Well, after getting some free time to continue working on my oscillator, I managed to generate sawtooth and square wave with PWM control. I'm happy because I was previously using the waveform from capacitor charge but I learned to charge a capacitor with a current-source (PNP here), so I managed to generate a ramp waveform properly.

Here's my circuit, note that there are not pots or switches yet in the schematic; SAW_OUT is the sawtooth output, SQUARE_OUT the square wave generated using the comparator. With a pot, I managed to modify the duty cycle perfectly.


I would like to receive some criticism or recommendations on the circuit up to this point (specially transistor biasing which I'm doing in too much "trial-and-error "style). The amplification stage with the chained 2N2222s won't be part of the VCO but a future amplification section. It's there for checking up sound.

Here are the generated waveforms:





I also want to ask what about using JFETs/ MOSFETs? They are easier to setup and bias in comparison to BJT transistors?

Thank you for your help.

 

Q3 emitter and collector have been transposed. Works in a sim but might not be so good in practice.
Setup/bias for FETS is different; not necessarily easier. Depends on the circuit they're used in.