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The printed image will not be warmer, except for pure whites and very, very light colors. The paper profile maps image colors based on the paper color – the purpose of a profile.
One of the purposes of ‘natural’ papers is to avoid fluorescent brightening agents (FBAs), generally called optical brightening agents (OBAs) by paper companies, because it sounds better.
Fluorescent agents receive light in the non visible ultra violet region, and emit light in the blue end of the spectrum; effectively making the paper seem whiter. They were in the past known as ‘bluing agents’. This is how you can have papers with a ‘brightness’ (reflectance) of more than 100%; they actually emit light in the visible spectrum.
There are several potential problems associated with OBAs. Any UV protective coatings: including UV glass or acrylic, and UV protective sprays, will largely nullify the bluing effect. If the OBAs don’t receive UV light, they can’t emit blue light, and the paper white will not be white. This is the reason why higher end paper/ink profiling devices come in UV and UV cut versions.
The other major problem with them is that they burn out when they are allowed to work. The brighter the light on them, the shorter they live – the paper turns even yellower than it would have done had it originally not contained OBAs. When this happens, all the colors in the printed image change, unlike the profiled colors on less bright paper.
I print professionally. I have no idea where my client’s images will be displayed and how well they will be protected. They could put them in a south facing greenhouse window for all I know. I eschew OBAs for this reason, and for most of my own images prefer a more natural paper color. If you are only printing for yourself, then the decision is more open. I do stock some bright white papers, and some images do work better with them (and some work better with less bright papers too).
My reasons for choosing Canson Rag Photographique 310 over Hahnemühle Photo Rag 308: the Canson paper contains no OBAs (it uses minerals for whitening; probably titanium dioxide. barium sulphate (baryta), and/or a form of silica oddly known as white carbon black), the Hahnemühle uses a small amount of OBAs; probably not enough to worry about. The Canson paper stays flat after printing, the Hahnemühle has a tendency to sometimes slightly recurl (even from sheets). The Hahnemühle doesn’t handle dark greens as well, but I found it somewhat better for black and white; and it is a little less expensive.
The Hahnemühle bright rag has a much greater OBA content, but nowhere near the quantities of Aurora or Moab Entrada bright.
Put a new sheet of Aurora bright against the white area of a print you have had up for a while. If you are not having problems, then you may not have to worry one way or the other.
I would really suggest buying a Hahnemühle matte sample pack and a Moab sample pack if your choice is to lie with these two.