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Message from discussion The true origins of the 16:9 HDTV aspect ratio!

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More options Jul 13 2003, 9:30 am
Newsgroups: rec.arts.movies.tech
From: mor...@albireo.sce.carleton.ca (Bob Morris)
Date: 13 Jul 2003 13:27:29 GMT
Local: Sun, Jul 13 2003 9:27 am
Subject: The true origins of the 16:9 HDTV aspect ratio!
To my knowledge, the explanation below:

(a) Is not well known.

(b) Has never been published in any home theatre journal.

(c) Is true: Dave Richards told me so.

Note: I derived the examples.

The Origins of the 16:9 aspect ratio!
The choice of 16:9 as the HDTV widescreen ratio was not arbitrary!
16:9 derives from the geometric mean of 1.33, the "traditional" cinema
screen aspect ratio, and 2.35, the now-classic widescreen 'scope ratio!
That is 16/9 = 1.777 is (approximately) the square root of
1.33*2.35!
But what does this mean?

The figure below shows a 1.33 film frame windowboxed within
a 16:9 border. The height is 1.0, the full width is 1.77, the interior
1.33 image width is 1.33.

-------------------------------------
|        |                |         |
|        |                |         |
|        |                |         |
|        |                |         |
|        |                |         |
|        |                |         |
|        |                |         |
|        |                |         |
|        |                |         |
-------------------------------------

The total "wasted" area is thus (1.77-1.33)*1 = 0.44 square units.

The figure below shows a 2.35 film frame letterboxed within a 16:9 border.

--------------------------------------
|                                    |
|------------------------------------|
|                                    |
|                                    |
|                                    |
|                                    |
|                                    |
|                                    |
|                                    |
|------------------------------------|
|                                    |
|------------------------------------|

The width is 1.777, the full height is 1.0,
the interior letterbox 2.35 image height is 0.765,
since 1.777/0.756 = 2.35.

The total wasted area is therefore 1.777*(1-0.756)
= 0.43 square units.

A simlar figure would show that if a 1.33 film frame is
presented cropped on a 16:9 screen, the lost area at top and bottom is
1.777*(1.333-1) = 0.59 square units. Similarly, a 2.35 film
cropped on a 16:9 screen loses (2.35-1.777)*1 = 0.57 square units
of picture at the sides.

Thus, for either windowboxing/letterboxing, or cropping, the two
classic screen ratios -- 1.33 and 2.35 -- are treated approximately
equally when presented on a 16:9 screen: both waste about 0.43 units of
screen area when letter/windowboxed and both have about 0.58 units of
picture area lost when shown cropped.
Finally, "flat" movies, which have a 1.85 aspect ratio, are
presented approximately uncropped or unletterboxed on a 16:9 screen.

Bob Morris (Note: Thanks to Dave Richards...)