And on a related note, what measurements - if there are any - show the difference in sound between SS and tubes?
Could one see this on a frequency chart?
Yes. Look at distortion vs frequency- if it begins rising much below about 10KHz you will have a brightness problem since higher ordered harmonics will be higher than the THD suggests.
The other thing to look at is the distortion profile. Smoother sounding amps have a greater degree of 2nd and 3rd harmonic than amps that tend to sound bright and harsh. This is simply because the 2nd and 3rd in the latter amps is insufficient to mask the higher orders. Our ears interpret the higher orders as harsh and bright using the same metrics that cause tone color in musical instruments.
Start by looking at the distortion profile of an SET. That will give you an idea of the relationship of the 2nd and 3rd harmonics to the higher orders, so you can start to see what you're looking for in the measurements.
BTW you don't need the 2nd harmonic- the ear treats the 3rd very much as the 2nd as long as its not too profound. But it needs to be more profound on a percentage basis than the succeeding harmonics in order to mask them.
We've had the tech to measure this stuff for about 30-35 years but the understanding of the significance has been lagging. So we now have a direct link between measurements and what we hear. Unsurprisingly, these measurements can be a bit hard to dig up...