The use of Matte Black (MK) in the Epson K3 inkset results in an improvement of around 0.3 in maximum density (DMax)compared with the use of Photoblack (PK) when using matte art papers. In the case of Hahnemuhle Photo Rag (HPR) the DMax with MK is 1.60 here. I would be very interested if anyone obtains better results on a matte art paper. I am yet to see sensitometric analysis of current Canon and HP offerings.
Many other papers I use come very close, and for practical purposes are equivalent in this respect. For instance Crane Museo Max and Awagami Okawara White come in around 1.55. Both these papers have no optical brighteners and the latter is handmade and heavily textured.
It is not only DMax that is improved with the use of MK over PK. The darkest black is included in most of a grey scale to some extent, especially of course in the low values. Thus MK results in extended and deeper tones in monochrome prints on matte paper.
This also applies to coloured images where colours appear "Richer".
Lustre and glossier papers should use PK. On these papers DMax up to 2.75 have been reported , but I suspect this may be somewhat speculative. A paper like Crane Museo Silver Rag comes in around 2.25, and the Innova equivalent has been quoted around 2.55 and higher . If true this is not necessarily a good thing. More important is the ability to separate shadow tones. A bucket of lamp black on a piece of paper may be very black but .....
Using MK on these papers often gives obnoxious surface effects and poor blacks.
There is another interesting point here. In an attempt to increase DMax and consequently dynamic range, various approaches may be made to put down more ink. Not only may this result in blocked shadows it may also cause a curious reversal , like solarization in the deepest tones .
It's a tricky busines!