So in my head there are quite a few unnecessary connections, and the other day I realised that I think about music in a similar way to how I think about maths, and that lots of people do one or the other but the crossover is smaller than I'd like it to be.
So I'll start off with the obvious and move toward the less obvious - read less grounded connections.
Trigonometry. I think of trig (as the cool kids call it) like the piano, when you were younger someone else made you learn it and most people insist that they'll never use it again and move on with other things, but some people keep at it and it opens the door to all the other cooler mathsy/sciency things. It gets used all the time, in places you wouldn't expect it. I suppose this is where it falls apart a little because
Engineering Maths. I'm tempted to say this is like blues or jazz, really cool and requiring lots of skill to become famous but you'd know I'm lying. Engineering maths is more like the difference between a musical theorist and a composer, you have to know why this chord resolves into this one or what this instrument's tone is, but the composer takes all that stuff and then makes really cool stuff with it. No offense other mathematicians or music theoreticians. It just seems like this is where the people who like to have it all planned out gravitate towards.
Euclidean Geometry. Definitely the triangle. There was a time when saying things like "A line is a unique connection between two points" would have gotten you the gold star in maths, just like being able to reproduce a single note would get you a caveman Grammy. Those times are past and no one cares about plane geometry.
Non-Euclidean Geometry. The theremin. This is the maths to do with three dimensional space, which is much more bendy than you would think, and that of even more dimensions. So think of how a square is just a cube that you are looking at side on, non-euclidean geometry deals with shapes which are what you see when the cube isn't the end of the story, like if the cube is the three dimensional drawing of a higher dimensional shape. Then there's the whole Doctor Who opening theme.
Physics. I think of physics as the whole of musicology, because there's obviously maths in there, but there's also a stack of stuff you can't do with maths, or at least maths won't do with you because it isn't easy or nice. So it's like reading an Oliver Sacks book, long and oftentimes really cool, but you can only tell the funny anecdotes, no one wants to hear about all the science bits. Like the one about the entomologist whose perfect pitch was so accurate that he could tell the insect's wings vibrated at a C and were therefore buzzing at 32 Hz.
Calculus. The violin. Everyone knows it, and it's been the big papa in music for ages and ages. Fiddles and violins and other bowed instruments have been around longer than calculus by a long shot but both have dominated. When I think about music I confess the first instrument I think of is the violin, and all the famous melodies it's gotten. The same is true of calculus. When you do maths, there's a lot of calculus, you can't run away from it. It's the maths of change, and everything in the world is changing, all the time. You can do maths without calculus, but if you didn't have it at all the world would be a very very different place.
There are more kinds of maths and there are obviously more instruments and things, but those are the ones which are all tangled up inside my head.
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