# The true origins of the 16:9 HDTV aspect ratio!

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### Bob Morris

Jul 13, 2003, 9:27:29 AM7/13/03
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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.

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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.

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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...)

### MitchGross

Jul 13, 2003, 10:55:14 AM7/13/03
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All just a reall fancy way of saying that 16:9 is pretty much dead center
between 1.33 and 2.35.

Mitch

### MitchGross

Jul 13, 2003, 12:04:48 PM7/13/03
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Also, wanna have a little fun? Take a 4:3 (1.33) video camera and stick one of
those popular 1.33x anamorphic adapters on the front. Instant 16x9, right
(with many artifacts I know, but go with me here)? Now take that same 1.33x
anamorphic and stick it on a 16:9 camera (or at least a cheap 4:3 camera that
has an electronic 16:9 compression like the PD-150). Now you have a 2.40
frame! Instant CinemaScope, although I'd be very afraid to see what such an
image would look like blown up to 35mm 'Scope. Uhg.

Mitch