I've read the Yamaha book and heard the science but I can tell the difference between 500 and 750 watts and even smaller differences.
All with CLEAN power too I hope, and with equal voicing. Because otherwise the comparison would be melons and cumquats ; }
Anyway, that's over 1.5 dB so that's no great surprise. At moderate levels I can sometimes hear a 0.5 dB change in broadband material and always 1.0 dB. But it's hardly worth upgrading a rig's power amp for, which brings us to your next bit:
"make increases by a factor of at least four to be worthwhile."
I didn't write that, but you appear to be arguing something entirely different here... or you think that buying a new amp for only a small gain in clean power that translates into a dB or two is worthwhile. Might as well get a few more dB than that by my reckoning. Fourfold would be 6dB, but I'd sometimes find a 3dB increase worthwhile - TWICE the power. Just depends on where you are at and where you want to be and what's the cost...
So the difference between 600 and 900 watts is significant because is represents the break between the clean and unclean power for my style, cabs, and EQ preference. I just think that once you get above a threshold, the issue changes. Plenty of loudness to gig is not the same as headroom.
Are we jumping tracks here? Nobody was talking about distorted power stages previously when questions were being asked about dB and such. Sure - this is something to consider - but it certainly doesn't make the discussion that has gone on before in any way flawed.
If you use a 700 watt amp--but clip more than you like--but not a lot more--a change to 900 watts is significant in my opinion because it might bring you just above the minimum you need. What's wrong with that? And to tell someone that the difference is insignificant misses the point.
Your example is perhaps not so well constructed because that is just a smidgeon over a 1 dB gain - IF no speaker power compression is allowed for, if you haven't already exceeede xmax, etc. And if you are clipping past 700, going to 900 hasn't even bought you that 1 dB and you can almost hardly call THAT headroom. When it's that borderline you haven't really made sure you escaped the problem.
But the point itself is of course valid, though I'd be thinking more in terms of gaining THREE dB of true headroom.
.......on tube amps, the difference between 300 and 200 watts seems a lot more than the science would indicate. The 300watt tube amp feels to me at least 50% louder than 200watt and very significant and certainly worth the upgrade if affordable.
Uh, what science are you talking about here? There's plenty of additional understanding about the whys and wherefores for this phenom. It's mainly distortion causing harmonic emphasis, power stage compression, preamps/amps with differing gain structures, transformers.
Why do so many people want to take an incomplete understanding of their own and make it science's fault? Isn't it science that made this stuff available in the first place? There's a lot more science to these topics yet, and I'm sure more will continue to be discovered. But not by poo-pooing or ignoring current understandings.