audioguru, you can get a fully off and fully on with this circuit.
I know you know this but other people might not, so I hope some people find this information useful. ;D
I've done a simulation, look at the graphs.
The comarator on the output will turn off only when the inverting input is higher than the non-inverting input.
The 1st one is fully on, the voltage on the non-inverting pin is greater than the peek value of the triangle waveform on the capacitor.
The 2nd is nearly fully on, the voltage on the pot is about 6.4V so it turns off only when the wave form on the inverting pin is >6.4V, but it is below this value most of the time so the output is on more than off.
The 3rd circuit is nearly on becaus the voltage on the pot is 6V this makes it on for half the waveform and off the the other half.
The 4th circuit is nearly fully off because the voltage on the pot is 4.7V and the voltage on the capacitor is normally above this value so the circuit doesn't turn on very often.
The 5th ciruit is off as the voltage on the pot is less than the mininum part of the waveform so the op-amp will never turn on. ;D