Comment by jonas21
4 days ago
There's a minor issue with the calculations. It should be:
60 * 445 / 216.276 = 123.453365145
60 * 445 / 216.282 = 123.449940356
Not the other way around. And since the timing is only given with millisecond accuracy, the bpm should be rounded to the same number of significant digits:
60 * 445 / 216.276 = 123.453
60 * 445 / 216.282 = 123.450
So, it's the YouTube version that's 123.45 bpm to within the rounding error.
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)
Not sure if it adds anything, but a factoid I know is that CD timing is expressed in minutes, seconds, and frames, where each frame is 1/75th of a second.
I'm not sure but I think this is also the smallest time resolution.
Then each frame is composed of samples, but they seem to be counted in groups of 1/75th os a second anyway.
That's only relevant for navigation from the TOC. The samples are always 22.68us apart. That is the finest resolvable timing difference.
4 replies →
Thanks for catching that. The durations were reversed but the BPMs were correct. Updated!
> And to confuse matters more, in a 2013 interview with Time Magazine, Bangalter says:
> > So we've never actually made music with computers! [laughs] Neither Homework nor Discovery nor even Human After All were made with computers.
> Was he contradicting himself from 12 years before? Or did he forget? Or maybe it's a terminology thing?
The thing is—and this is coming from someone who has been making electronic dance music daily for over 35 years and counting—when Bangalter spoke earlier in their career about a PC (likely an Atari ST or Falcon) it was being used as a MIDI / SMPTE timepiece and master sequencer, nothing more. Later when he speaks about never making music with a computer, the context of the discussion has changed, as by that time computers were becoming more accomplished at DSP. The comment he is making is that they didn't use computers for audio domain tasks, like Pro Tools, Digital Audio Workstation type action.
That said, computers were still deeply embedded in their workflow just not in the way most modern producers would recognize. Even the SSL 9000 J console at the heart of their studio relied on an onboard computer system for total recall, automation, and channel configuration. The distinction Bangalter draws is really about where the actual audio lived: in 12-bit sampler memory, on tape and through analog audio circuits, not as samples and waveforms being crunched inside a CPU. The computer was a conductor, not a performer.
PS: All of this got me thinking about the past and dislodged a bunch of memories from my old crusty techno battered brain. In that early interview where Bangalter loosely mentions their production setup: an E-mu SP-1200, an MPC3000, and "Logic on a PC." He doesn't specify what kind of PC, and he doesn't say who made the software—just the word "Logic." One thing is for sure he wasn't talking about an Apple computer or software product.
I was working in studios around Europe in the late '90s and if you said "Logic" in a studio context, you were certainly talking about Emagic Logic, and "PC" didn't mean a Windows box. In that era, particularly in France, "PC" was often used colloquially to mean any Atari ST or Falcon, which had been the backbone of European electronic music production for a decade. Given Daft Punk's roots in the French house scene and the timing of Homework's production (1996-97), there's a strong chance they were running Emagic Logic on Atari hardware, because at the time, the ports of this program to other platforms were garbage and were not to be trusted.
The lineage of the software is an entire saga unto itself. What became Apple Logic started life as C-Lab Notator on the Atari ST in the late '80s which dominated Euro electronic music. In late 1992, after a dispute with C-Lab's owners, the core developers, one of whom was Apple's own Gerhard Lengeling, walked out and founded Emagic. They rewrote everything from scratch as Notator Logic, which eventually dropped the Notator prefix and just became Logic.
Around '02, Apple came knocking and swallowed the whole operation. They immediately killed the Windows version, and dropped the Emagic branding entirely with Logic Pro 7. Like I said, Gerhard Lengeling is still at Apple, now their 'Senior Director of Software Engineering for Musical Applications' according to his LinkedIn.