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Why do some people recommend 640x480 and some 720x540?
These are both Square Pixel "Corrections" to the video frame. (Video is always 720x486
- non square, no matter which scaling setup you choose to use.)
If you do the math on this, they work out to the same ratio. The principle behind one
over the other is based on which edge you are scaling to.

To fit a Computer's pixels into a video screen, some sort of scaling must occur.

The merits of one over the other depend on what you need to do. To save as much space
possible, a computer might choose the 640x480 route to cut processing requirements. (This
would cut the amount of space needed by more than 81,000 pixels per frame - that is a
lot of space saving!)
In the professional industry, generally the best possible quality is desired. So
using a frame size that contains more picture than you need is the highest quality
you can achieve - hence 720x540.

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I thought NTSC video is 525 scan lines. What is this "486" and
where does the "720" come from?

The NTSC video signal has 525 lines of information, not all of that is
picture. The visual part of the signal is 486 scan lines tall.

720 is a theoretical limit that describes how many black and white lines (or
"phase changes") you could draw from top to bottom next to one-another across
the screen and still be able to see them as lines (as opposed to blurry gray
mush). This is a theoretical limit, because "real" TV doesn't get close to
this number. VHS Tape for instance rarely gets higher than about 250 lines.

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Updated July 1, 2007