My transformer is an Elma TT iz1892 transformer.

On the primary side, static measurements are as follows:

Winding	Resistance (sample #1)	Resistance (sample #2)	Windings
4Ω	0.56 Ω	0.55 Ω	18
8Ω	0.66 Ω	0.61 Ω	30
16Ω	0.83 Ω	0.81 Ω	48

Secondary

Winding	Resistance (sample #1)	Resistance (sample #2)	Windings
10W	110 Ω	117 Ω	300
5W	157 Ω	168 Ω	400
2.5W	220 Ω	234 Ω	600
1.25W	318 Ω	336 Ω	725
0.625W	469 Ω	492 Ω	900

There seems to be quite some variance between samples on the secondary winding.

A property of transformers is that their impedance depends on the frequency of the signal.

Measurement setup: 12v p2p sine wave from TPA3116, 4Ω ohm series resistor, 4Ω/10w (16.66 winding ratio). We either short the high side contacts, or leave them open. Open resistance is calculated based on the peak circuit voltage and the peak transformer voltage. This is only an estimation because of phase shift.

Frequency	Contacts shorted	Contacts open
100 Hz	1.06 Ω	8.90 Ω
200 Hz	1.08 Ω	17.10 Ω
500 Hz	1.16 Ω	28.43 Ω
1,000 Hz	1.17 Ω	42.19 Ω
2,000 Hz	1.06 Ω	58.39 Ω
5,000 Hz	1.18 Ω	39.39 Ω
10,000 Hz	1.23 Ω	17.71 Ω

Here is the data of all windings, at 1000hz.

Winding ratio	Windings	Contacts shorted
6.25	16Ω 10w	3.30 Ω
8.33	16Ω 5w	2.60 Ω
10.00	8Ω 10w	1.76 Ω
12.50	16Ω 2.5w	2.12 Ω
13.33	8Ω 5w	1.49 Ω
15.10	16Ω 1.25w	1.88 Ω
16.67	4Ω 10w	1.07 Ω
18.75	16Ω 0.625w	1.61 Ω
20.00	8Ω 2.5w	1.21 Ω
22.22	4Ω 5w	0.90 Ω
24.17	8Ω 1.25w	1.07 Ω
30.00	8Ω 0.625w	1.03 Ω
33.33	4Ω 2.5w	0.82 Ω
40.28	4Ω 1.25w	0.85 Ω
50.00	4Ω 0.625w	0.70 Ω

Assuming transformer is not near saturation, resistance can be estimated with:

$$ \text{resistance} = \text{primary winding resistance} + \frac{\text{secondary winding resistance} + \text{load resistance}}{\text{winding ratio}^2} $$

The body current can be estimated, with reasonable accuracy, using this formula.

$$ \begin{align} \text{resistance} &= \text{series resistor} + \text{primary winding resistance} + \frac{\text{secondary winding resistance} + \text{load}}{\text{winding ratio}^2} \\ \text{primary current} &= \frac{\text{voltage}}{\text{resistance}} \\ \text{body current} &= \frac{\text{primary current}}{\text{winding ratio}} \end{align} $$

A low turns ratio results in a 'constant voltage' device. This is better for low stinging.

A high turns ratio results in a 'constant current' device. This is better for safety.

4ohm series resistor, 6v peak, electrode resistance 1000Ω. The electrode contact is bad, we assume resistance increases to 2000Ω and electrode area halves.

Winding ratio 10: with 1000Ω current is 38mA, 2000Ω current is 23mA. This represents an 28% increase in current per area.

Winding ratio 20: with 1000Ω current is 39mA, 2000Ω current is 29.5mA. This represents an 51% increase in current per area.

We hypothesize that this makes output less stingy.

4ohm series resistor, 6v peak, electrode resistance 1000Ω. Something happens that causes the resistance to drop to 50Ω.

Winding ratio 10: base current 23mA, Current with lower resistance 95.5mA.

Winding ratio 20: base current 39mA. Current with lower resistance 56mA.

Suppose that you believe 50mA is the maximum safe current. Then a higher winding ratio provides higher power while staying within safety parameters.

One consideration for selecting the turns ratio is the maximum power that can be delivered from a certain voltage source. This depends on the load resistance. My measurements (with 4Ω series resistor) suggest the following:

Load	max power winding ratio
< 250Ω	6.33 (16Ω 10W)
250Ω < x < 800Ω	10 (8Ω 10W)
800Ω < x < 2000Ω	16.66 (4Ω 10W)
> 2000Ω	20 (8Ω 2.5W) 22.2 (4Ω 5W)

For some reason the low wattage windings such as 18.8 (16Ω 0.625w) and 15.1 (16Ω 1.25w) do not perform as well as 16.66, 20 or 22.2.