It's not so clear whether the vocalizing of primates has a similar function, but I've never seen any evidence that primate vocalizations either attract or repel potential mates. However, like birds, certain primates vocalize interactively, often in the form of antiphonal duets between male-female pairs, but also in so-called "chorusing" activities, where an entire group will vocalize in an interlocking manner very roughly reminiscent of Pygmy/Bushmen vocalizing. For more on this, see post 21 et seq.
An interesting fact about music in humans is that most (but not all) of us are born with certain innate musical gifts. But some of us have little or none. And this group does not seem to be at any serious disadvantage as far as success in finding a mate is concerned. On the other hand, a small minority of humans appear to be born with extraordinary musical gifts, which often manifest themselves very early indeed, as early as the age of 3 or 4 and many go on to become so-called musical "prodigies." Great musical gifts do not, however, ensure success with the opposite sex, and as is well known, some of the greatest musical prodigies (I'm thinking Mozart, Beethoven, Brahms, Schubert, for example) were not particularly prolific where progeny production is concerned. [Added August 20: An anonymous commenter has informed me that Mozart's wife, Constanza, had several miscarriages and that the couple wound up with two surviving children, which means that he was in fact relatively prolific in producing offspring, though certainly not above average for his time. I was not aware of any miscarriages and assumed he'd had only one surviving child. Sorry for the misinformation.]
Now the element of natural selection that produces truly remarkable effects, such as the wings (and songs) of birds, the eyes of animals, the human brain, and musical prodigies, is not simply mutation and the variation produced by it, but the much more complex and sophisticated process of adaptation, which fine-tunes a species to its environment. And if there is no obvious adaptational "payoff" to musical ability among humans, then the existence of such truly amazing musical gifts among certain extremely young, untrained children is very difficult to explain. The only explanation I can think of is that musical ability must, at one time, have had a very strong adaptational function, which is now largely lost.
Which returns me to a consideration of the music of the Pygmies and Bushmen, where musical abilities are taken for granted, and someone with a "tin ear" or no sense of rhythm, would be at a distinct disadvantage.
(to be continued . . . )