Clock generation of 9 phases of clock
It sounds like a circular shift register will do this.  Have the processor produce the shift clock probably via PWM hardware or something else that runs without firmware intervention once set up.  The output frequency will be the shift clock divided by the number of bits.  If the shift register is originally loaded with a adjacent chunk of half the bits on and the other half off, each output will be a square wave with 1/bits fraction of a cycle out of phase with the next.