Interesting comment. I can see where you're coming from but I'm not sure I agree that "dirt" is the only path to harmonic richness, For example a symphony orchestra sounds amazingly warm/rich without any distortion or even amps at all. My (quite possibly wrong) thinking is, I'd rather start with a clean sound then add-in effects as needed, than have a rig that can't avoid applying the same tone over everything. I'm quite happy to be schooled though.
The thing about the Mesa is that in one review I read it said it sounded a little wooly which is concerning... I'll take all the low bass/subsonics I can get but I'm trying to avoid that muffled/boomy midrange sound that many small cabs have, especially the cheaper ones.
Well it has to do with aliquot tones (and other additive noises that can positively warm up the sound). The more you try to "clean up" your amp by focusing the tonal projection into a specific range the more processed the sound is. Ok I realise that this is a very subjective thing but there is a reason why tube amps sound warmer and more pleasant to the ear than SS amps do - they are better at throwing out the extra harmonic material that adds up to the tone, making it sound richer and therefore warmer.
The word "warm" is subjective as well because you can find people who claim a sinus wave to sound warm. Which in fact it could, if you consider there is usually no special harshness to the "tone" of it. No spikes, nothing.
But when I think of warm, I think of harmonically rich sound, supported by a nice blend of aliquot tones with nice projection and a nice warmth in the mid range area (read: nicely bumped controlled mids). It is how I would describe a nice tube amp sound. Notice that the warmth doesn't come from crazy subsonic freqs, nor does it come from crazy extended high trebles. Most of the warmth to the tone comes from the 175ish + Hz up to around 400-500ish. It is considered the "body" of the bass sound even though your base frequency of the actual tone is way lower than that. So you are actually bumping the aliquots of your base tone to achieve warmth, not the other way around.
Most cabs that are considered very "clean" tend to have a scooped mid (the so called smiley face voicing/EQ) or at least a flat response curve. This inherently contradicts the common definition of a warm tone which in fact focuses and relies mostly on the scooped/flattened region of the clean cabs.
This is also what we like to call hi-fi. A low end and top end pleasant sound with scooped mids to get rid of the unwanted aliquot tones which do produce a slight "dirt" in the sound. This consequently means less harmonic detail, more pronounced base tone with added top end clarity, meaning less "warmth".
You will especially notice this in the mix. A mid rich sound (with pleasant non-spiky mids) will give you that nice buttery feel that we usually associate with a warm tone. When you isolate the bass line the bass may in fact sound relatively dirty and this has nothing to do with actual distortion (which even further accentuates the aliquots). There is just a lot going on in that sound. It really will not want to sound like a clean bass. Most of the old recordings sound that way, especially since it was all recorded with mostly analog tube equipment and lacked the technology to clean up the sound as surgically as we can today. A lot of artists actually relied on this specific tone. One artist that comes in my mind is Eric Johnson. His recent recordings sound A LOT cleaner than they did in the 80s and 90s yet his sound lost basically all character he had back in the day. All because we strive towards a cleaner sound which inevitably means a more processed, smoothed out tone.
A lot of people may argue with this, but honestly you will not convince an "old-school" vibe oriented bass player/musician that you have a very clean and also warm tone. It's not how it sonically works out in your ears.
Hence, the cleaner the tone, the less warmth it will have. It is inevitable.
Pardon my engleesh, hope i was able to kind of clarify this in an understandable way.
Edit: Marcus Miller is known to have one of the most processed and clean sounding bass sound out there. Does it sound warm? Really not. Clean? Absolutely.