Huh. Get out your red string and pushpins because this inspired a theory.

So if the correct pair of values there ends up being 445 / 216.27000197, then it'll be:

60 * 445 / 216.27000197 = 123.456789

Or, since one of those programs had four decimals:

60 * 445 / 216.27015788 = 123.4567

Or, if it's 444/446 rather than 445:

60 * 444 / 215.78415752 = 123.4567

60 * 446 / 216.75615823 = 123.4567

But I see that they cut the "whooshing intro" at the front, which I imagine is part of the beat — they're in the hands of the machine now, after all! — so if we retroactively construct 123.4567 bpm into the silence (which, they estimate, is 5.58s):

5.58s * (123.4567bpm / 60s) = 11.4814731 beats

Assuming that the half a beat of slop silence there has to do with format / process limitations with CD track-seeking rather than specific artistic intent, we get:

+11 intervals @ 123.4567 bpm = 5.346s

Which, when added to the original calculation, shows:

60 * (445 + 11) / (3:41.85 - (0.5.58s - 0:5.346s)) = 123.4567 bpm

And so we end up with a duration of 221.616 seconds between the calculated 'first' beat, a third of a second into the song, and the measured 'last' beat from the post:

60 * 456 / 221.616 = 123.4567 bpm

Or if we use the rounded 123.45 form:

60 * 456 / 221.628 = 123.45 bpm

And while that 22+1.628 is-that-a-golden-ratio duration is interesting and all, the most important part here is that, with 123.4567bpm, I think it's got precisely 0.2345 seconds of silence before the first 'beat' of the song (the math checks out^^ to three digits compared against the first 'musical beat' at 5.58s!), and so I think there's actually 456 beats in the robotic 123.45 song!

:D

^^ the math, because who doesn't love a parenthetical with a footnote in a red-string diagram (cackles maniacally)

5.58s - (60 * 11/123.4567) = 0.2339961 ~= 0.234

5.58057179s = 0.23456789 + (60 * 11/123.4567)

Thanks for catching that. The durations were reversed but the BPMs were correct. Updated!