SMPTE Time Base: NTSC and PAL magic numbers for droppedFrames

[alexandercerutti]

Hello there, I was studying ttml2 standard to create a personal implementation (for a subtitle system available on my Github profile).

I was reading about ttp:dropMode and droppedFrames in relation to SMPTE standard (I.3) timings. I was able to find the explanation on the standard document and on external sites, but I wasn't able to find what are the magic numbers for NTSC and PAL used in droppedFrames calculation:

NTSC:

(hours * 54 + minutes – floor(minutes / 10)) * 2;

PAL:

(hours * 27 + floor(minutes / 2) – floor(minutes / 20 )) * 4;

Do you know where can I find the reason for which those numbers are used?

Thank you!

[skynavga]

Look for "108" in the following. And note that in the above formulas you have hours 54 2 = hours 108 for NTSC and hours 27 4 = hours 108 for PAL.

https://blog.frame.io/2017/07/17/timecode-and-frame-rates/

[alexandercerutti]

Hey @skynavga, thank you for your reply. Sorry for the late reply but I took a few days to understand a little bit more everything. I had to dig further down and look for more mathematical articles to understand the reason behind every single piece of that formula (which, the article you provided me didn't provide).

I was able to find an old technical article made from Adobe for Premieré (https://studylib.net/doc/18881551/an-explanantion-of-drop-frame-vs.-non-drop) that explains perfectly, so I understood NTSC Drop mode.

What it is not yet clear to me is how drop mode applies to PAL, as it never had a frames reduction like NTSC (30->29.97 - PAL also works at 25fps).

So, is dropPAL mode perhaps made for the case in which an higher fps is provided, e.g. 30fps? That's the only possible explanation I can see right now.

Thank you very much.

[skynavga]

See the following comment in TTML2 §7.2.4:

[alexandercerutti]

Okay, thank you @skynavga. I was looking for more deep explanations about the M/PAL drop-frame, but I could find none.

Based on what is written in TTML2, I was able to understand the formula and put almost all the pieces together (or, at least, I found a direction, but I don't know if that's correct) but there are still some details and reasons for which we are using certain numbers that I cannot catch.

That is, why was it decided to skip the drop-frame every 20 mins, instead of 10 mins just like NTSC (M/PAL uses the same fps as NTSC)?

I don't know if you are the right person to give me those answers or perhaps you know something more, but if know something more, I'd be very grateful for any explanation.

[skynavga]

AFAIK, the formulas in the TTML2 spec are correct. If you depart from those formulas, your implementation would technically be non-compliant w.r.t. TTML2 semantics. On the other hand, if you find evidence that one or both formulas are incorrect, then please file a new issue. If you so so, be certain to provide adequate evidence showing your position, as well as sample TTML2 files (and related media) that demonstrate the problem.

[alexandercerutti]

Maybe there was just a misunderstandment: I'm not saying that formulas are wrong and I don't want to depart from them: I just wanted to know the technical reasons behind those numbers to understand them completely :)