For virtually everyone who teaches music, melody is one of the basic elements. Though music teachers may vary slightly on what melody is, most definitions will at least include the requirement of a sequence of notes which each have pitch and duration. This fits nicely with a view of music being humanly organized sounds recognized as musical and perceived over space (pitch) and time (duration). Beyond these essentials, understanding melody in a way that is at once both inclusive of all cultures, and exclusive of sequences of pitches and durations that are not musical, at least by common consent, is more challenging.
Relatively little of the world’s music adheres to the Western European system of harmony that many of European descent take for granted as what music sounds like. For example, Arab music is based on a division of the octave into quarter-tones, and features a drone with no harmonic implication, and there are no cadences in the Western European sense of tonic, subdominant and dominant functions, but instead a much more complex harmonic structure that sounds unusual to Western European acclimated listeners.
Some propose that in order for a sequence of notes to be a melody, a listener must be able to memorize and remember it. Such a view not only disqualifies many avant-garde works, but music such as the one featured in the above video. With quarter-tone tunings and rapid and complex melisma, I would be hard pressed to memorize that melody, yet it nevertheless is a melody.
Some cultures have no harmony at all in their melody. Listen to this traditional music from Tanzania. It is rhythmically and vocally exciting, but with no harmony. Because of this, an accurate understanding of melody cannot place the requirement of Western harmony or harmony at all on a melody.
Many insist that melody must have both pitch and rhythm. Indeed, I began with a definition in which I asserted that very thing. But even this is open for discussion. Durations are one thing, but rhythm is another. Rhythm is perceived in the context of a beat. There are sequences of pitches with different durations from which the listener cannot establish a beat or meter. Pointillistic music such as Mode de valeurs et d’intensites by Messiaen is a good example of this. A sequence of pitches perceived as a prominent line is perceivable, but no rhythm in the sense I have just described is discernable.
So melody must have pitch and durations, but not necessarily beat, rhythm, meter, or tonality. So in the end, that is what we are left with. Melody is a series tones that have pitch and duration. That is all that is needed. Anything beyond that is culture or style specific. That means that those atonal pieces many of you thought had no melodies is actually full of them.