I'm still waiting for a cogent response to a question that I posted in another thread which is how can one make an informed choice between matching a particular amp with a particular speaker.
Bruce, as the other thread makes clear there are many variables and matters of degree that are involved. Therefore I don't think that a one-sentence or other kind of cogent guideline can be formulated, beyond Ralph's suggestion of trying to determine what the designer's intention was.
I think that your other comments above are well said, except that with respect to this statement ...
In the case involving typical tube amps, current (amps) remains relatively constant regardless of impedance, but voltage varies. As a result, power (watts) doesn't change as much over the frequency range where impedance changes all over the place.
My ARC tube amp power rating is pretty constant regardless of impedance load, which is consistent with the Power Paradigm as described in Ralph's white paper.
... I would put it that in the case of a tube amp both current and voltage vary somewhat as a function of load impedance, with the net result being that power delivery varies significantly less than it would with a solid state amp that acts as a voltage source.
Also, the similarity of the MAXIMUM power ratings of a tube amplifier's 4 ohm and 8 ohm output taps involves different considerations, that are not directly related to the variation of power delivery as a function of load impedance WITHIN the amplifier's rated capability. The latter results from the interaction of amplifier output impedance and speaker impedance.
In considering all of this, it would probably be helpful to digest this Wikipedia writeup on the
voltage divider effect. And to consider Z2 in Figure 1 as being the impedance of the speaker, which varies as a function of frequency, and Z1 as being the output impedance of the amplifier, which is essentially zero for a solid state amplifier, and typically one to several ohms for most (but not all) tube amplifiers. Then assume that in both cases Vin is being provided by an ideal voltage source (i.e., one having zero output impedance), and do a few calculations of power delivery for various combinations of Z1 and Z2. The power delivered to Z2 being equal to the square of the voltage across Z2, divided by Z2.
That is a bit oversimplified(!), because it neglects impedance phase angle, but a few such calculations should make clear what is happening with respect to the interaction between speaker impedance variation as a function of frequency and amplifier output impedance.
Best regards,
-- Al