Okay, there's just a little more that I didn't get around to showing. The two quadrant example shows in graphic form how Zone System in camera testing works. The idea is to meter a grey card and stop down four stops to find Zone I.
As you can see on the camera image / flare curve, the affects of flare are minimal at the point of the meter reading (Zone V). And that is with a full range subject. A grey card has only a single tone. This means that there will be almost no flare at the meter reading.
Stopping down four stops shifts the camera image curve down 1.20 log-H units. You can see that the exposure will fall below 0.10 Fb+f on the film curve (assuming the test is at the film's ISO). In tone reproduction theory, the shadow exposure falls even lower down on the curve, but flare will bring it back up to around the 0.10 Fb+f density point.
For the Zone System, with it's no flare in camera test, the EI is adjusted in order to bring the Zone I shadow exposure up to 0.10 Fb+f. The difference is about 2/3 of a stop. This is why most people find their personal speeds to be 1/2 to 1 stop below the box speed with Zone System Testing.
This 2/3 stop added exposure is important in the negative density part of the Zone System test. Once you have your personal film speed, the next step is to find the aim negative density range for the processing. According to the Zone System, this is done by metering a grey card and opening up 3 stop to Zone VIII. The exposure range from the Zone System with the Zone System test now covers 2.10 log-H units from Zone I at a density of 0.10 Fb+f to Zone VIII which is around 1.15 to 1.25 over fb+f. That represents the exposure range for a subject with a 7 stop luminance range.
But a seven stop luminance range will produce flare in the camera which will bring effectively change the exposure range from 7 stops to around 6 stops. This will translate to the highlight falling at a point lower on the film in normal shooting conditions as opposed to the testing conditions.
This isn't going to change the resulting negative in anyway. Basically it's a numbers game. Adams found the right processing to match the film to the paper, but he is using a different set of variables. Variables that didn't correctly define the actual conditions, but ones that will produce the same results. Personally, this is what lead to my confusion why two stated NDR aims still printing well on the same grade of paper. The reason is that one of them isn't the one that you will get in actual shooting conditions, it's the one that works for the test.
The second attachment shows the two sets of variables on the same curve. The highlight densities on the curve are read at different places on the same curve. That means that for whatever the scene photographed, it's going to reproduce the same. The reason why it is possible to be able to come to this conclusion between two different testing methods (in camera and sensitometric), is by finding the variables common to the two methods and to applying them.
The Zone System has a seven stop luminance range for the test with a aim negative density range of 1.15 to 1.25. Tone Reproduction has a 7 1/3 stop luminance range for normal with a negative density range of 1.05. The subject luminance range becomes the log-H range along the x-axis of the film curve. The negative's density is plotted alone the Y-axis. From this we can calculate the slope or gradient of the film curve. Slope is a number indicating how steep the curve is and can be used to determine the output value expected (density) from the input value (exposure).
Slope = RISE (Density Range) / RUN (Exposure Range)
Zone System variables as stated in book, The Negative:
1.25 (NDR) / 2.10 (7 stop exposure range) = 0.60 gradient
Tone Reproduction variables
1.05 (NDR) / 2.20 (7 1/3 stop exposure range) - 0.40 (flare) = 0.59 gradient
The two gradients deduced from the different variables are practically identical. That means if either of the two methods are followed, they will produce the same negative.
As flare exists in the real world, we can assume the resulting negative density will not be 1.25 but 1.05. The big question is why do people believe the Zone System method produces a 1.25 NDR when it is in fact producing a 1.05 NDR? My guess is that few follow up and check the negatives produced in normal shooting conditions. They do the test and move on happy to have a good working negative. Second, even if some attempt to read density range from a negative shot in the field, it's there are many potential difficulties. What was the actual scene luminance range? How much flare was there? Zone I to Zone VIII do not represent the complete subject luminance range. There is always accent black somewhere and specular highlights. This can confuse the Zone to density relationship. You might be reading a density produced from a Zone VIII exposure. Finally, as the Zone System uses two points of density and not a negative density range, any changes in exposure will increase the highlight density but not the density range. The increase in overall density can easily be mistaken for an increase in the density range.
The last attachment shows how additional exposure shifts the entire exposure range to the right. While there's a slight increase in the negative density range from the shadows moving off the toe, it is essentially the same. However, if you to only read the highlight density, you can easily assume the NDR was 1.25.
Here's the kicker. As I have shown, the Zone System method consistently produces personal film speeds 1/2 to 1 stop below the ISO rating. This is less about your personal conditions and more about them being two different testing methods. If you were to have identical processing conditions, the resulting film speed values will still fall 1/2 to 1 stop apart. Again, the reason for this is flare.
So while the adjustment in the EI with the Zone System method is necessary to bring the exposure up to produce a negative density of 0.10 Fb+f in the test, flare from the actual shooting conditions will add to the exposure. Technically, the Zone System testing method will over expose the film 1/2 to 1 stop when the personal film speed EI numbers are applied in the field.
So if every step is properly followed in the Zone System testing, the placement of the exposure on the film will be closer to exposure B than exposure A. And that is a possible reason why it's possible to confirm the 1.25 negative density range while it continues to remain a ~1.05 ish density range.
To finally conclude, let me just say, that there's nothing wrong with any of the results obtained from Zone System testing. There's nothing wrong with the actual NDR just the perception of what it should be. The example at the beginning of the thread was kind of a trick. All I did was to present two identical conditions in different ways.
There's also nothing wrong with the slightly greater exposure. Not only doesn't it hurt quality but it can actually improve it by allowing for greater shadow separation as they move off the toe. Remember that film speed were a stop slower before 1960 and that didn't hurt quality. The difference in film speeds before and after 1960 also is proof that the Zone System method does lead to some over exposure. The 1960 change was do to a change in the way speed was determined. Partly because of the introduction of lens coating, and improvements in exposure meter accuracy, a one stop safety factor was eliminate from the standard. Films like Tri-X went from having a 200 ASA to a 400 ASA.
While the ASA standard changed, double the b&w film speeds, the Zone System method didn't. The one stop safety factor from the pre-1960 standard essentially masked the fact that the Zone System didn't factor in flare. When the standard changed and the Zone System remained the same, this difference became noticeable as personal film speeds suddenly were different from the box speed.
BTW, all the graphs come from plotting programs I've written. While there are a number of plotting programs on the market, none of them offered the tools to allow me the degree of analysis I wanted. I've found my programs to be an essential tool in helping me understand tone reproduction and exposure theory.
Thanks to those who patiently stay with me on this.