You mentioned the frequency depends on the inductance of the primary and the parallel capacitance, you were right.
Seeing as the capacitance is across the entire winding then that ios our interest, the whole winding, even though 1/2 is active at anu one time, the capacitance is always present.
The cap and coil are a bell, and the trannies are clappers.
If this were a blocking oscillator or something then you'd be looking at one coil as the other would be feedback only.