How do you output a frequency/note with a 1V octave keyboard controller?
What does the CV output do at key-up when measured with a meter? 

It should go to zero or negative depending on the opamp supplies.

Are you using the -12V as shown or ANY voltage there. That is the "stop" circuitry. 

If you short the 555's pin 5 to ground that is the best stopped sttae you can expect unless you use a -12V supply as they suggest.

You need to provide SOME way to stop the 555 on key up.