Hi,
what does a warm sonic signature mean technically? Does it mean more harmonics? Is it preferred for classical music?
The meaning of words is usually a function of context. The problem is that your question is vague in that regard. And unfortunately, some make the mistake of thinking that a vague question, leading to a variety of different answers, means "nobody really knows what it means, it's not a helpful term." Instead, it's just standard communication to use a word in..context.
So are we talking about whether a vocal recording sounds warm, or is lacking warmth? If it's lacking "warmth" that usually means it's sounding a bit thin, lacking the natural body we hear in people's voices, and possibly bright. A good mixer will know which EQ range to boost for more "warmth" in, say, Johnny Cash's voice.
Are we discussing whether a piano recording sounds "warm" or needs more warmth? Well that might take a boost around 75Hz - 200Hz.
Are we talking about "warmth" in terms of timbre and harmonics? We can say that the woody resonance of a cello sounds "warm" vs the striking of a tubular bell sounding more "cool/metallic." But we can even talk about "warmth" for metallic instruments - e.g. the tubular bells, or acoustic guitar strings. That can be an expression of harmonic richness - richer, ringing sound may sound more harmonically lush and "warmer" in that regard, vs say an overly damped metal string or bell.
Are we talking about the overall sonic signature of a sound system? Well, again, context. A more typical that would involve things like a general tilt towards the lower frequencies - i.e. a rolling off of the highs and rising towards the bass...or specific boosts in "warmth" region like the lower mids/upper bass too.
There's also, to my mind, another sense of "warmth" in the sound of a system, which is more like the timbral/harmonic quality of an instrument. Some systems just sound "warm" more in the way wood sounds "warm" vs metal, like they do wood sounds particularly convincingly, there's a sort of warm upper mid "glow" I associate with warmth too.
Here's more talk about "warmth" from sound on sound:
You don't need a wand to conjure up sonic magic, just a few well-chosen recording tools.
www.soundonsound.com
Now, the person who looks at all the above and throws up their hands saying
"aagh, there's just too many meanings of 'warm,' so that makes it useless" has, for some strange reason, simply forgotten how communication works. You learn what something means by the context in which it is being used, and the good communicator is aware the audience knows the particular context, or if not gives the context.