Oscillators work in two basic ways: they can be locked to a reference, or free running. A voltage-controlled oscillator (VCO) is free-running by default. If it is forced to lock to a reference signal, it will become a signal with a non-balanced duty factor. This causes inter-modulation distortion of the waveform, but at least the phase will stay locked to the reference.
To get balanced signals that stay phase locked, the oscillator needs to accumulate and cancel out phase errors. The phase-locked loop (PLL) does this for rational multiples like 1/2, 2/3, 4/5. To generate arbitrary frequencies, a counter and divider is needed. This is direct digital synthesis (DDS).