Gee, Bill - I should've read your initial post a lot more carefully, as the frequency formula isn't correct.

I posted a thread on it here:
555 HYSTERETIC OSCILLATOR formula for "f" incorrect
Instead of:
f = 0.7 / RC
It should've been:
f = 1 / 0.7(RC)

I thought you were right when I first looked at it, but here is my logic.

This is a RC charge and discharge curve with the 1/3 and 2/3 points lined off. Note the time constants.

I estimate each half of the wave form is 0.7TC (actually I figure it as 0.69 TC). Since it takes both halves to make a full waveform the period is approximately 1.4 TC. Period is inverse of frequency, so the final formula is:

F = 1 / (1.4 RC)

This translates into 0.7 / RC, since the inverse of 1.4 is 0.7, these numbers are major approximations due to the fact the top of this curve is not Vcc, but 1.3VDC less. Given this fact 1 decimal place is appropriate. The CMOS 555 would be a lot more accurate, and more decimal places could be used.

I knew drawing the RC charge curve over time constant would come in handy. I was thinking in terms of graphics at the time though.

 

I'm so building these this weekend

 

There was a flaw in my thinking that made no difference overall. RC time constant define a rate of change from initial conditions. If a capacitor is charged and starts at 1/3 Vcc it will still take 5 TC to reach Vcc. The journey between 1/3 Vcc to 2/3 Vcc (which is 50% of the voltage change) is still 0.69TC, just as the discharge from 2/3 Vcc to 1/3Vcc. There may be a mathematical reason for these numbers to be the same between the two graphs on this post and #21, I don't know.

I think it is interesting how linear the line appears, you see some curve, but not as much as I have been drawing.