I have found success! Once I figured out how sound actually works and wrote it all out, I figured that I wanted an exponential function as opposed to a root, which was what I had originally. Here's the final code:
int speakerPin = 13;
int potPin = 5;
float frequency = 0;
void setup(){
pinMode(potPin, INPUT);
pinMode(speakerPin, OUTPUT);
}
void loop(){
frequency = analogRead(potPin);
frequency = (sq(frequency) / 100);
digitalWrite(speakerPin, HIGH);
delayMicroseconds(frequency);
digitalWrite(speakerPin, LOW);
delayMicroseconds(frequency);
}
And I'll probably end up putting a small capacitance sensor in there too to have actual notes instead of a constant sound. I might actually end up doing one for pitch and one for volume like a theremin, but that's later.
Here's a picture of the final product, just to show it off some:

and the top and bottom compartments:


And I'm not sure if it'll embed the pictures correctly, so here are the links:
http://img535.imageshack.us/i/photo10dr.jpg/http://img245.imageshack.us/i/photo11xj.jpg/http://img257.imageshack.us/i/photo12kz.jpg/I guess you're right about the pot not being good quality. I got the scale pretty good and all, but the blank space is still there at the end. Oh well. Just for future reference, any recommendations for quality pot distributors?
Thanks for all the help, everyone!