Lots of good posts here! @Bryon - Johnson is correct that many currently produced tube amps are not warm at all. In fact, the trend seems to be the opposite. Many companies are now making much more high-powered tube amps, so people don't have to change speakers to use them. In that respect, it makes sense. However, with the added power comes added brightness and a loss of warmth. Johnson's Audio Research example is a good one, another American company doing this is Rogue Audio. If you want a modern tube amp company that has a warmer sound, I would suggest PrimaLuna or Cary.
@Newbee - excellent post about decay. Agree 100%. This is one of the major reasons why many of us musicians prefer tube amps.
@Hifibri - I think we are still not quite understanding each other. You wrote "If live music were only composed of primary frequencies this statement would be true; ‘For a musician thinking about his sound, the "warmth" of it has nothing to do with the frequency being produced, but has to do with the "color" of the sound, or in audio terms, proper reproduction of timbre, not frequency response.” However, live music is not just primary frequencies but a combination of lots of different overtone frequencies that create harmonic structure, warmth, tone, and timbre."
There are a couple of problems with this. First, there is no such thing, if we are speaking of acoustic instruments, as live music composed only of primary frequencies. That could only happen with electronically produced (and then electronically altered) music. Second, when a musician alters the "color" of his sound, this does NOT change the frequency, including the overtones within the sound - these overtones are determined by the frequency being produced, not by anything the player is doing. Now if the player's tone is not pure (is a little or a lot unfocused), this can mess with the overtones that are produced, as the intonation will be off. But usually only jazz musicians sometimes deliberately "bend" notes in this way on purpose. This isn't done in classical performance. I am talking about much more subtle changes of timbre. But the main point is that the musician cannot change the natural overtones produced by the frequency being played. This can be done to a recording of an acoustic instrument electronically, of course (something that digital processing is frequently guilty of) but that is not what we are talking about here.
@ Bryon again - I know we hashed this out on your neutrality thread already, but I still cringe when I read someone assuming that "warmth" must be an "addition" or "coloration." I still vehemently disagree with this. For me, again because of the types of music to which I listen, if "warmth" is not present, that is a definite "subtraction," and therefore an inaccuracy. Measurements be damned! :) I guess this has alot to do with your question about caring more about reproduction of the recording or the actual event.