Gen 8040a

Well, I don't necessarily want to argue about it, but let me discuss things a little deeper in layman's terms.

When an amplifier distorts, it's running out of voltage headroom because it's running out of current drive ability.  Ohm's law applied here, the load is the same but if current demand goes up, voltage must come down. 

If we ignore all real-world filtering and just take the image of a sinewave and limit the amplitude by compression (the term for amplifiers running out of headroom, AKA clipping) then the distorted sine takes on an approximation of a square wave when viewed in the time-domain (oscilloscope style). 

What is a square wave? 

Mathematically it's defined as an infinite number of sinewaves within a given bandwidth.  Since the bandwidth is defined by the frequency of the input sinewave, we're left with a cascade of harmonics at intervals of the input frequency when viewed in the frequency-domain (spectrum analyzer style).   A 100Hz sine will produce harmonics at even and odd frequencies such as 200, 300, 400, 500, etc with the amplitude of each harmonic being related to the degree of symmetry of the clipping.  For this we'll assume that it's clipping with perfect symmetry so that all harmonics in the band would have similar amplitudes and as such, the power of a pure square wave is the power of the sinewave squared, or roughly twice the power.

Now, since we know that a squarewave is nothing but a stack of harmonically related sinewaves and that the power of a square to a sine is voltage^2, then each harmonic is related in power to the fundamental signal (f1).  Taking odd harmonics as an easy rule of thumb, the harmonic number is related to it's voltage, so the 3rd harmonic is 1/3rd the voltage, the 5th harmonic being 1/5th, etc.  But for power, since it's squared voltage, that means the 3rd harmonic is now 1/9th the power, the 5th harmonic is 1/25th the power, etc. 

As you see, the power spectral density (PSD) of harmonic content quickly becomes irrelevant, and more so as you increase the fundamental frequency since AC power is related to period (frequency) in a way that can be describe in calculus integrands, but for the sake of keeping this short I'll offer this tidbit:  Given an equal peak amplitude, the power of a sinewave decreases as the frequency increases due to the decrease of signal period.

But what does this all mean?  

It means that aggregating both the natural reduction in harmonic power in a clipped signal as frequencies increase, as well as the reduction of the fundamental power as frequencies increase, we see a far greater decrease in spectral power as the input frequencies increase. 

Since lower frequencies consume much greater powers to amplify to a given sound power (SPL), that amplifier will naturally clip at lower frequencies first.  If we include the series high pass element in a speaker crossover for the tweeter then we'd arrive at some very small fraction, but without long math it would work out to something on the order of perhaps 1% higher power to the tweeter for an amplifier clipping at almost 50%.

So since I'm needing to get back to work I'll close out by saying, if your amplifier is clipping by 50% and yet you're still listening, and somehow your tweeter would blow by increasing it's power by 1%..  You might have bigger issues than asking why your speakers keep burning out!

However, it also begs the rhetorical question, if distortion harmonics are the cause of tweeters blowing up at low power levels, then why aren't purposely distorted signals such as grungy guitars not blowing tweeters when fed to the speaker at a similar power level?

Or another rhetorical question, if we ignore all systemic filtering effects in a system and distort a sinewave to a perfect square, the result is 2x the power so a theoretical 100W amplifier (that can somehow continue to add current despite being 100% clipped) would supply 200W to the load, right?  So how is that different than increasing the power of an amplifier to 200W?  This is the situation where someone claims that a 100W amplifier would be "underpowered" yet supplying 200W to a load yet a 200W amplifier supplying 200W would not be underpowered?   

And that's the paradox of the "underpowered" amp, it somehow supplies too much power to harmonics that don't necessarily add a significant amount of spectral power, yet an amplifier that can supply the same amount of total spectral power to the same frequencies as the harmonics is somehow not dangerous?

BTW I deal with high powered RF amplifiers and compression-related distortion all day at my day job.  

I can say without a doubt that harmonics do not destroy loads of any type.  Power excursions do.  

You know your electronics and theory my friend, but the real world of the limitations of mechanical devices is very different. Clipping or square waves particularly if consistent will shed the suspension of just about any speaker. Before you go into any theory go ask your local recone guy he will tell you from experience, conventional speakers just can’t take it.

Good catch.  I had forgot to add the second half of my statement, which is "in a system with finite current sourcing ability".  As an amp tries to supply current beyond it's capability, the voltage collapses as the current sourcing ability becomes increasingly limited.

Well, I'm not arguing against physical destruction.  I'm merely saying that increased harmonic content from clipping doesn't add enough power to a signal to destroy a tweeter.  Power excursions, such as big thumps, pops and clicks can have instantaneous peak amplitudes well above harmonic power densities and those can in turn cause very fast and large power dissipation peaks in coils that can burn them quickly like a fuse.  If the coil is lucky enough to survive, the power excursion might lead to a physical excursion and damage the speaker in ways you mention.

Power rating is almost purely subjective..  There's no real standard for measuring it.  Some measure it at different frequencies while some measure it as a varying percentage of total dissipation, while still others might add or subtract overhead or derating for whatever reason..  It's how you can get amps that claim 5000W peak power but only have 100W RMS available, they mean that it can theoretically source 5000W for 1uS as a function of collapsing coil inductance in an 8 ohm speaker causing voltage transients..

Anyway, an amp might be underdamped and allow transients with high peak voltages through as they ring out.  The situation would be catastrophic if a very inductive crossover was used with an amp that has very high Gain-bandwidth product (GBW) meaning that it maintains extreme slew rate over bandwidth at high gain levels but without the current to refrain from developing transients.  Technically this is not unlike how switch-mode power supplies work in step-up mode.  Also technically this would mean that the crossover and/or amp would have been poorly designed as well as probably one or the other poorly matched to the other.

In the land of designing gear that must be BIGGER FASTER STRONGER yet somehow interface with anything and everything, it's impossible to predict every match and account for poor outcomes without compromising one of the BIGGER FASTER STRONGER attributes.

However, I think a very simple explanation could be made..  An underpowered amp is often turned up louder..  which makes it more susceptible to pops and clicks if the system is underdamped.  I've personally seen/heard a couple speakers die during the turn-on/off thump/click because myself or someone else left it turned up too loud.

Yes, pretty much!