[sdiy] frequency doubling follow-on

[Mountain Man]

Thanks for all the suggestions on frequency doubling; as usual, I've
learned quite a bit from all the suggestions.  I guess I should have
stated the application.  I've assembled a divide-by-three circuit from
Scott Gravenhorst (thanks, Scott!).  I don't like the fact that it drops
the tone by over an octave, so I'd like to boost by frequency doubling.
The circuit puts out square waves with 5 counts high, 1 count low.

I realized on further thought, however, that the first stage of the
circuit creates square waves with a 50% duty cycle, which then feed the
divider.  It seems like the approach that Nils suggested of converting
to triangle, full-wave rectifying, and then using a comparator to get
back to square should work well.  I've created triangles using an RC
integrator.  I'm not sure how to full-wave rectify, however.  I thought
to use a 2 diodes and 2 op amps - filter out positive and negative parts
of the signal, invert the positive, and then feed inverted positive and
negative to a summing amplifier.  When I fed the positive half to a
unity inverter (using a TL072), I got a square wave out, for some reason
:(    I'm wondering if there's a better/easier way to do the
rectification.  I've looked at write-ups about bridge rectifiers, but I
gather that this requires two signals 180 degrees out-of-phase.  Any
suggestions?

Thanks guys,
Elby