Assymetric Square-Wave LFO with OpAmp (Relaxation Oscillator)

[Labaris]

So, at the end of this day I'm very relaxed with this circuit 
But I want to create an assymetric square-wave from it, with the positive cycle being shorter than the negative one. The goal is to create "flashes" with the LED.
I've read a little and with BJT oscillators it's as simple as building two different RC time constants instead of making them the same value.
the thing is, in this circuit there's only one time constant (I'm I wrong?) wich is in the inverting loop. So I need to find the way to add another RC time constant and what I think is that I could add a Cap in the non-inverting loop.

Here it is what I got on breadboard right now:



Another question I have is how to stop the oscillator and keep the voltage on the LED exactly the same. I'm tryng to use the LED to show 2 different states of a pedal.

I've not really understood the theory behind this yet, so that's the mystery now. Thanks in advance! 

[garcho]

Adjusting R1/R2 should alter the symmetry.

[garcho]

Check out the LFO in the Tremulous Lune. It's a good place to start when modifying a standard op amp LFO to your liking.