flips its melodic contour upside down — a rising interval becomes a falling one of the same size. Augmentation stretches the motif's rhythm to be slower, while diminution compresses it to be faster. None of these techniques changes the fundamental identity of the original idea beyond recognition; a listener can usually still hear the connection back to the opening statement, which is precisely the point — development is about extending and transforming an idea while keeping it recognisably the same idea, giving a long piece of music a sense of unity that simply stringing together unrelated melodic fragments wouldn't produce.
What we're still unsure about
The core techniques of melodic development — repetition, sequence, inversion, augmentation and diminution — are well documented and consistently taught across music theory, and their use in landmark works like Beethoven's Fifth is extensively analysed. What's more a matter of interpretation than settled fact is exactly how much of a listener's sense that a piece feels unified and coherent actually depends on consciously or unconsciously tracking these motivic relationships, versus other factors like harmony, rhythm, and orchestration doing the bulk of that perceptual work — music psychologists don't have a fully settled account of how much motivic development specifically drives a listener's felt sense of a piece "hanging together."
This sits inside Melodic Writing & Development, one of seven topics in Composition, one of four domains in Music, one of seventeen subjects the app can quiz you on.