I recently did an experiment on doing math-based music. I used the formula for a cube’s volume and its surface area. I mapped this out on paper using notation first. I played it on my piano, hoping the whole time that it would blow my mind.
Boy am I disillusioned. Try this one at home. If you’ve been told that music is based on math, you’ve been told a cherished assumption. I think music is more earcandy than math, even though notation is used, the number concept does not go above general counting, iterative counting and I think that’s it.
So to all of you, I am kind of crazy, but I at least know what I think companies know about who make the music equipment based on math. They know it’s mostly a matter of just beats and tones making one want to “jump around, get up, get up, and get down” to quote House of Pain.
I cherish your enthusiasm for geometric structures myself. I still insist that you try doing this with some formulas. Use the one I used: V=s^3 (volume is leng of side of cube cubed). See if doing 3/1 music with quarter notes helps you achieve a desirable result. It is the best kind of music if that is what you like. I was just warning those who find such things fascinating that it can be a turn-off to a woman if you advertise yourself like this without doing the math required.
There’s plenty of music based on mathematical rather than tonal harmonic practices.
Starting with a premise as simple as yours is basically tantamount to throwing out 3000 years of musical research for no reason - it’s not like these ideas never occurred to anyone before, it’s that our musical system evolved differently because the mathematical - yes, mathematical - relationships between tones suggest musical relationships that are more complicated (and beautiful) than what you’re describing.
Something as simple as, say, the relationship between surface area and volume isn’t even a fully formed musical idea, it’s just a single relationship. Music usually contains many, many relationships in different proportions and at different scales.
So, how do people usually use math in the creation of music? You could base it on some predetermined set of mathematical relationships and work that up thematically according to rigorous guidelines; this is essentially what a lot of mid-20th century composers did (e.g Xenakis, Babbitt), and their music is interesting if not exactly appealing. Or you could do what people have done more recently, which is create some kind of mathematically generated music using tools akin to the ones that people use to make fractals, except the output is a sound instead of an image. Music created in this way sounds basically like music that’s created using any arbitrary process: it sounds arbitrary. Without an artist shaping the results it doesn’t sound like much of anything.
So again, our tonal system is based on a set of mathematical relationships, but in order to create satisfying music it probably makes more sense to reference the musical body of knowledge rather than the mathematical body of knowledge. The complex mathematical interrelationships that make satisfying music are already baked into our set of musical aesthetics, and if you look at a group of mathematical relationships divorced from any musical context it would be pretty hard to discern which relationships were more musically satisfying. Basically, that work has already been done for you.
Maths is a super broad subject, and so it wouldn’t surprise me if music can be eventually composed using some subset of probably complicated maths, as yet unknown.
But even at the basics, the 12 tones of the scale can be represented as 2^(n/12), and rhythm moulds happily into multiples of 2 and 3, creating 64, 48, or 72 lines per ‘pattern’ for instance.
As for using arbitrary math based on some kind of geometry relation, the results are going to be disappointing of course. However, use that same math to make sound effects and I bet you’ll have a lot more leeway in regards to what you can achieve.
I remember this applet that could analyze a piece of music (a midi file), and determine the underlying structure in respect to rhytmic and tonal properties. Whenever it recognized a pattern, it drew a rainbow from point A to point B, making most scores look like lots of tiny rainbows littered all over.
What is interesting here, is that I tried to analyze a piece of Bach’s well-tempered clavier, and IT DREW A HUGE RAINBOW OVER THE ENTIRE PIECE.
Some Boards Of Canada and Plaid have definitely got geometric patterns. There is one BoC tune which is 7:06 long and on my mates CD player it always counted up to 6:66 (was named something about the beast or devil or something.) How you can get a CD player to count more than sixty seconds in a minute is beyond me though!
Source of my images on this post. Couple of others and descriptions in the link.
instead of notes, use patterns and motifs, as your musical data set.
also, you must remember, people make music that sounds non-mindblowing too. It’s very subjective. based on your involvement a form of guided variation could be used in quickly getting something near what you want.
like when musicians have something in their heads, it’s a continuous cycle working itself out, all until deemed adequate by said musicians.