In terms of relative warmth of the matte black inks, I did a draw-down test (Mayer rod pulling drops of ink over paper) of 3 that I have on hand, including the new Epson UC HD MK from the P600. Included in the draw-down were dilutions of the MK to 30% MK, 70% generic dilution base. Diluting MK is the route to the cheapest (and most archival, but matte paper only) B&W inksets. So, the relative warmth of the dilute MK is probably more important than the relative warmth of the MK itself.
The Jpeg of the draw-down is here: http://www.paulroark.com/BW-Info/MKs-P600-Eb-Eco-3-2017.jpg
I'd call it pretty much a draw, so to speak. The MIS (www.inksupply.com
) "Eboni" MK (STS Inks wj1082 wholesale) used to be by far the most neutral, but version 1.1. of the ink made it almost indistinguishable from many others. The EcoTank 774 is probably the least expensive MK available that I'd trust. In a past test I thought it was a bit warmer than Eboni, but it's close.
My interest in the relative warmth of carbons is for my B&W dedicated inkset formulas (open source). I use these and want them to be easily made from competing sources so that the B&W "darkroom worker" type of person (myself included) has the best and least expensive materials. So, while it is a bit OT, let me also add another piece of that puzzle.
All of the carbons need a light blue toner to neutralize the carbon warmth if a neutral B&W print is wanted. I think the best is made with Canon Cyan an Blue, diluted with 75% generic base. See page 3 of http://www.paulroark.com/BW-Info/3880-Eboni-Variable-Tone.pdf
. This toner formula appears to be universal for carbon -- matte and glossy. My glossy carbon variable tone used the same toner. MIS sells its own version of this premixed at https://www.inksupply.com/roarkslab.cfm
(bottom of the page) (MIS and I have no connection. I do not receive any royalties; all my formulas are open source. I do allow MIS to use my name in their URL as long as what is there are materials I've used and tested. That makes it simpler for those who follow my work to find the materials.)