i'm not at all convinced that we're any closer to understanding warmth. i do not agree that it's as simple as boosting or cutting frequencies, i do not agree that it's as simple as adding harmonics, i do not agree that it's dependent upon the type of equipment used.
i do agree that all of the above can be useful to making a good mix, but prefer to use terms like width, depth, and clarity, or refer to what's happening in specific frequency regions, than to try to convey any kind of useful meaning with the term 'warm'. even among engineers.
....
heck, i don't even know if warmth has to do with something physiological, or if we just associate it with the kinds of recorded music familiar to the last several generations of humans. who's to say that, in 50 years time, what we call 'cold and digital' today will sound natural, and all those tube and tape tracks will sound flawed?
so here's my challenge: i challenge anyone to come up with a definition for warmth that:
1. everyone can agree upon
2. doesn't use the term warm
3. leads to a specific set of steps to achieve the goal
there are many terms in audio engineering which i assert fit the above criteria. get a room full of audio engineers together, and we'll pretty much agree what it means when someone says, "de-ess those vocals", "widen the mix", "give the guitars more depth", or "the mix is too bright", and what needs to be done to achieve it.
i assert this is not so with warmth, and i challenge anyone to demonstrate that it is.