What is “warmth” and how do you get it?

What is particularly interesting to me is your discussion of different amplitudes of the harmonics having such a big effect. I am starting to come around, but it would be good to find some info on that in particular. That would certainly seem to be one of the biggest differences between live and recorded sound, then, and probably a much bigger difference than I have thought.

For a bit more background, I'd recommend that you do a bit of reading on the theory and history of electronic synthesizers and speech synthesis. In electronic music composition, this timbral relationship between the fundamental and its harmonics is commonly referred to as "formant", the change of parameters across the duration of a note is called "envelope", and the periodic change within a note is called "modulation". Approximate, crude parallels to acoustic instruments are that formant = timbre, envelope = articulation, and modulation = vibrato.

It is of course possible for analog electronics to generate their own harmonics - this is how analog synthesizers work. I've personally implemented patches on early synthesizers (ARP and Buchla) that can deliver pretty convincing flute, bell, and string sounds. Ironically, it's not so much the timbre/formant that's hard to emulate, rather it's the envelope.

Even earlier, the acoustic principles of building formants are very structured in a thousand or so years of the art of building and tuning pipe organs. Emulation of orchestral instruments became a very common goal - this style of organ-building probably reached its zenith in the very early years of the 20th century with builders such as Willis in the U.K. and E.M. Skinner in the States.

An interesting side note on timbre - I have found it a commonly-held view in vocal and woodwind pedagogy that poor tone production produces a set of overtones that are in fact not in tune with the fundamental, rather they tend to be flat. Although I have not seen any measured evidence to back this up, I tend to agree with it - as the perception of intonation problems as it relates to tone production cannot be corrected simply by raising the pitch. That is, some singers always sound flat, no matter what pitch they're singing.

all of the discussion regarding harmonics is useful and instructive, but does not address the question of whether warmth is a form of coloration. unfortunately, no one has definitively spoken on this subject.

Well, er, if "warmth" is imparted upon the timbres of instruments to a degree not present on the recording, then yes. Otherwise, no.

To "add warmth" at the studio or FOH console, I would usually first reach for a band of EQ in the 1500-2000 Hz range, moderate-to-wide Q, and cut a couple of dB. Another technique that works in the studio is to cut the upper bass (200Hz-ish centered) area in the side chain of a compressor -- this makes it a function of envelope as well as timbre, and can add "bloom" to drums and vocals.

Does that help?