I know a little about harmonics. Probably not enough. It seems we can now add both odd and even harmonics to individual tracks in a mix. Actually it isn't recent since adding harmonics though old hardware is something that's been happening either knowingly or unknowingly for some time. Obviously harmonics isn't restricted only to electronic circuitry and affects pretty much everything we hear.
I think the difference now is we can become selective in the harmonics whereas in the past we were left with the effects of whatever mixing board or or preamp  we happened to be using. Take Waves Scheps Omni Channel for example, it gives you the option to add either even or odd harmonics to a track and adjust the sensitivity. In my thinking, the even harmonics seemed the most desirable, yet they can also reinforce frequencies we don't want to reinforce. A good mix of even harmonics can help to add an airy cushion of warmth to a track if it is done using the correct harmonic relationships.
 
My guess is that the uneven harmonics come in handy for those off color chord shapes or unusual darker frequencies. Maybe to add a feeling of dissonance. Or maybe to balance the effect of too much even harmonics.
 
I'm wondering if anyone here approaches a mix looking deeply at the harmonics of it and how you use that to an advantage?

It is odd (pun intended) that you should ask this while MCharacter is one of the 4 plugins offered in Melda 26 in the deals forum. I made a comment in that thread because that plugin allows tailoring tone to such a surgical level (way beyond even/odd) that you can alter instruments (monophonic is best use) in very creative ways. Demo is 15-days, and the sale is good through Jul 1, but that particular plugin takes what you are talking about to the "next level." If this is something you are curious about, the best advice it to play with it. MCharacter on the driest possible source is most effective, then feed it into an FX chain. Bear in mind, however, that some FX chains will re-introduce harmonics that MCharacter has removed.

Thanks for that heads up Michael. I had not seen this plug in.. seems to allow extensive manipulation at the harmonics level. Cool.

Starise
I know a little about harmonics. Probably not enough. It seems we can now add both odd and even harmonics to individual tracks in a mix. Actually it isn't recent since adding harmonics though old hardware is something that's been happening either knowingly or unknowingly for some time. Obviously harmonics isn't restricted only to electronic circuitry and affects pretty much everything we hear.
I think the difference now is we can become selective in the harmonics whereas in the past we were left with the effects of whatever mixing board or or preamp  we happened to be using. Take Waves Scheps Omni Channel for example, it gives you the option to add either even or odd harmonics to a track and adjust the sensitivity. In my thinking, the even harmonics seemed the most desirable, yet they can also reinforce frequencies we don't want to reinforce. A good mix of even harmonics can help to add an airy cushion of warmth to a track if it is done using the correct harmonic relationships.
 
My guess is that the uneven harmonics come in handy for those off color chord shapes or unusual darker frequencies. Maybe to add a feeling of dissonance. Or maybe to balance the effect of too much even harmonics.
 
I'm wondering if anyone here approaches a mix looking deeply at the harmonics of it and how you use that to an advantage?

I do, but in a more automatic and random way lol. So I start a composition or mix, and the first thing I decide is console emulation using Wave's NLS which gives three flavours of harmonic distortion. Although, and I've just spent an hour or so trying to determine this, I was under the impression that the Neve emulation was tube based, and I don't think it is...meaning you get three odd harmonic distortion choices. It doesn't matter, because each module does have a different flavour. So for me, I will choose the TG12345 emulation for pop or a mid 60s sound. The TG12345 has a slightly metallic sound, that can be further enhanced by using the TG12345 channel strip plug in conjunction with the NLS. The SSL module is the clearest of the three modules, and I would use this for a really big mix...50 tracks plus. The TG12345 can make the low-mids a bit woofy, and in a big mix it can make clarity or separation between tracks hard. The Neve is in-between option. I use this module as my classic rock module. 
 
Now, this is only layer one of the harmonic distortion mix. Next, depending on the instrument another layer of harmonic distortion is added. For electric guitars and vocals, I use Sonar's very un-flashy tube pre-amp emulation. This adds in a layer of 2nd harmonic distortion. Basically, I'm following the rock avant-gardes' signal flow on their classic recordings. If you do some research, up until the mid-60s...there was only tube based audio recording technology. I'm not sure when, but The Beatles first replaced their tube based Vox amps with transistor based ones...their sound changed. It seems this was in 1966. What Oasis called The Beatle sound was in fact, a tube mic recording a transistor based amp and being fed into before 1969 a tube based desked, and after 69 a transistor based desk. 
 
On other instruments, particularly orchestral or drums I will use tape sims. For orchestral instruments, I tend to use the J37 tape sim from Wave's, which I think was tube based and on drums I like the really plain tape sim on the prochanel. 
 
On the mix bus, I always use Wave's Kramer Master Tape, which I know is a tube based tape machine. 
 
So you can see how I approach a mix from a harmonic perspective hopefully. 
 
It's much more detailed than this...but hopefully you get the drift.
 
You can hear what I am talking about on my last work, a cover of Nights in White Satin https://www.youtube.com/watch?v=3XcQVCAJakM my harmonic technique is all through this work!
 
Ben

Ben, Sorry it takes me awhile to get back sometimes. 
 
I have been using the console emulation in CbB along with Kramer Master Tape or the included Tape emulation in CbB. IK's Tube warmer, the included warmer in the PC which seems to be the same plugin found by Softube found in the free Focusrite plug in set. I have Waves NLS on my radar...seems like a good program.
 
My ears didn't hear anything significant until I listened to the cumulative effect. For me, it works more like a glue that blends the mix elements. Softens some of the sharp edges of the digital sound..or at least it seems to.
 
One Console emulated daw I listened to didn't do a lot for me. I couldn't tell any significant difference with that demo.
In hindsight, if I had a 50 track mix I probably would have noticed it more since this is all cumulative.Smaller mixes  less  harmonics input.Less effect. Although in a recent experiment I added Kramer Master Tape which I think had the most dramatic effect as compared to single track emulation. It all added up though.I also have Scheps OMNI channel on using even harmonics with a few tracks.
 
The main thing I want to become more knowledgeable about is the nature of the "secret sauce" some describe as warmth.
 
Here is my experiment. This is a ROUGH 1st tracking unedited mix. Done in a  short time....more of a scratch track/experiment that needs a LOT of work. It might go in the bin after this. Please don't grade me on this. It's just the first runs..Even though the picking is edgy here I feel there is a kind of sheen to the mix. Makes a good way to see the difference. The files were exported in 256 mp3 which probably doesn't help the end result.
 
ALONE AGAIN- without added harmonics-
 
ALONE AGAIN- with added harmonics-