Negative Format (Size and Shape)

Enlargement in this discussion refers to linear enlargement. An 8" x 10" print from a 4" x 5" negative is described as "2x". Admittedly it has four times the area, four times the silver content, four times the pixel count, AND four times the area NOT covered by silver. Arguments can rage between the usefulness of linear vs. areal measurement of enlargement, but as a photographer, not a physicist, and since linear measurement is the basis for "lines per inch", "pixels per inch" and "dots per inch", I will use "linear" measurement to describe enlargement.

It is noteworthy that advances in film technology, designed to produce APS results comparable with that of the 35mm format, also mean better film for the Minox!

The aspect ratio of negatives range from

a square, with a ratio of

1

through the 4:5 ratio of

1.25

to 35mm with a ratio of

1.5

and finally compared with the Golden Section (see below) at

1.618...

The aspect ratio of the final image has a significant impact on the degree of enlargement required. Higher aspect ratios favor the 35mm, APS, and panorama formats, while lower ratios favor "medium format" square negatives. Since each image has its own "best" shape, which rarely matches the shape of the negative, comparisons of one format with another are risky.

The following table shows various formats with the enlargement factor necessary to produce prints 3.5 inch high. Some loss of data in the final print is always present when producing standardized print sizes. It is worthwhile noting that the APS "Panoramic" format requires nearly as much enlargement as the Minox format!

the Golden Section

The Golden Rectangle is a figure possessing the dimensions of the Golden Section, in which the ratio of the smaller element (blue rectangle) to the larger (white square) is the same as the ratio of the larger (white square) to the whole. It turns out to be about 1:1.618 and can be calculated using the Fibonacci Series.

It is noteworthy that the blue area is also a Golden Rectangle, and if a square is added to each succeeding Golden Rectangle the figure below appears.

 

The arrival of the computer made great sport of Number Theory exercises, and the Fibonacci Series was a favorite. It is generated by supplying the first 2 elements, both "ones", then by successively adding the latest element to its predecessor to provide the next.

If an arc is inscribed in each square, as shown at the left,, the spiral resembles the familiar seashell, illustrating one application of the relationship to nature.

If the process is continued, the point of convergence for the spiral approaches a point near 72% and leads me to wonder if this might be the origin of the Compositional Rule of 1/3s.

Once a Golden Rectangle has been constructed (top left drawing), additional Golden Rectangles may be constructed by merely swinging the long dimension 90 degrees to describe a new rectangle. By so doing, a spiral can be drawn, growing infinitely larger rather than infinitely smaller as in the drawing above.

For an exhaustive discussion of this topic, an internet search for either "golden section" or " fibonacci series" will yield rich resources.

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