It must be that however short and unique a given clip is, it nevertheless stimulates the ear according to a prior, similarly framed aural experience so that an equivalent response is thereby triggered. And if that's what indeed happens, then this tiny matrix of sonic data hits our brain like a zip file, immediately opens its contents and we respond to that data almost the instant we hear it.
In other words, very small packages can produce very, very big feelings.
As it happens, I think there's a lot to learn from this phenomenon, especially if one is in the business of music or sound design, or otherwise involved in the craft of creating sound for commercial application.
So, the question I want to know the answer for is not how long a clip has to be in order for someone to recall the title of a familiar work, but how small can an unfamiliar sample of sound be edited, and still produce an emotive response?
In other words:
How much information can be conveyed and decoded from within a fraction of a single edit, sample or beat?
Certainly, we can convey a mood and much more with even a single beat. Sample enthusiasts do this all the time, lifting a kick or snare, say, and dropping it into one's mix, with the result often being a sort of verbal shorthand for a specific era. Gated snare drums, for instance, recall the eighties, and by extension, a general feeling of the entire decade. Whether or not it’s fair or honest to reduce a decade to a single feeling or vibe is yet another question, but this is often what happens in the production of any period reconstruction for theater, film or video.
Feelings of nostalgia and evocation of mood aside, no doubt a single sonic event can transmit a complete message, so long as there is general consensual agreement that certain sounds, combinations of sounds, or treatments of sounds signify extra musical meaning (which is what I mean by 'message'). It may be that such terse transmissions do work upon us because what ever is there, however obscure, provides just enough aural evidence that a listener receiving this incomplete communication can reasonably assume to fill in what is missing, like reading words without vowels, or when someone cuts us off before we've finished speaking because they already understand the point.