I'm not really directly challenging Ralph's approach. In fact, Ralph and I am in close agreement with most of the goals and conclusions. We just tend to disagree on the theory. I have a lot of respect for Ralph and there isn't anything I'm saying here that we haven't already discussed. What I am attempting to do is what you yourself have admitted. I wish to convey the importance of understanding the material to the point so you can come to your own informed conclusions. Approaching any material with a good amount of informed skepticism is just good methodology and it will help avoid the risk of dogma. My advice is to always ask yourself "why" and follow where it leads.
I've attached three nomographs. One is from Ralph's Way Beyond Monochrome. One is from Basic Materials and Processes. And one from Materials and Processes.Actually I was referencing the nomograph on p. 140 of WBM. There is a similar version of it on p. 66 of Stroebel's book "Basic photographic materials and processes" (p. 66 here) (which in turn was taken from a Kodak Publication from 1976) but the neg density ranges that nomograph lists differ from the one in WBM by quite a bit. e.g. the ISO std CI of 0.57 (in 1976) matches a neg dens range of 1.05, but in Ralph's nomograh the ISO std of 0.58 matches a neg. dens. range of 1.29 (which I rounded up to 1.30 and used that in the formula I gave above.
Now why do the two nomographs differ so much ? I think it is because Ralph made a different assumption than that in the footnote (*) of p. 66 which reads "these are the typical negative density ranges that result when normal luminance range subjects (7 stops range) are exposed with moderate flare level lenses and developed to the contrast index shown in the left scale".
Here's my perspective on the three aims for a negative under normal conditions intended to be printed on a diffusion enlarger. There is no difference between them. That being said, I admit that it wouldn’t be very hard to come to the conclusion that they represent very different models, but once we take a closer look and break down the variables, they are virtually identical.
First, I do need to make a small correction in your interpretation of the negative density range that matches 0.58 or the 0.57 that is used as the aim avgGradient in the WBM monograph. I’ve drawn a line through the average conditions to the point that is labeled “Typical Diffusion Enlarger“. As you can see it has 1.20 as the negative density range for an avgGradient of 0.57. So, we need to adjust your 1.30 down to 1.20.
Let’s take a look at the variables (they are also in the attached word document):
WBM - NDR = 1.20, LSLR = 2.1 (7 stops), Starting CI = 0.57, Required CI = 0.57
Kodak - NDR = 1.05, LSLR = 2.1 (7 stops), Starting CI = 0.57, Required CI = 0.57
M&P - NDR = 1.05, LSLR = 2.2 (7 1/3 stops), Starting CI = NA, Required CI = 0.58
The biggest difference is between the aim NDR of WBM and the other two.
Let’s take a look at how the variables work together. The equation to determine gradient is Rise / Run. Or the Output (NDR) divided by the Input (log-H as it relates to the LSLR). (This can also be viewed in the word document.)
WBM: 1.2 / 2.1 = 0.57
Kodak: 1.05 / 2.1 = 0.50
M&P: 1.05 / 2.2 = 0.477
Since the Kodak and M&P numbers don’t equal the aim gradient, there can only be two possible conclusions. They are either wrong or there’s a variable missing. If you look at the bottom of the M&P monograph, it reads “corrected for average flare conditions.” Flare has been incorporated into the M&P monograph, but is missing from the above equation. We can also assume the Kodak monograph has also corrected for average flare. The WBM monograph works as is. Does this mean it hasn’t been corrected for average flare?
Equation incorporating flare: NDR / (LSLR – Flare) = CI (average gradient)
To find the value of flare: (CI*LSLR – NDR) / CI = Flare
WBM: (.57 * 2.1 - 1.20) / .57 = 0
Kodak: (.57 * 2.1 – 1.05 ) / .57 = 0.26 or ~ ¾ stop flare
M&P: (.58 * 2.2 – 1.05) / 0.58 = 0.40 or 1 1/3 stop flare
As you can see with the Kodak monograph, if you start on the left at 0.57 and move through 7 stops luminance range to the middle scale at 0.57. Then if you draw a line through moderate flare, the final CI is at 0.57. If you repeat all the steps except draw the line through the high flare (box), the final CI needed to process the film to is 0.61. It’s exactly the same with the WBM monograph, but there is a small difference.
With the Kodak monograph and the M&P monograph, the scales have been “zeroed” out for normal flare although flare remains as part of the equation in determining the average gradient. With the WBM monograph, flare appears to have been eliminated from the “normal” 7 stop conditions. This is the only way to have identical values for the LSLR and CI variables while having a different NDR value. The WBM monograph works just as well as Kodak’s with determining the beginning and ending CI (avgGradient). The only difference is a question of the aim negative density range.
Can the different values just represent different preferences for the negative density range? That would make sense except it wouldn’t balance the equation. If the preference is for a negative density range of 1.20 with a luminance range of 7 stops that included flare, the final CI would have to be different than 0.57. For a one stop flare factor, the projected CI would have be 0.67 for the equation to work with a 1.20 NDR. If you have the same CI, luminance range, and flare, you can’t have different resulting negative density ranges, so the difference in the NDR can’t be attributed to NDR preferences.
No matter the assumption for the normal luminance range or the assumption for the amount of flare, if the film is developed to the same CI, the negative density range for a given scene will be the same. The M&P uses a 2.2 log luminance range, but it uses a higher flare factor, so the CI is basically the same as Kodak’s with a 2.1 log luminance range and a smaller flare value. I can argue that 2.2 is statistically more accurate as is the flare and Kodak only used 2.1 because it’s a nice round number and by doing so they had to fudge the value of flare in order to make the CI conform with reality. But no matter the reason, as long as the film has the same CI value, the results will be the same whether the luminance range is 2.2 with .40 flare or 2.1 with .30 flare. The end results are the same even though conceptually and theoretically one is more correct.
How the WBM NDR works depends on how you look at it. And this answer also answers how the Zone System can have an aim NDR of 1.25, while the WBM can have an aim NDR of 1.20, while (lack of a better term) the sensitometric aim NDR can be at 1.05 and all have almost identical aim CIs.
It’s all about how the data is interpreted. The Zone System uses a camera to make the test and the goal is to produce two points of density representing the end points for a seven stop exposure range: 0.10 over Fb+f and 1.35 over Fb+f. With this data, we can determine the aim CI or gradient: 1.25 / 2.1 = 0.59. What most people don’t realize is that while the test is shot with a camera, there is almost no flare using the single tone subject and the point where the exposure is made on the film curve (you are really just under and over exposing the mid-tone exposure). As not flare is involved, the aim NDR has to be made artificially higher in order to balance the equation and produce the necessary CI.
1.25 / 2.1 = 0.59 is really the same as 1.05 / (2.1 - .32) = 0.59. One calculation incorporates the flare factor with a realistic NDR and one has a NDR that doesn’t factor in flare. The concept becomes even clearer working with film curves. The proper way to produce a film curve is to contact the step tablet. This forms a non flare curve. If you have a curve with a CI of 0.59 and you measure a 2.1 log-H range from 0.10, the resulting negative density range would be 1.25. Since we know all scenes contain flare, the effective log-H range isn't measured at 2.1 but 2.1 minus the flare value. Both methods will indicate a negative processed to the same CI, so the results are identical. You can think of this as the difference between the sensitometric exposure or the non flare contacted step tablet exposure and the photographic exposure or the exposure that represents the variables encountered when shooting.
Zone System: 1.25 / 2.10 = 0.57
WBM: 1.20 / 2.10 = 0.57
Sensitometric: 1.05 / (2.2 - .40) = 0.58
With the variance of flare in shooting conditions, the small difference in aim CI values between the three methods is inconsequential.
Therefore, there is no difference between the results of these three systems as there really is no real difference between the three nomographs; however, there is a difference conceptually. The Zone System and WBM NDR values are derived from interpreting results from the film curve with out incorporating flare to the subject luminance range. While all three methods will produce identical CIs, conceptually only one is technically correct (what is “correct” is a whole different post).
By understanding the “whys” of the variables, you are in control of the process and not the other way around. Don’t forget to keep this in mind when using the Film Speed and Development Test spreadsheet.