What does it mean to ask 'is music real?' The obvious answer is 'of course it is!' with perhaps, if one is careful, 'at least as real as anything else...'
And there's the rub. Any study of music itself to a sufficient level must at some point come across some fairly fundamental questions. Music is, after all, one of the major perceived art forms, and through its major manifestions - listening and performing/creating - it uses, arguably, all of our senses (except, maybe, smell and taste). It also uses quite voluminous quantities of brain power, whether in coordinating body movement or in more conscious decision making.
It should be inevitable that when asking fundamental questions about music, we should be asking fundamental questions about ourselves, the way we think and the way we act physically.
This is, of course, true of any fairly fundamental activity, and so i hope that what I have to say may be of relevance to other art forms, especially those 'multi-media' ones like music .
Roger Penrose, in his book The Emperor's New Mind and elsewhere calls upon fractals as evidence for the platonism of mathematical reality:
Exploring by computer is equivalent to exploring by experimental apparatus
Mandelbrot himself, in his book The Fractal Geometry of Nature suggests that the proof of his argument is in the 'seeing' of his computer printouts. He also suggests that some printouts are indistinguishable from 'high art' and draws especial attention to a couple of printouts caused by computer 'bugs'.
Clearly music itself is real in the sense that it is a physical phenomenon - disturbance patterns in air pressure. However, equally clearly, it is the patterns created in our minds by these disturbances that are equally real. Many books about mathematics include examples from music...