Why does duty cycle affect frequency in this 555 based circuit?

[raw_circuits]

Thanks to all for your help and your patience.  I believe I am slowly beginning to grasp the math.  I've attempted to work through the equations from KVL.  I think I have worked out the charge circuit but I haven't quite got the discharge side down - I haven't had much time to focus on it in the last few days.  And trying to recall differential equations from 30 years ago... ouch.

[MK14]

Thanks to all for your help and your patience.  I believe I am slowly beginning to grasp the math.  I've attempted to work through the equations from KVL.  I think I have worked out the charge circuit but I haven't quite got the discharge side down - I haven't had much time to focus on it in the last few days.  And trying to recall differential equations from 30 years ago... ouch.

A number of people have said they think you have accidentally put in zeners instead of diodes, in your breadboard circuit.

If so, then that can easily explain the problems with the timings being wrong (at different voltages) etc.

[StillTrying]

The scope pics in Replies#14 and #21 show the correct voltages and no zener diode action.
Of course you could put a scope channel on each side of a diode and see the 0.65V conduction voltage.

[MK14]

The scope pics in Replies#14 and #21 show the correct voltages and no zener diode action.
Of course you could put a scope channel on each side of a diode and see the 0.65V conduction voltage.

They do appear to. But when the OP experienced the wrong/unexpected frequencies (which may not be on the scope pictures we have), maybe the pot/trimmer position(s) were changed and the possible zeners, were influencing the situation ?

I'd prefer to clarify the situation, rather than take lots of assumptions.

So far, I can't see any schematic (of EXACTLY what he did), we have a picture, which might have completely different components to what we were expecting, and the scope traces may have been taken under different settings, to what he was complaining about.

tl;dr
I would prefer to have solid facts, rather than lots of unknowns.