Question I couldn't find an answer to so far.
Do tube amps "create" a sound signature with different headphones based on the impedance curve of the latter?
Or do headphones not have noticeable impedance curves? (is a 32 Ohm can just linear 32 Ohms?)
Where am I coming from with this?
I have an EL34 tube amp with a distinctive "sound" on my Bowers & Wilkins speakers because the speakers don't have a linear impedance across the frequency range, so the tube amp will not "amplify" all frequencies the same which changes the sound signature of the speakers quite considerably. (the impedance curve zig-zags between 2 and 16 ohms, iirc)
The amount of variation is related to how big the ratio change is (amp/transducer) at each frequency. Speakers have their wildest impedance changes often caused by the crossover circuit between several drivers. They also happen to have extremely low impedance, which can maximize the amount of FR change when changing the amplifier's impedance.
For a single dynamic driver headphone (most headphones), you will find smaller variations as there is no cross over circuit. What's left is just one resonance at a given frequency (usually low freq). And on occasion if the headphone really has big design issues, a few other blips on the impedance curve. But those really tell you to not worry about impedance ratio and just go get another headphone^_^.
Overall it tends to be pretty stable so long as the headphone doesn't have a low impedance. If a headphone has impedance variations going from 350 to 600ohm, only a 100ohm amplifier will manage to cause a frequency response change that's worth noticing. A headphone with impedance going from 25 to 60ohm for example would be more of a concern for the final FR and how the amp's own impedance will affect it.
Dynamic driver will have the resonance(impedance bump) I mentioned. Planars tend to have an extremely flat impedance curve (they are almost fully resistive within the audible range). If you go look at IEMs and multidrivers in particular, then we're back to models more similar to speakers, with low impedance and sometimes really wild impedance variations.
So your example of 32ohm, which is usually only reliable for 1kHz where it was measured, will follow those rules of thumb for the relevant driver type.
Another possible cause for frequency variation, strictly related to impedance ratio (as there could be other reasons for a FR change), is if the amplifier also happens to not have a very flat impedance curve over the audible frequencies (depends on design, but they're usually pretty flat with some changes at really low or really high freqs, so we tend to ignore that aspect. Also, almost nobody will measure amp impedance over a frequency range. We can't be too concerned with information we can't find).
About tube amps, as they tend to have higher impedance than SS amps with strong negative feedback, they can indeed take the impedance curve of a headphone and boost the frequency area near a dynamic driver's resonant frequency (where an impedance bump would show). Some tube amp design could also exhibit some significant roll off in the subs (usually made worse with low impedance headphones). So I guess that too could count as impedance curve and impedance ratio impacts on the frequency response of the headphone.
But obviously a tube amp could also have a good deal of distortions that, without changing a frequency response graph, could change our subjective perception of something like timbre, and we might end up interpreting such changes as frequency response changes.