The linked TED talk on the article explains it nicely. A phone book is created with a finite set (numbers,letters, words in English), but that finite set can be used to produce an infinite set. You can always produce a new result by appending to previous result.
In contrast, a musical melody is created by a finite set, and is bracketed by a duration. You can't keep adding more notes to a composition without extending its duration. Doing so makes it non melodic. If you do it enough, it becomes noise (white noise, pink noise..)
