A further link to lightness:
What I'd say is that print may look too dark to me (based on how I have been printing lately). If the Dmax is 2.10 and Zone I is 2.04 with my print viewing lighting, those will probably look the same to me.
Another interesting thing your chart brings out is the ambiguity as to if the zone's reflected density is defined at the junction between the zones or in the middle of the zone. In your case the 0.5 density is in the middle of zone V.
Please note that a free pdf version of the chart is available at:
It's interesting thing or coincidence that paper's 18% reflectivity is near 0.75 density which... Happens to be about old Zone system's middle gray density.
A long time ago, I got myself in the brainless strict variation of ZS, where the calibration was done by printing using only one print exposure time: The time that gives pure black from the film's base fog.
The calibration was real PITA (no wonder that I later abandoned such system). First had to find EI, it's easy part. Just the exposure value that gives just barely distinguishable black tone from pure black. It's still useful approach.
The calibrating middle and highlight tones was troublesome. With that one fixed enlarging exposure time, the print of negative where graycard (put on zone V) should gave equal tone as real gray card when compared each other.
That was hard and often required going for complete different developer and/or film.
Then came the highlights, where was two important things. First, the graycard exposed to zone IX should be barely darker than bright, unexposed paper white and rough gray paper/canvas exposed to VIII should gave some structure in print.
Not an easy task to get all these right! When concentrating only to zone I and VIII (or IX), it's quite easy and straight method to got calibrated zone system. But the weird requirement of getting subject's 18% reflectance as 18% reflective tone to print was.... insane.
(when I messed with that, I was young (still teenager) and could get better guides. There was no internet, ... And library had long queue for adam's books and then there was requirement for densitometer.. )
I don't know where the idea of getting zone V in print to match exactly reflectance of gray card come. It wasn't in the material I studied then. Perhaps it came from Minor White?
However that experience gave me strong idea of visualizing print tones before making exposure. And it gave the lesson that there's no sense to try to be too accurate with ZS stuff. There's always so much variables involved.
What makes any discussion about middle gray difficult is that there are many different types of middle gray - physical world, camera image, meter, perceptual.
The first three types are cover in some detail in the thread "Is the F factor relevant or should I cancel it out?"
According to exposure theory, 100% reflectance falls at a point approximately 0.92 log units above the metered exposure, which makes it Zone VIII. The shadow falls approximately 1.28 log units below or 0.6% reflectance. Flare brings the shadows up 0.34 log units to have them fall 0.94 log units below the metered exposure. The metered exposure will then fall at 12% reflectance. I've attach an example showing the range of Reflectances, Reflection Densities, and exposure values w/ and w/out flare for the average scene.
Color is a psychophysical phenomenon. We don't see tones in a linear way as Ralph's reference to Fechner describes. Munsell found that 18% was the perceived middle gray using a 10 step scale. In the early 1940s, the Optical Society of America's Committee on Colorimetry, chaired by Loyd Jones, found it to be 19.7%. They published their findings as a book sometime in the fifties under the title The Science of Color. I've attached a comparison of both scales.
Ralph, am I correct in assuming your equation comes from CIE? Could you break it down more and define the source of the variables?
It is confusing because it is easy to think that the 18 percent refers to a position on a tonal scale; it does not. It refers to the percentage of light that bounces off of something.
As for a a middle grey card not appearing middle grey if you expose off of it (was it IC-Racer who said that?), this is very true. Because of this, the instructions for using a grey card are not to expose right off of it. You are supposed to expose right off of it and then open up 1/2 to 2/3 of a stop, the way I have always been taught.
shows the development of this equation from Priest (1920) through Munsel (1933) until CIE (1976).