Specifically: you can compose a mixed drink like a piece of music. Mix high notes (light, sweet), low notes (dark, smoky or molasses-y) and midrange into a complex composition. With rum drinks it isn't terribly difficult, though I don't know that I've seen the Tiki-as-Jazz formulation of the idea before. But there are a number of drinks that are clearly, *clearly* mixed based on this formula.
So: the really good idea. No, not that first bit. That's an only-okay idea, a metaphor.
The good idea is this: start a small drink in a large glass -- so, mostly empty. Line it up next to a series of shotglass-or-smaller cups, in order. The idea is: take a sip. Add a half-shot. Take a sip. Add a half-shot. Continue until you've drunk about a full drink, with perhaps a third of a drink left afterward, but the drink changes with every sip. You're aiming to pour in just slightly less than you drink at each stage.
What you're doing is composing a more interesting piece of music, but with a rum (or whatever) drink. An example composed off the cuff, so it may be awful:
Starter: coconut cream and white rum (better: Rhum Agricole or cachaca). This is the initial high note, like a flute solo beginning a story-rich orchestral piece.
Next half-shot: orgeat and/or milk, to add a richer mouthfeel but keep it light and sweet.
Next half-shot: gold rum, something old and pleasant, to add mid-range to the drink.
Next half-shot: juice, a semi-return to the high notes while adding acidity. Pineapple juice, perhaps, if you added orgeat -- it would curdle milk.
Next half-shot: dark rum, perhaps mixed with spiced or overproof rum. Add a hint of low notes without going overboard. Now you have a leaning-sweet but balanced-feeling drink.
Next half-shot: orange curacao and/or simple syrup, possibly mixed with something less sweet. This emphasizes the other flavors, but needs moderation.
Next half-shot: dark rum. Now you're bringing it home with the equivalent of kettle drums -- dark, low notes, but you're about done. This is the finale.
So that's fun and all... But somebody must have had the idea of composing a drink in distinct stages before me. It would be straightforward to do it self-serve. A taster flight of wine/scotch/etc is a bit like this, but with much less continuity. It's basically "Peter and the Wolf" in drink form.
Seriously, this is a simple, great idea. Who out there already thought of it and did it better than I would? Anybody know? I can't be the first.