I am reading "A Generative Theory of Tonal Music" by F. Lerdahl and R. Jackendoff and I don't understand the difference between grouping overlaps and elisions (this is explained in section 3.4).

The authors use visual forms to explain it, and it seems clear that an overlap happens when the end of a grouping structure is also the beginning of the next grouping structure and an elision happens when something is missing in one of the grouping structures. But when I look at the elision's musical example (3.26), the D (m.16) chord - which is the end of a grouping structure and the beginning of another one - is there and has its function in both grouping structures. So I don't understand why it isn't a grouping overlap.

Because of this example, I don't understand what is the difference between these two concepts. Can someone help me understand this?

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    Seeing this question reminds me that I want to read that book sometime. Unfortunately, that means I can't help at the moment. But now I'm curious about the answer. – Caleb Hines Mar 6 '16 at 20:30

Let's start with what overlaps and elisions have in common have in common which is they both are the end of one grouping section and the start of another so the overlap will function in both (as noted how the D in the elision). How they are different though is the that in the overlap the transition for the transition is seamless as the start and end of the grouping line up very well. The elision however the end of the one grouping section and the start of the other class a bit. It's not completely different in nature, but contrasting with some aspect of the other grouping section. Figure 3.29 with the two hexagons with overlapping sides and figure 3.30 with the square and triangle intermingled represent the overlap and elision respectively.

Let's look at both examples in the book to break down the differences.

Overlap Example:

In the overlap example from the book shown below, it's easy to see how measure 1 and 3 are the exact same and how the first beat of measure 3 resolves from the end of measure two and restates the previous grouping system at the same times.

enter image description here

Elisions Example:

The elision example is a little bit easier to listen to than look at as the contrast in the groupings is extremely easy to hear. In measure 13 to the end to measure 15 we hear the statement of one idea (grouping system) which resolves in measure 16, however measure 16 musically is very different in dynamic, texture, and overall feel. The author even explains in the paragraph above figure 3.27 that the fortissimo in measure 16 elided the the last event of the previous grouping system. The D obviously functions in both, but the idea of each grouping system is very different.

enter image description here

Check out the score on IMSLP and listen to the recording of the piece to hear what it sounds like. On the video below the section in the book occurs from about 2:15 to 2:40 and for the IMSLP score the section can be seen on page 3.

Not only does the fortissimo give you a sense of a new section while the previous section is ending, but the instrumentation changes also and the new grouping section feels very different.

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