So I was playing around with some ways of putting math into music (because I actually like math when it’s not what is taught in school, because what they teach in school may be important to know, but it is exponentially more boring when compared to the fun part of math, which involves some fun doodle games and bending the rules of algebra or coming up with reasons as to why 0.999... equals 1), and I figured I would try my hand at making a melody out of Pi, one of the most commonly known irrational numbers.
The most digits of Pi I’ve memorized at a time was somewhere near 85, but I’m sure that that number has decreased since then. Anyway, I love Pi. However, Pi is not as practical in equations as you might think it is. See, to find the circumference of any circle, people usually use 2πr, r being the measure of the circle’s radius, and while this is technically true, it is unnecessarily obscured and made more complicated.
The problem with C = 2πr is that stray 2 on the right side of the equation. You could just as easily say C = πd, d being the measure of the circle’s diameter, in fact, it’s easier to say that. (Plus, it gives us a way of remembering it as “Crust equals pie dough.”) This also has some problems, however, because it seemingly implies that the sum of 2 radii only goes around the circle’s circumference 3.14159265358979... times if the two radii are exactly 180 degrees apart, which is not true.
However, since the 2 in the right side implies multiplication, we can apply it to EITHER the r or the pi. So if we were to multiply pi by 2, we get Tau (τ). Tau is just 2π, but it is also a well-known irrational number, not as popular as pi, but certainly still popular. This new equation, C = τr, doesn’t really raise any assumption problems like C = πd did. Tau is superior to pi in this regard, and is much easier to notate and to calculate than C = 2πr.
Anyway, that’s my rant about how Tau is better than Pi (don’t get me wrong, I still love Pi. I mean, I’ve memorized ~80 digits, how could I not love Pi?), but back to actually talking about the music.
I had heard versions of both Pi and Tau turned into music, which each digit corresponding to a different note. Usually, 1 is middle C/Do, 2 is Re, 3 is Mi, and so on. I did this as well, but I thought I would put my own little twist on it.
I ended up making both Pi and Tau in music, up to 43 digits each (repeating the 43rd digit to make the transition from the end back to the start more fluid), and putting them into a nice harmony. I ended up taking the whole thing down 2 half steps (or 1 whole step I guess) because it just seemed to sound better the lower i went, but I felt like I had to stop soon or I would get carried away. I played around with different speeds and found that this little ~37 seconds long 70BPM tune was the best I could find. Doing the same in 280BPM was also fun, but I liked this one better.
I’ll make this a lot longer in the future, seeing that it’s only 37 seconds long and this instance doesn’t even loop. Plus, I’m curious to see what the later digits have in store. I’m going to use this theme for a story that me and a few of my friends (@prindraws as well as 2 others, one would like to remain anonymous and the other doesn’t have a Tumblr) are working on, and I might put it in a game that I’ll make in the future.
I hope you like it even though it’s short and unfinished, I’m sorry for flooding your dash with a math rant (I’ve probably already lost followers as I was typing it), and I hope you have a great day!
-JM
