Your music theory analogy is apropos, because one of the common terms for what it seems you're after is flavor "notes."
Unfortunately, there's not a lot of standardization in terminology for the temporal perception of flavor. The most common term is of course aftertaste, which is sometimes also known as the "finish" of a beverage or food. The link gives a bit more detail on temporal perception and flavor dynamics.
The succession of taste perceptions is more commonly discussed in beverage tasting (particularly alcoholic beverages, though I've occasionally seen it mentioned regarding coffee or tea). The first part of perception often occurs before you even put the food or drink into your mouth, since volatile aromatic compounds are a large part of what we think of as "taste" (but which are actually smell). Those components are sometimes referred to as "the nose" or "bouquet," again particularly in beverages, those I've sometimes heard of the term applied to foods with distinctive smell profiles like chocolate.
Once the food or drink is inside your mouth, you experience the immediate taste sensations on your tongue, but the volatile compounds also waft up through the back of your mouth into your nasal cavities. There are various technical terms for these components of flavor, including "sapictive" for flavor notes sensed in the mouth, "olfactive" or "olfactory" for notes sensed in the nasal cavities, as well as other elements that influence taste perception like hot/cold sensations or texture/chewing sensations. Most of these terms are not commonly encountered in food writing in general, but you sometimes see them in technical studies of flavor or food science.
In some cases, as you chew, other flavor components are released (by evaporation of more volatile compounds or breaking down of the food mechanically through chewing or chemically by saliva), which again may be sensed in the mouth or the nose. The only term I've commonly heard for these in casual food writing is "middle notes," and I don't know that people consistently use that term to mean the same thing. The process of changing flavors during this part of tasting can be referred to as flavor "structure," "depth," or "development," among other things. There's not really a standard term that I know of. Once the food is swallowed, as I've already mentioned, the terms "aftertaste" or "finish" are used to describe any further taste experiences. In technical literature, the overall progression is sometimes referred to as a "temporal profile" of flavor sensations for a particular food.
I know that this answer probably isn't particular helpful or specific, but that's partly because your question is discussing a relatively new area of research in food science. There are a few books published just in the past couple years that deal with flavor science and the psychology of flavor perception. While some of them deal with the temporal succession of flavor perception (and the nerve pathways and sensations that create them), I don't think there are common terms yet that have emerged which you could search for, other than the somewhat imprecise and casual terminology I've mentioned here.
EDIT: I realized after reading the comments that you mentioned that you may be interested in more technical terminology from food science; when I originally read your question, I assumed you were looking for more casual terms that average culinary folk actually use. In any case, there are a number of terms for specific analytical techniques that reference the order of sensations, some of which are relatively new:
- Time-intensity flavor profiling (TI)
- Progressive profiling
- Temporal dominance of sensations (TDS)
- Temporal order of sensations (TOS)
- Multiple attribute time intensity (MATI)
These tend only to be mentioned in the technical food science literature, and each has a different "protocol" for evaluating the interaction of flavor sensations over time. Most are, as I said, relatively new -- older literature will usually employ a more generic term like "flavor profile" or perhaps "temporal profile." Anyhow, searching for any of these terms is likely to turn up more technical articles on the kind of information you're discussing.