Music, mind and mathematics: theory, reality and formality

I consider the nature of music as a cognitive and cultural construct and discuss the relationship between mathematical systems and musical ones. I propose that mathematical modelling of certain kinds may be appropriate to model certain musical relationships, but this is so because of underlying cognitive principles. The conclusion is that to model music mathematically is essentially to model (parts of) cognition mathematically, which means that to model music in the abstract, as though it were itself a mathematical construct, divorced from its source in the human mind, is misleading. For a true understanding, the power of mathematics should be applied to the process of musical behaviour, not merely to its product. That process lies in the embodied human mind.