pro's and con's of a 4 ohm speaker?

8 ohm speaker will also double your damping factor

Although that will not be true in the case of a tube amp, assuming the 8 ohm speaker would be connected to the 8 ohm tap, and the 4 ohm speaker would be connected to the 4 ohm tap. In those cases damping factor would be the same.

Not that it matters in many cases. Damping factor is mainly significant when either:

1)A tube amp (or other amp with high output impedance/low damping factor) is used with speakers whose impedance varies widely with frequency. In which case higher damping factor may or may not be better, depending on the particular speaker. Or,

2)Woofer damping and control is particularly important to the particular speaker, and the damping factors of the amps being compared are not especially high.

Best regards,
-- Al

Is there any benefit of using lower impedance speakers with tube amps?

Hi Kijanki,

Not as far as I am aware. As you may have seen, Atmasphere (Ralph) has commented a number of times that the sonic performance of pretty much any amplifier, tube or solid state, will be better when it is working into a higher impedance. And Audiokinesis (Duke) made essentially the same observation earlier in this thread, while rightly adding that that may very often be outweighed by performance differences between the speakers themselves.

As I understand it combined plate impedance gets divided by speaker impedance to get transformer turn ratio.

Actually, as with any transformer the impedance looking into one side of the transformer equals the impedance that is connected to the other side factored by the SQUARE of the turns ratio. For an output transformer, typically the number of turns on the secondary side for the 4 ohm tap is 0.707 times the number of turns for the 8 ohm tap. That results in the output impedance of the 4 ohm tap being half of what it is on the 8 ohm tap, as you indicated, as well as resulting in a maximum power rating that is approximately the same when a 4 ohm speaker is connected to the 4 ohm tap compared to when an 8 ohm speaker is connected to the 8 ohm tap. As well as resulting in the output tubes seeing approximately the same load in both cases.

Best regards,
-- Al