Thanks Ross, my muddled thinking at first was that a 1:1 transformer had the same turns on the primary and secondary.

Well yes, a 1:1 transformer would have the same number of turns on primary and secondary, otherwise it wouldn't be 1:1

I am guessing that taking turns off increases the primary current and therefore the magnetic flux.

It shouldn't significantly change the current in and of itself.

In an "ideal" transformer, the power into the primary will be transferred perfectly to the secondary, even in an air-cored transformer (with no iron or ferrite core). If you put in 1 watt on one side, you'd get one watt out the other side, and this is where the turns ratio comes in to play.

If you have 10 turns on the primary, or 100 turns, or 1000 turns, doesn't matter. If you have the same on the secondary (so it would be a 1:1 RATIO), if you put in 1 watt at 10 volts, that's 100mA of current in the primary, and also 10 volts at 100mA out the secondary.

If you had 1:10 ratio (so 10 turns primary and 100 secondary, or 100 primary and 1000 secondary), the voltage out the secondary will be 10 times what is on the primary. (Think if each turn as a single turn winding, all connected in series like tiny little batteries).

With a 1:10 (step-up), 1W at 10V in will produce 1W at 100V out (so only 10mA).

Connecting the transformer the opposite way (calling the secondary the "primary") would make it 10:1 (stepdown).

100V in would give 10V out, at 10 times the current. (This is how welders get such high current).

I'll leave CTs (Current Transformers) as a thought exercise. If you have a single turn primary (typically a busbar or conductor) and some thousands of turns (for the secondary), why the burden resistor is absolutely critical, even though it may be passing very low current!