Amplifier stability with very low impedance, high efficiency mid/tweeter section???

OK. I understand that speaker impedance fluctuates with frequency.  I think what you're pointing out is that a low dip in a speaker's impedance (no matter at which frequency) is going to present a problem for a typical amplifier to track a flat frequency response because most amps cannot double their current when dropping from 4 to a 2ohm load (and tube amps halve their current).  And that a low impedance can blow up an amplifier even if it's not playing current demanding material (bass), correct?  I also didn't know that an amplifier's output impedance fluctuates with frequency response... 

It's a power and heat sinking problem. The lower the load the amplifier sees the more heat has to be dissipated by the output transistors. Transistors have a maximum operating temperature and they'll fail at that temp so amps are designed with thermal cutoffs well below that limit if the heat sinks get too hot. 

But... if you lower the volume then there is less heat dissipated and if that volume level is loud enough (courtesy of the high SPL of the speakers) and the amp is happy and not overheating at that volume level, then it's not a problem. The amplifier does not care what the SPL rating of the speaker is, that is between the speaker and it's crossover and internal volume -- the amplifier sees an inductive load only.

To give you an idea of the heat sinking requirements:

say I want an amplifier with only one pair of output devices, 50 watts at 8 ohms, biased low A/B, with 36 volt rails. At peak signal input (say 1.2 volts) the power the transistor dissipates at peak is about 45 watts. At 2-ohm loading it's 150 watts. Can't do it, needs more pairs of transistors so the amp is limited in its power output to not lower than 4 ohms.

But if you cut the input voltage with the volume pot down to, say, 200 millivolts -- and that is loud enough for you -- the power dissipated at 2-ohms is 50 watts, which is within the max power spec at 8 ohms.

I understand that the lower the load the more heat has to be dissipated, therefore the more output devices and heatsinking.  I just thought that it was low frequencies that were responsible for the majority of this demand, not higher midrange and up.  

And yeah the amplifier doesn't care about the SPL rating but it does care how hard it has to work.  And a high sensitivity speaker makes it work less hard for the same SPL.  No?

I am old school. If your amplifier cares about the speaker I say look, you're an amplifier, this is your job, tough luck. If you want it easy go back to school, learn how to be a AVR, nobody cares as long as you have a lot of knobs and switches and stuff. But for now, get on with it.

I did lose one to Amplifier Protective Services but that was before I learned to not let them have a cell phone. Take my advice, make an example out of one, word gets around fast, you won't evert have any amplifiers whining about how hard you work them. Trust me. Haven't heard one word of complaint in 20 years at least now.

To understand this better you need to understand what happens when you have an ideal voltage followed by two impedances.  One of the amp, one of the speaker.

V ---> Z(output) --> Z(speaker)  or for simplicity in a DC world:

V--> Ro --> Rs

You need to understand a little about how the varying Z (or R) will affect the voltage at the speaker.

You also need to understand that Zo/Ro is almost never flat, so the amplifier's output impedance is also changing.  The inability of an amplifier to double it's output as impedance is halved is related to this.

So a 100W amp that can't double all the way down to 2 Ohms will also probably not be able to double at 1 Watt output.