...the impedance at the end of the wire is much more, 'say' 750 ohms. Now I have to match it to a 75 Ohm aerial socket on the radio, so I imagine need a 10:1 transformer.
Not quite right.
The voltage ratio of a transformer is equal to the turns ratio, but he impedance ratio is proportional to the SQUARE of the turns ratio.
So to match a 10:1 impedance ratio, you would need a 3.16:1 turns ratio.
then does it matter whether I wind 10:1 or 20:2 or 50:5 as long as the ratio is the same?
For a 10:1 ratio, no it does not matter, all these will theoretically work.
BUT, and it is a big BUT!
Depending on the frequency of interest, a coil with 1 turn may end up looking like a short circuit at a low frequency and the transformer will not work very well, if at all.
I am experimenting with simple wires, so 'say' 20Mtr long.
OK
I am trying to make end feed aerials
OK
so where it might be 75 ohm at the centre of the wire I understand that the impedance at the end of the wire is much more, 'say' 750 ohms.
A half wave dipole will have a feed impedance of about 75ohms (at the centre), but it is not particularly helpfull to try and think of the impedance at the centre of an end fed wire antenna.
We are not connecting to the centre of the wire, so lets not worry about it (Yet).
The impedance at the end of an end fed wire antenna depends on the length of the wire at the frequency of interest.
If the frequency is such that the wire is a quarter wavelength long, then the impedance will be low, about 30 to 100 ohms depending on the configuration of the wire.
If the frequency is such that the wire is a half wavelength long, then the impedance will be high, several 1000ohms depending on the configuration of the wire.
All this assumes that we have something against which we can measure this impedance, usually a "good" earth connection.
Rather than worrying about a transformer, although this may be a reasonable solution to matching a high impedance antenna to a low impedance receiver, your efforts may be better concentrated on making a simple ATU (Antenna Tuning Unit), more correctly described as an AMU (Antenna Matching Unit).
JimB