Regarding the statements that have been made about losing half the power vs. not losing any power, if the nominally 16 ohm speaker is connected to an 8 ohm tap, in most cases the truth lies somewhere in between. It depends on the output impedance of the particular amp, and in some cases perhaps also on the current capability of the particular amp.
The output impedance of the 8 ohm tap of most (but not all) tube amplifiers will be considerably less than 8 ohms, corresponding to a damping factor considerably greater than 1. As a consequence of that, and assuming that power delivery into 8 ohms is not limited by current capability, the amp will not be able to deliver as much power into 16 ohms as into 8 ohms, but the reduction will be smaller than in the case of a solid state amp having near zero output impedance. The reduction will be MUCH smaller if the amplifier has a particularly low damping factor/high output impedance, such as SET amps commonly have.
An actual increase in power delivery into a 16 ohm load connected to an 8 ohm tap, compared to an 8 ohm load connected to the same tap, would occur in the relatively uncommon situation where the amplifier has a damping factor significantly less than 1, corresponding to an output impedance significantly greater than 8 ohms, and/or if its 8 ohm power capability is limited by current capability.
A separate question relevant to connecting a 16 ohm load to an 8 ohm tap (assuming the amp is not an OTL and has output taps) would be whether or not a perceivable increase in distortion might occur in some cases. Perhaps Ralph will speak to that, as I don't know the answer.
Regards,
-- Al