The density rang of a normal paper is usually between 1 and 1.2. This range should
equal the product of the log exposure range of the film and the contrast index.
Working the other way, divide density range of the paper by the exposure range of the
scene to get the desired contrast index. An exposure range of 5 stops is a log
exposure of 1.5 to government accuracy. Thus, normal development would be whatever it
takes to get a contrast index of about 0.66 , depending on the paper. Extending the
exposure range by 1 stop would make the log exposure range 1.8 and decrease the C. I.
to about 0.56, while decreasing it to 4 stops would increase the C. I. to 0.83.

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  Contrast Index is a method used by Kodak to specify
contrast in a way that does not depend too much on the shape
of the film curve. I applies to the film only. CI is a
measure of how the density on the film relates to the
exposure but it is averaged because the ratio of density to
exposure on film is not always linear. An earlier contrast
measure is called Gamma. Gamma is the slope of the film
characteristic over its straight line portion. CI and
Average Contrast AKA Bar-G were devised because many films
do not have a straight line section.
  In any case, the measure is Log density over Log
exposure. So, if a range of exposure equal to Log 1.5
results in a density range of 0.8 the CI, or Gamma, or bar-G
is 0.53. An exposure range of Log 1.5 is equivalent to a
exposure range of about 32x or 5 stops. What this translates
to in a print depends on the contrast index of the negatige
and the contrast grade of the paper. Given a CI of 0.53 as
on our example, the density range of the negative will be
log 0.8 or a linear variation of about 6.3X. The variation
of brightness at the paper will be similar. Grade-2 paper
has an exposure scale of around 1:12 so the above example
will need harder paper, around Grade-4 to print from paper
Dmax to paper white. If we increased the negative contrast
to around 0.8 the exposure range for the paper will be
increased to 1:15 about right for Grade-2 paper.
  Note that Gamma (the tangent of the film curve where its
is not deflected), Average Gradient, and Contrast Index may
all have different values for practical film. Theoetically
they would be identical if the film curve was straight all
along its length. Mostly CI looks a little low compared to a
Gamma measurement for the same film.
  Now something else. I occurs to me that you may be asking
about exosure adjustment when film is developed to various
contrast indices. There really is no fixed rule but a rule
of thumb is to increase exposure over the ISO value when
film is decreased in contrast about one paper grade, and to
decrease exposure when the film is developed to a contrast
higher than about one paper grade. The ISO speeds are
measured at a CI about right for contact printing or
diffusion enlarging. On condenser enlargers these negatives
will be about one grade too contrasty for Grade-2 paper. For
most films the time adjustment is about minus 33 percent
with an exposure increase of about 23/4 stop. For T-Max and
some other films, the time adjustment is only about 25
percent but the exposure adjustment is the same. For
increasing contrast the ajustments are the same but in the
other direction.