Are output transformers "tuned" for their specified primary:secondary setup?

[Deke609]

I assume the answer is yes, but I'd just like to check the experts.

I ask in light of my recent realization that OTs don't really have fixed primary impedances or secondary load handling capabilities, but rather a primary:secondary turns ratio by which the load on the secondary determines the primary impedance. And yet manufacturers spec their OTs by fixed primary:secondary numbers - e.g., 5K:8ohm. So I figure this is either (a) for the convenience of potential buyers, most of whom presumably will be looking for standard primary impedances matched for the usual 4/8/16 ohm speaker loads; or (b) because the OT has been "tuned" for best performance (e.g., frequency response) when used in the spec'd setup.  Are OTs "tuned" for their spec'd primary:secondary setup?

many thanks, Derek

[Paul Joppa]

Output transformers are tuned for a  primary impedance, balancing primary inductance and magnetic flux for bass against leakage inductance and capacitance for treble. Then the secondaries implement the turns ratio for maximum power delivery to the target load impedance.

[Deke609]

Many thanks PJ.