Yeah, there is the warmth of tube audio amps. And that seems to be all about the even order harmonic distortion that people find pleasing to the ear. But when the term is used to apply to solid state amps, then it seems that maybe it is used to describe the emphasis in the mid-bass region. And that is two distinct uses of the same word to describe different things.
As has been discussed, when someone uses the term "warm" in audio it will depend on the context - what specifically they are apprehending as "warm." There's the addition of thickening harmonics or distortion in some cases, or there is the increase in low midrange frequencies (or upper bass), and even in the latter there is going to be some specific technical variation - the frequencies you push to make a female voice "warmer" are going to be different from making a Tuba "warmer." If you are working in a specific context you may automatically know what someone means by "warm," but if you are unfamiliar with a certain context it makes sense to ask ("what do you mean by 'dry martini..or dry humor?').
But since you raise the "warmth" of tube amplification, I happen to have been, yet again, just experiencing that. (As usual, in this context, this is a for-sake-of-argument example, putting aside for the moment the fact tube amps don't necessarily always have a 'tube amp sound' and ideally we want to untangle sighted bias). But simply as one sense in which I am looking for "warmth" in sound:
Think of the difference between "warm flesh and blood" and "cold, hard metal." (E.g. robot vs a person).
Sonically, human voices have this "warmth," this "organic signature," in that our voices have the timbral/detail characteristics of being produced by the the wet damped organic fleshy material (vocal chords, throat, mouth, tongue, chest resonance, etc). And emanating from a person, in this sense a human voice has the sense of "density" and "body" and acoustic projection from that source, of an actual person projecting their voice from a point in a room.
In contrast what I find in the majority of vocal tracks reproduced through hi-fi systems, is a deficit in almost all those characteristics. The voices tend to often sound tipped up in the high end leading to sibilance that is harder, sharper, more electronic sounding. The phasey sonic images sound incorporeal, transparent, ghostly, like I can wave my hand through it. Timbrally voices sound more like produced by pieces of technology than human flesh. Also, to my mind's eye, voices are often the "wrong timbral color" (either a sort of blanched of tone, or too dark, rarely the 'bang on warm' tone I get closing my eyes listening to real voices). So the reproduced voices are often missing those elements that combine where a voice sounds "warm and human."
I've found that my tube amps/tube preamp can nudge the sound slightly in almost all the directions that make voices sound "warmer and more human."
For instance, I was running my CJ tube preamp through my Benchmark LA4 preamp which allowed me to level match between them, and then switch instantly between the Benchmark LA4 solid state preamp going directly to my amps, vs having the signal run through the CJ tube amp.
The LA4 consistently sounded more transparent, slightly more revealing of sonic details (e.g. even the subtlest reverbs). But nothing was ever "the right timbral color" to my ears, so nothing ever sounded natural. Whereas running the signal through the CJ preamp seemed to "flesh out" the sound, vocal sibilance seemed to merge better in to the rest of the voice, sounding less artificially detached, the voices took on a bit more body and density and softness, and crucially the "timbral color" seemed to lighten to what sounded "more life-like" and present to my ears.
The same went for tracks which had hand claps. Through the LA4 preamp all the sound was just super clear and vivid, yet hand claps just didn't sound right - a bit too sharp on the leading edge, and then sort of "black and white" or electronic in tone. When I lightly clapped my own hands the difference between real flesh clapping and the clacker-sounding hand claps through the speakers was distinct. Whereas when I had the tube preamp in the chain, the tone lightened to sounding more "texturally present" claps weren't artificially hardened, they filled out with a bit more density and body, and now when I clapped my own hands the timbral signature between my claps and the ones coming through the speakers felt almost bang on. Like I could have been one of the audience clapping. So now hands sounded "warmer, more human."
Also, everything from brass instruments to sax to acoustic guitars also had more of the type of timbral warmth I hear in real acoustic instruments.
That kind of stuff really turns my crank, and I find when I get that nudge to "timbral believability" in my own perception, I simply enjoy the sound more. And as I've said one of the general distinctions I hear between real sounds and reproduced is a sense of timbral "warmth" where the reproduced versions seem stripped of the richness of tone and harmonics.
*(starts zig-zagging to duck tomatoes...)
