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There is a technique in composition where certain notes in a familiar melody are entirely skipped, so that they are not played but are still imagined. This usually happens (or is noticeable) in the later stages of a piece, when the melody has already been introduced and is being repeated. It could also be used with a melody that is previously familiar to listeners.

What is this technique called, and what is its intended effect?

I'm not a musician so I don't know the technical details, but I found the terms "pensato" and "melodic expectation" that seem to describe the mechanics of it.

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    Got an example? – Old Brixtonian Nov 25 '19 at 7:54
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    @OldBrixtonian - I'd think the children's song "Bingo" is an extreme example of this. – Dekkadeci Nov 25 '19 at 12:24
  • @Dekkadeci Thanks. I'd never heard that. [The tune's very like the traditional song 'Landlord, fill the flowing bowl.'] I don't know what that's called. Sorry. – Old Brixtonian Nov 26 '19 at 1:34
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I think Pensato and Melodic Expectation may indeed be what you're looking for. Maybe also look into Ghost Notes (although they are more muted notes so they are "actually there").

The idea behind the missing notes, I think, is to - after the melody has been established - engage the brain of the listener even more by having it fill in the blanks and maybe even create some slight variations in the melody created by this filling in, which may be individual to each listener. Don't quote me on that though, it's just my guess ;)

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You could call it framework of the tune or reduction to the skeleton.

Maybe your putting the cart before the horse:

The later reduction of the melody is actually the tune and what we've heard before have been variations and embellishments of it.

Edit:

I think I've misunderstood the question, if this is what Dekkadeci shows with the Bingo song.

We call this "tunnel singing" as the what you hear is compared what you see through the window when a train passes a tunnel. But I don't think this is a general used term.

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In jazz we call them ghost notes, but that is more in the context of improvisation.

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In the context of songs and nursery rhymes, if this technique is applied succesively, the result is a called "Lückentextlied" in German (literally: cloze song). With every repetition, more and more letters, syllables, or words are replaced by rests. The example "Bingo" was given by Dekkadeci in the comments. Another example being "Auf der Mauer, auf der Lauer" (in German).

If the muted words are replaced by gestures, it is a "Singspiel". However the term "Singspiel" is not very specific, since it is also applied to songs created via other systematic variational techniques, such as altering vowels.

The opposite of a "Lückentextlied" is a cumulative song, for example "Old MacDonald Had a Farm". For further information in this direction see Donald E. Knuth, "The Complexity of Songs" (1977, reprinted 1984), doi:10.1145/358027.358042.

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