Hope this is not a duplicate post.
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After many years of absence, I re-started black and white printing last week, particularly using QTR. I am well versed and experienced in creating QTR curves from scratch. Previously I used Epson 4000 for BO printing on some papers. Particularly I found was Moab Entrada Natural (from 2006/2007 timeframe) produced very good results on the 4000. I remember for the Epson 4000, BO printing on "gloss/luster" papers was never satisfactory. I now use Epson P900, and yesterday I printed and linearized BO on the P900 using QTR set at "2800 Super." The resulting print is gorgeous. The 3880 printer likely has "2880 Super" setting also. At arm's length, the highlight dots are not visible, the ramp is very smooth visually. I can separate tones in 2% increments from paper white to Dmax. In any event, the characteristic of BO that I find most appealing is the graceful way in which the highlights naturally go towards paper white (a and b) tones. If your picture has a white border, the print looks organic to the paper, and the overall tone does not seem to fight against paper white. If there is any interest, I will be glad to send my linearize measurements of L, a, and b from paper white to maximum black. The weird thing on the paper (again, left over from 2006ish timeframe), Dmax is only about 1.6, yet the visual appeal of the resulting print is as good as on Epson Exhibition Fiber (Dmax > 2.4).
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Short answer. Yes it can be done with QTR. And The results can be gorgeous if you have the right paper match.