Leaving aside the topic of-adic numbers (I feel as though I should learn more about it myself before I make any mistakes), I’m going to get back to a subject I hinted at a couple of posts back: the role of mathematics in music. When I tell people that I studied music before switching to mathematics, they often say something along the lines of that the subjects are very similar/interconnected/both use “the left side of the brain”. This isn’t really quite as true as seems to be commonly thought: you can certainly find a lot of mathematical patterns and structure in music; but so can you in any art, and indeed – arguably – in anything if you look hard enough! And while I am personally averse to “side of the brain” arguments, if we are stooping to that level then I would argue that there is a creative right-side element integral to the creation and appreciation of music which is largely absent from mathematics.
However, it is true that many mathematicians are also involved in music – especially classical music – to some degree . And it is true that the mathematical and logical structure of music is much more apparent and easier to appreciate than with other art-forms. One of the best ways to see this is to look at tuning systems.