In the absence of other opinions, I'll offer a perspective. In short, this is probably beyond the limits of our current understanding of neuroscience, but we have some guesses.

When people have lesions in the dominant temporal lobe they have trouble with recognising or linking the meanings of sounds and words. There is an equivalent semantic agnosis for some kinds of visual stimuli usually associated with lesions in the parietal lobe. In general, the brain tends to infer a pattern that explains disparate stimuli. The term for this is "gestalt". This is a high level function that is quite sensitive to lesional disruption - see The Man Who Mistook Hos Wife for a Hat for examples.

Semantic content in auditory stimuli, processed by the temporal lobe, is far more temporally dependent than other stimuli. Note that the term 'temporal' is shared between the lobe and the nature of it's processing is purely coincidental - it was named for the tendency of the hair of the overlying scalp to gray, showing age, before other areas of hair.

In any case, when the temporal lobe receives a segment of data that activates a specific semantic 'gestalt', it likely continues to seek confirmation of that 'gestalt'. For smells or tactile senses, or visual stimuli, it's simpler, because you just sniff or feel more, or double take. For songs, the new stimuli only adds to the gestalt if it occurs in a specific temporal sequence. As such, you need to continue the tune, either in your head, by humming, or listening to the song.

Edit: Source - I'm a neuropsychiatry registrar in an epilepsy unit, and I've read the first few chapters of Lishman's?