I'm not sure there is so much to understand there.
The motor is wound with additional coils which generate a signal relative to the activity of the motor. That signal is 6 equally spaced pulses per motor revolution. I guess that is what is meant by symmetric frequency generator in this context.
The (maybe indirect) output of these coils is fed into the analog comparator of the attiny2313 mcu. That gives a clean pulse with a frequency of 6 times the motor speed. The mcu uses a 2KHz clock to measure the signal from the motor coils and switches the motor control pin as needed to achieve a constant motor speed. 55.55 Revs/sec from the motor gives a 333.33 Hz signal because the sensor coils give 6 pulses per motor revolution. 6 ticks of the 2KHz clock also give a frequency of 333.33 Hz.
Of course, if the motor in your system does not have the sensor coils, then you'll need your other solution.
You saw the schematic:
And here is how the (AVR) internal analog comparator can be used:
https://www.gammon.com.au/forum/?id=11916