I've designed and used a lot of different inkset approaches over the last decade and, for a variety of reasons, I now have all but one of my printer positions containing 100% carbon pigments. Carbon is, of course, warm by nature. That leaves one position for a bluish toner that can pull the warm carbon to neutral (and slightly beyond for some parts of the grayscale).
How many "gray" inks does it take? I think the concept most economists can relate to is that there is decreasing marginal utility to more inks. Very likely, the more the better, but in any case, with only a single color "toner" position, I'm maximizing the number of channels in the profiles while still having the ability to print with tones from neutral to carbon warm.
What I do is currently is "hard wire" the toner's ratio of color inks -- in my case cyan and blue. For a typical setup and the toner formula I use, see
http://www.paulroark.com/BW-Info/3880-Eboni-Variable-Tone.pdf, page 3. People can vary this ratio to taste rather easily. So, as a practical matter, the the color "profiling" is split between the mixing and the printer profile that determines how much of the toner to use. For me, and from what I can tell from those who use my formulas, this makes a good compromise between flexibility and simplicity.
One of the factors I have considered is simply ease of profiling the inkset. I found that most people cannot achieve a smooth Lab A & B with more than a single "color" ink they are varying. That is, I doubt the typical B&W photographer can balance a CMY inkset. With only a single color toner to offset the carbon warmth, I have simplified profiling about as much as is possible and still allow a range of useful print tones.
I'm agnostic on the OEM's "ABW" approach simply because I want more control and also want the least amount of color pigs in the blend as possible. That color is going to fade a lot faster than carbon, and the color inks will fade at different rates, causing a color shift over time. So, for B&W, my view is the less color the better.
Also, note that my selection of the color used was based in part on achieving the smallest hue angle between the colors. In a CYM setup, the carbon is warm yellowish. As such, C & M are used to offset this. Some inksets have a "blue" ink. The hue angle between that B and C is much less than between M and C. The lower hue angle reduces the extent to which the colors are simply offsetting each other. As such, it takes less total color ink to achieve the carbon offset. Also, I believe, the narrowest possible hue angle reduces the extent to which the fade path will be pulled toward the stronger color as they fade faster than the carbon.
Typically, the C is much stronger than the M. Assume the profile is neutral. Ultimately, as the color fades, the print will end up carbon warm. Before that point, however, if the M is fading faster than the C, the print tone gets pulled into a greenish look. This takes a long time, but if one is selling art as "fine art," then I think for reputation (not to mention pride in one's craft/art) considering the very long run is worth the effort.
Unfortunately, I have found no inkjet pigment that is a perfect offset for carbon warm. In watercolor pigments, the Smith Indanthrone blue is very close. However, as an individual, I don't have the scale economies to do all that is needed to prepare a pigment for inkjet use. I did do a quick fade test of the pigment, and it appeared competitive. There may well, however, be good reasons the ink makers have not used it. As a practical matter, I stick with the OEMs for the best, well-tested colors. Carbon pigments, on the other hand, are readily available to third party sellers.
As such, finding the inkset with blue ink that looks the best in Mark's fade tests was part of my ink selection process.
In short, in a field that is characterized by decreasing marginal utility to number of gray inks, ease of profiling was a significant factor. Happily, I found a single toner ink blend could do it. That left me with all the rest being able to be 100% carbon. This allows enough inks to have two partitions of carbon and a single toner channel. With that in the Y position, this opens the systems up to ICC control and printing. (See QTR's Create ICC-RGB) While I don't usually use that approach, it's there.
FWIW
Paul
www.PaulRoark &
http://www.paulroark.com/BW-Info/