Melody refers to a rhythmic sequence of notes meant to lodge itself in the listener’s mind, perhaps through repetition, perhaps through strangeness, perhaps through utter beauty. Melody can exist without harmony (common in many cultures), but melody and harmony cannot exist without rhythm.
“Melody without harmony is like painting without perspective, and our ears have become so accustomed to associating the two elements that an unaccompanied melody that fails to imply clear harmonies often sounds strange to us…. Melody is almost inseparable from its harmonic accompaniment.”
(Britannica Home Reading Guide, Appreciation of Music, 1944, p.3–4)