Sorry, I don't communicate well. What I'm wanting to build is a circuit that uses a microcontroller that outputs a voltage to control a VCO. Sooo, I guess:
Pushbutton Input>Microcontroller>Outputs Voltage>VCO is thus tuned by this output voltage.
I have a pretty good idea how I'm going to write the code, so I won't need help with that. I do appreciate the input you're giving me, though.
SO, the VCO I decided I will use is this simple 555:

From what I understand R2, and the capacitor make up the frequency range. I plan on using a 4.7uf cap and a 15K resistor, which is about 14 Hz at it's lowest. Which is lower than the hearing range, but whatever I just need to be able to get to 20.6 Hz (a low E0). Then I want my highest note to be a B7, 3951.07 Hz. I'm assuming I won't be able to get that frequency range with a 0-5V input (input voltage to the VCO/output of the microcontroller, it can only output up to 5V) with just the cap and resistor I previously mentioned. So, I'll build a couple different oscillators with different RC networks to accommodate that limitation. Only thing I need to figure out is how to predict what the frequency output will be with a given input voltage to the VCO.
In that specific picture I posted (it's from a blog that I found randomly on google images), they state that:

=
T=w+0.693R2C
I'm not sure what T or w stand for in their equations I'm only familiar with omega, w=2piF.
Anyways, just thought I'd post findings as I stumble just in case someone might find some of this garbage of use or if anybody want to give some feedback/input.