Has it ever occurred to you that people may avoid pointing out errors in what you say because of your combative debating style, not because they agree with what you said? I expect to be attacked just for saying anything that disagrees with you, no matter how correct or well-supported what I write is.
For the record, here is something I wrote (a long time ago) to explain where the magic numbers in NTSC come from. The ratio 63/88 does not appear anywhere in the original standard that I could see. There are a number of other ratios that do appear, and a particular product of them can be reduced to 63/88. So that value is theoretically exact - but knowing it doesn't tell you anything about where it came from. The note below does.
Dave
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This is based mostly on the NTSC committee's own report, with a little bit of guessing on my part (in the section about prime factors of divisors).
Original B&W standard:
- 60 Hz vertical frequency, so "hum bars" from poor power supply rejection are stationary on screen
- Horizontal frequency is 525*60 Hz. Odd number gives interlaced image, to give off better vertical spatial resolution in a fixed bandwidth
- Channel spacing is 6 MHz, with 4.5 MHz offset between sound and video carrier
- Video is transmitted vestigial sideband, with 4.2 MHz video bandwidth.
The new color standard needed to be compatible with existing B&W receivers:
- Colour information would be encoded on subcarrier; subcarrier would be visible on B&W receivers in areas of saturated color.
- To minimize visibility of subcarrier, lock subcarrier to H sync so any resulting pattern is stationary, not moving.
- Use odd multiple of half line frequency, so subcarrier forms a fine "checkerboard" instead of lines - less visible.
- The higher the subcarrier frequency, the less visible on B&W sets, but the less bandwidth available for carrying color information. Tests showed the best compromise frequency to be around 3.6 MHz.
- The two constraints above mean that subcarrier should be approximately 457/2 times horizontal frequency. But 457 is a prime number, and dividing by 457 is hard - there are no cheap digital dividers available in 1950.
- Looking at nearby odd numbers, 453 = 3*151, 455 = 5*7*13, 459 = 3*3*3*17, and 461 is prime. 455 is the easiest divisor to generate - all its prime factors are 13 or less. So subcarrier is set to Fh * 455/2.
- So, at this point, the magic numbers are: Fv = 60 Fh = 60 * 525/2 = 15750 Fsc = Fh * 455/2 = 3583125
But there's a problem: to minimize visibility of any beat frequency between color subcarrier and sound carrier, it is desirable to have the difference between the two be an odd multiple of half the line frequency.
- With numbers above, offset is 916875 Hz. 916875/Fh = 58.21 = 116.4/2. So nearest odd multiple of Fh/2 is 117/2.
- Thus new sound carrier offset should be Fh*(455 + 117)/2 = 4504500 Hz. This is (exactly) 1001/1000 times the old sound offset.
- But (in those days) TV sound used a separate FM transmitter and possibly a separate antenna; changing sound offset means retuning the sound transmitter.
- To avoid this, the NTSC moved all the *video* frequencies down by a factor of 1000/1001 instead, giving the desired relationship between subcarrier and sound carrier.
- So subcarrier becomes 3583125 * 1000/1001 = 3579545.4545 (rounded to 3579545 in the original standard).
- New frequencies (without intermediate rounding) Fsc = 3579545.4545 Fh = Fsc * 2/455 = 15734.266 Fv = Fh * 2/525 = 59.94
- The tolerance on these is 3 PPM, so the range of permitted values is entirely within the looser tolerances of the old B&W frequencies, so B&W TVs should continue to work at the new frequencies (though hum bars will now roll slowly).
- If you happen to have a precise 5 MHz frequency standard, to derive Fsc from it your need a multiplier of
(60 * 525/2 * 455/2 * 1000/1001) / 5000000 = 63/88 (exactly)
So the numbers 63 and 88 never appear in the NTSC standard; they are just the rational number defined by all those *other* numbers above, reduced to simplest form.