Information structure in music

The Vocal-Master once told me that the more popular and catchier a melody is, the more repetitions one can find in it. Take Memory or My Way or Dancing Queen as an example: almost every phrase is a repetition of one of the previous phrases with some variations. Similarity helps memorizing the song, variation helps not to get bored.

In fact, all the melodies I can think of contain repetition and variation in every phrase. But what strikes me is that it resembles the natural language information structure very much. Repetition is a kind of Topic (old, given, assumed information), and variation resembles Focus (new, highlighted parts of the sentence). A difference is that the music hasn't any devices to express reference except for repetition, while sentence Topic may not be seen in the discourse before. It may be an indirect or anaphoric reference (A phone rang. A nice female voice asked who she's talking to), or a real-world entity that 'everyone knows' (The president visited England). But I still see a great deal similarity. Both music and discourse are developing in time, introducing new themes and information. What was new in one sentence, becomes given in another one; we can repeat what once was a variation.

The music theory, of course, knows a lot of various ways of developing melody. Music even has phrases and sentences, questions and exclamations. Moreover, music and language are processed by the same brain systems and there are theories of syntactic processing in music. It may even have semantics! Seems that it's only me who didn't suspect this language-music relation until recently.

Topic-Focus articulation

As it is known, every sentence can be divided into two logical parts. One (Topic) is what the sentence is about, another (Focus) is what the sentence actually says about its Topic. Topic is usually something given or presupposed to be given, Focus is something new or emphasized. To me the Topic seems like data from the knowledge base whilst the Focus seems like an operation on this data, a function on the Topic. Since Topic-Focus opposition is one of the most important distinctions for me in the text structure, I can't omit it from the functional representation.

We know one thing that can separate anything from anything in functional composition: a Lambda abstraction. So we'll use it also to separate Topic from Focus.

Let's introduce a special auxiliary function (actually it's more like a macro) SENT, which will take both Topic and Focus as its arguments and then apply function-Focus to argument-Topic, probably marking them in some special problem-dependent way. Thus every sentence would look like a call of SENT function with Focus and Topic arguments.

Example sentence:

Father loves son.

Its core functional structure:

(loves father son)

By default Topic is 'father', Focus is 'loves son'.

(SENT (λx loves x son) father)

We can stress FATHER, promoting it to the Focus and 'loves son' - to the Topic:

(SENT (λx x father) (λy loves y son))

Here we have two abstractions. If we suppose that SENT does nothing besides applying its first argument (Focus) to its second argument (Topic), we'll get

((λx x father) (λy loves y son))
<= replace x =>
((λy loves y son) father)
<= replace y =>
(loves father son)

We can stress SON:

(SENT (λx x son) (λy loves father y))
which can be replaced by shorter
(SENT (λx x son) (loves father))

We can stress LOVES:

(SENT loves father son)

Here the Topic consists of two entities rather than one. This is perfectly normal, we'll just apply 'loves' to 'father', and then the result - to 'son'. We'll get ((loves father) son) which is by definition of currying equal to the core structure.

I don't know yet how to represent multiple parallel contrastive sequences, like 'Father loves son, while mother hates him'. But such an approach feels promising to me.