Exactly the argument I was trying to make in another thread, but you're coming at it from the other end. You're already making the assumption that as voltage amplifiers, tube amplifiers do better with high-impedance loads than solid-state ones. You're simply assuming that most amplifiers have no trouble generating voltage. However, solid-state ones do have that trouble, because they are limited by the silicon, germanium, whatever the solid-state construct is used. Similarly, tubes are severely limited in current, because they're trying to move a charge from one point to another through empty space.
I make that assumption because the maximum output voltage is almost always mentioned in the spec sheet of headphone amps. I have no doubt that the amps could reach the claimed voltage. Something that's not always mentioned is the impedance of the load (and the actual power drawn) when they measured the max output voltage. An amp might be able to output 10V into 1kOhms but not into 10Ohms because it lacks the power to do so.
The way I ballpark what amplifier a headphone needs is by looking at the sensitivity of the headphone which is typically in dB/mW (at 1kHz) and it's impedance (which is just an average value). I pick the desired SPL let's say 100dB SPL average is pretty loud already. Since most music is dynamic reaching an average of 100dB SPL requires to reach even higher values (let's just say 20dB headroom) depending on how dynamic the music really is. This would allow for a loud listening experience even with fairly dynamic music.
From the sensitivity, impedance and desired SPL I calculate the voltage the headphone needs to reach the required max SPL level. If the amp has a higher output voltage than I calculated there is already a chance the pairing will work (it will be loud enough for sure). So in this case one of the questions is can the amp actually output their claimed voltage into the headphone I want to use it with? The higher the impedance, the more likely it actually can. The question could be rephrased as well: I know the amp I'm looking at will have enough voltage to drive my headphones, the question is, will it have enough power to do so?
I understand that there are other requirements for the amps like low noise, low distortion but these usually aren't described in the spec sheets in a way it could be useful to me so after checking if the output voltage is enough I just bite the bullet, order the amp and hope I will like the sound.
There is no change in load with changes in impedance. "Load" is the power requirement and that does not change with impedance. The impedance dictates the direction of the vector result of Power (NOT the magnitude) in terms of voltage vs. current.
If you draw Power as a sloped line between axes of voltage and current (Y and X), the line will remain the exact same length, regardless of impedance (the slope of Y over X), but the slope - the angle of that line - will change.
P = I x R, period! You cannot create or remove the amount of energy required for the headphone. Yes, you can substitute Ohm's Law to replace I with V (or "U,", not sure what convention you got that from, maybe a typo?), but it does not change "P" for a given headphone. The only thing that changes is the ability of an amplifier to deliver current or voltage and at what ratio. That is determined by the output impedance of the amp and the impedance of the load.
I'll try to use V instead of U. Hmm, didn't you miss that equation as well? If I wanted to visualize P = V x I (power equals voltage times current) in a simple V-I graph I would think that the power is the rectangle that can be drawn after plotting the (V;I) coordinate. I think the product of two simple numbers, V and I, can be most easily visualized by the area of a rectangle (so the area corresponds to power which equals to V x I) where the sides' length are V and I because the area is calculated by multplying the sides' length anyways. If the area (power) is the given number, there are of course an infinite pair of V-I values that would draw a rectangle with the correct area just like how a certain load can correspond to an infinite pair of V-I values depending on the load's resistance.
So I think we are on the same page just looking at it differently. However there's one thing I still don't understand.
Moreover, the Senns have a pretty big impedance bump around 100Hz. On the HD800, the impedance goes from about 350 ohms at 10Hz, all the way to 650 ohms at 100Hz! It only averages 300 ohms from 20-20kHz. What does that mean? It means that all around the areas of mid-bass, where "warmth" generally comes from, power disappears with many solid-state amps, because they simply can't swing the voltage needed at that high impedance. A typical solid-state amp could be clipping at this point, but it depends on the gain. It might just sound bass-light or tinny.
I'm fairly sure headphones are meant to be driven with the same
voltage gain across the frequencies, and definitely not the same
power gain across the frequencies. Is this where we disagree?
If we don't disagree on that, then the idea of a headphone amp not being able to swing enough voltage at the frequencies where the impedance is high is still looking nonsense to me.
Why would it be harder for the amp to swing the same output voltage into a higher impedance compared to a lower one? Since it's actually easier to have a good output voltage into a higher impedance because that requires less power.