1000/1001

Historically the nominal 30 frames/60 fields per second of NTSC color television is usually multiplied by 1000/1001 (= 0.999) to produce slightly reduced rates of 29.97 and 59.94 Hz. This offset gives rise to niceties such as drop-frame timecode (dropping one frame per thousand: 33.3 seconds) and audio that also has to run in step with the video. Although having strictly analog origins, dating from the very beginning of NTSC color transmissions in 1953 as a fix-it to avoid a clash of frequencies, the 1000/1001 offset has been extended into the digital, HD and UHD world where 24 Hz becomes 23.976 and 30 frames/60 fields per second are again changed to 29.97 and 59.94 Hz. Of course, as the frame/field frequency changes, so do the line and color subcarrier frequency as they all have to be locked together. Note that this does not apply to PAL color systems as these always use the nominal values (25 Hz frame rate).

The reason for the 1000/1001 offset is based in monochrome legacy. Back in 1953, the NTSC color subcarrier was specified to be half an odd multiple (455) of line frequency to minimize the visibility of the subcarrier on the picture. Then, to minimize the beats between this and the sound carrier, the latter was to be half an even multiple of line frequency, and to ensure compatibility with the millions of existing monochrome TV sets, the sound carrier was kept unchanged – at 4.5 MHz – close to 286 times the line frequency (Fl). Then, in a real tail-wags-dog episode, it was decided to make this exactly 286 times… by slightly altering the line frequency of the color system (and hence that of the color subcarrier and frame rate). Interestingly it is said that the problem could soon have been solved with a little improved engineering, so avoiding the need for this awkward frequency offset and all the many thousands of hours of additional engineering and operational effort this has caused down the years.

Here’s the math.

Fl = frames per second x number of lines per frame
Nominally this is: 30 x 525   = 15,750 kHz

But it was decided that: 286 x Fl     = 4.5 MHz
So:                                     Fl = 4,500,000/286          = 15,734.265 kHz
This reduced Fl by:         15734.265/15750           = 1000/1001 or 0.999

As all frequencies in the color system have to be in proportion to each other, this has made:

NTSC subcarrier (Fl x 455/2) = 3.579 MHz
30 Hz frame rate (Fl/number of lines per frame) = 29.97 Hz

Following on, all digital sampling locked to video is affected so, for example, nominal 48 and 44.1 kHz embedded audio sampling becomes 47.952 and 44.056 kHz respectively.

As the reasons for ‘drop-frame’ were analog, it is not a requirement of digital television but still the frequencies appear in digital TV standards, and they are widely used, even though analog TV transmissions are now switched off in most countries.

See also: Drop-frame timecode, Embedded audio