# The Chain

Adams provided us with the data that is necessary to work out, digitally & mathematically, the entire chain in his Zone System. By this, I mean that we can follow through the process of exposure, negative development, and print creation to recreate the mapping between scene Values to Zone Exposures through to final print Values. Here is an example of what I mean.

From Adams’ book, The Negative, using Wolfram’s Mathematica program, I have fit the following function to data given in Appendix 2 for Kodak Tri-X sheet film with normal development.

Density versus Exposure for Tri-X

From Adams’ book, The Print, based on data in its Appendix 2, I fit this next function to data for Ilford Galerie Grade 2 paper.

In practice, an intense light is shone through the negative onto the print. Where the density of silver is low on the negative, the transmitted light is intense, yielding a greater exposure of the print, and therefore, a higher density. The final density of the print is a logarithmic function of the light transmitted through the negative. The light transmitted through the negative depends upon its density. The density of the negative depends upon its original exposure Zone. By adjusting the relative exposure of the print so that Value V on it matches Zone V on the negative, it is possible to produce this overall curve:

Print density vs Zone, Tri-X, normal, Grade 2 paper

But we can do better than this. We can give this in terms of L* values for the print:

Print L* versus Zone, Tri-X, normal, Grade 2

I trust that you find this as fascinating as I do. It tells us that if we had a “normal” range subject, placed Value V in the scene on Zone V with our exposure, shot Kodak Tri-X film, gave it “normal” development, printed on Ilford Grade 2 paper, and set up our enlarger and printing system to get Zone V of the negative at Value V of the print, then this is what the entire shooting match amounts to. Paper white is around 95%. Print $D_{max}$ is around 2.1, corresponding to an L* of about 8 (aka 8%). Zone VIII is practically paper white. Zone I is practically $D_{max}$. Zone V (of the exposure) is on Value V of the print. If Value V of the original scene was placed on Zone V of the exposure, then we have an exact correspondence between print and scene in the mid-tones.

This is a pretty vanilla approach. Normal scene, normal exposure, normal development, normal paper grade. But we can play around. First, what do we mean by paper “grade”? Paper was (is) available in four grades, labelled from “1” to “4” in terms of contrast. Here there are, together again (Ilford Galerie):

Density versus paper grade, 1 through 4

The graph above shows these papers in terms of density against a fixed logarithmic exposure scale. But, be adjusting them all to the same Value V mid-point, we can show them together in the same, end-to-end, chain as I did for just the Grade 2 paper:

Printing on different papers, by Grade

You can see the results in terms of the mid-tone contrast, and, especially for Grade 1 paper, the maximum black value. In fact, this shows that Grade 1 paper is probably not a great choice for printing a negative with normal development. It doesn’t get to its maximum density fast enough.

We can also change up development. The following graph, again based on data from Adams’ The Negative, shows the variations in density for Kodak Tri-X sheet film with N+2, N+1, Normal (aka N), and N-1 development:

Development of Tri-X film

As you can see, the “+” development methods increase the sensitivity of the film, while the “-” development decreases it. N-1 or N-2 development would usually be applied to compress the range of light in a situation with more than normal scale in a scene. On the other hand, N+1 or N+2 development would be used to expand the tonal range of a scene that was “short-scale”.

Let’s see how these different development methods print out on Grade 2 paper.

Variations in development, end-to-end

I won’t show it here, but you can imagine, for example, N+2 development on Grade 3 paper, for example. The variations come down, in the end, to more or less mid-tone contrast. In other words, for our purposes using digital methods to emulate all of this in the digital dark room, these are just curve layers. A truly sharp contrast curve is equivalent to, in the wet dark room, N+2 development and Grade 4 paper. An extremely soft contrast curve is N-1 development and Grade 1 paper. And so on.

Now, imagine a couple of other variations. Imagine we are dealing with a difficult subject; for example, the dogwood blossoms that I mentioned in a previous page. They should be exposed for Zone VIII perhaps, but we place them on Zone VI 1/2 instead; that is, we underexpose by 1.5 stops. Value V falls on Zone III 1/2 in the exposure. Like Adams, we use N+1 development to push the blossoms out to Zone VII 1/2. They are only underexposed by about 1/2 stop on the print relative to the original scene, just enough to retain their fine textural qualities. Value V and the shadow tones still come in somewhat lower than the original scene, but these heighten the contrast between the white of the blossoms and the background.

Or, perhaps, we have a “short-scale” subject. We get a dull, flat image on the negative. So, we use N+2 development and print on Grade 3 or 4 paper, thereby expanding the range of the subject significantly. If we want, we can also translate Value V from the original scene up or down a stop to emphasize either the highlights or the shadows even further.

Having seen this once, I suggest that you go ahead and forget the whole thing. Luckily, you do not have to mess with all of those chemicals in order to get the same impact.

Take just this away… You can do almost everything Ansel Adams used to do in a dark room with levels and curves in Photoshop. Get the original exposure properly, and all of this falls into place. The rest is in selective enhancement of image elements. Oh, and that pesky printer, and the ink, and the paper, and the calibration… Well, maybe there is more to talk about after all.