Hi Eldartford, actually the 16 ohm tap is twice the number of turns as the 4 ohm tap. The 8 ohm tap is in between. The impedance of the winding goes up by the square of the number of turns. So the 4 ohm tap is the center tap between 0 and 16.
Also, the voltage of the 8 ohm tap is higher but it is not double! The difference is about a factor of 1.414, assuming that you have the same amount of power into your speaker loads of 4 and 8 ohms and the taps are properly loaded.
If you put a 4 ohm load on the 8 ohm tap the tubes will not be able to make the right amount of power and it is possible that your output voltage may go down rather than up. This depends quite a lot on the way the output section is constructed.