I play music and I’ve always been good at maths. It seems whenever anyone puts these two facts together, I’ll then be told “I think there’s a link between maths and music”. I was skeptical of this statement, partially because I don’t consider myself to be a good musician, but mainly because I just didn’t see the link between being good at sums and being expressive with your instrument. However when I came to study music theory, the links became very clear. Here was where my naturally analytic mind really came through. This was the link between maths and music that my anecdotal evidence supported.
I'm glad you like it, Someone's got to. I've had to learn a lot of "set theory" (12 tone, serialist) in my bachelor's degree/masters degree. I know some people love it, but to me, it's the most uninteresting part of music theory. I can see how it's fun to tinker with, and respect the people who compose in the style., but I find much of the music composed with strict serialist ideals in mind to be not only restrictive, but also difficult to Listen to and alienating to both the audience and the performer. It basically takes the breakdown of "Traditional" western harmony that occurred over the 19th century and early 20th century, then brings it back into the Baroque period where music was in many ways more complicated. faster harmonic rhythm ( often changing every beat), more complex musical styles (specifically the fugue) combined with the tonality (or more specifically, the lack thereof) and the difficulty of the intervals to tune correctly (we're not used to hearing tritones and semitones as easily as 8ves, 5ths and 4ths) makes for music that is difficult to hear, difficult to play, and requires a lot of knowledge to appreciate. As I said before, I'm glad you like it and that you found this link between your two passions. I just wish that it wasn't so prevalent in New Music (indeed, composers are steering away from it) because I feel like it is responsible for the hesitancy for orchestras to program new works and audiences to listen to them.
Thanks for your reply, I hadn't considered the link with the Baroque era tonality that's a really interesting comment. Shame you had to endure it for your degree, I would not wish something like this on someone who hates it. Oh behalf of mathematicians: 'Sorry'.
No problem, mi amigo, and no need to be sorry, either. Frankly, I think I'm at a point where I can (usually) appreciate the music, but hate the people. The people who compose hardcore atonal and serious works have a tendency to be the pretentious fuckers of the classical music world. Them, violinists, and cellists.
If you're interested, this blog did a recent post that covers the first question with regard to major chords http://metinmediamath.wordpress.com/2014/03/16/overtones-what-they-are-and-how-to-compute-them/ As for the second question, I would hazard a guess that the circle of fifths could shed some light. However, these things are subjective, I happen to quite like the progression I -> III!