Hi,
Just a few points.
1) Density Range in f-stops is (Dmax-Dmin)/log(2). Log(2) is very close to 0.3
2) Dynamic range in capture and on paper are different things
3) You may check this page:
http://www.normankoren.com/digital_tonality.html it's a bit heavy on graphs but go to the bottom of the page for some good illustrations
4) In practice there is always some kind of tonality mapping. Normally we use an 'S-curve', thus adding toe and shoulder characteristics. This is done by film, in cameras shooting JPEG and also normally in RAW-processing.
Regarding DR in capture things are more complicated. There is a technical definition of DR and that is that Maximum Signal/Noise floor. On digital sensors both values are measured in electrons, on DSLRs the maximum signal (known as "Full Well Capacity") used to be around 50000 and the noise floor about 3-15 electrons. That would give a dynamic range of about 5000:1 that is about 12 stops, this assuming that we expose to the right, that is maximize exposure without blowing out highlights.
Now things are not simple as that! To begin with about one percent of the light passing trough a lens will be reflected on the glass surfaces and just bounce around in the lens. Also lens barrel and mechanical parts of the camera will also be illuminated and will reflect some light on the sensor. This will be seen as either veiling flare or ghosting. So even if we had a sensor of infinite DR it would be limited by camera and lens. How well camera and lens is made matters. Some are probably better than others. large white surfaces (like windows) cause much flare while small bright areas (specular highlights) cause little flare.
Regarding the "noise floor" the engineering definition of DR says SNR = 1, signal noise ratio is one. This means quite noisy. On the other hand the dark areas in print will be compressed due to the S-curve so the noise may be much less visible.
The most important factor in transferring the dynamic range of a scene to paper is the tonality mapping.
Finally, the perceived dynamic range of a print will depend much on how the print is illuminated. Bright light increases the perception of contrast, the brain works that way. A print that is boring on a dark wall will come to life if illuminated with a bright spotlight.
Best regards
Erik
It is not quite clear why you want it expressed in F-stops. The reason may require a different answer. Also, gamut is more about saturation at a given brightness level than about maximum density/brightness level differences.
However, assuming a glossy paper, a net density above base can reach a value of 2.1 or a bit more, which would be similar to 7 'stops' of exposure difference. BTW, this has little to do with the dynamic range of a camera, because the signals that the camera records will be altered by Gamma adjustment and non-linear tonemapping. With HDR tonemapping it is possible to fit a huge capture range into a small output range of densities.
Cheers,
Bart
