4 ms·
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 b
by altairprime 10mo ago
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)
- ggus 10mo agoNot 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.
- kevin_thibedeau 10mo agoThat's only relevant for navigation from the TOC. The samples are always 22.68us apart. That is the finest resolvable timing difference.
- frumiousirc 10mo agoI was also wondering about the inherent resolution for the BPM precision claims. Besides the sample period, the total number of samples matter for frequency resolution (aka BPM precision). 44100 Hz sampling frequency (22.675737 us period) for 216.276 s is 9537772 samples (rounding to nearest integer). This gives frequency samples with a bandsize of 0.0046237213 Hz which is 0.27742328 BPM. Any claim of a BPM more precise than about 0.3 BPM is "creative interpretation". And this is a minimum precision. Peaks in real-world spectra have width which further reduces the precision of their location. Edit to add: https://0x0.st/Pos0.png https://0x0.st/Pos0.png This takes my flac rip of the CD and simply uses the full song waveform. This artificially increases frequency precision by a little compared to taking only the time span where beats are occurring.
- deleted 10mo ago[deleted]
- mrgriscom 10mo agoThis is plainly false though. You're saying beats can't be localized to less than one second of precision (regardless of track length, which already smells suspect). Humans can localize a beat to within 50ms.
- frumiousirc 10mo agoYes, I got lost in the numbers and made a blunder by misinterpreting what we mean by frequency resolution expressed in "BPM" instead of Hz. It is correct to say "0.0046237213 Hz which is 0.27742328 BPM". My mistake was to interpret 0.27742328 BPM as the limit of frequency resolution in units of BPM. Rather, any BPM measured must be an exact multiple of 0.27742328 BPM. Thanks for pointing out my mistake! > (regardless of track length, which already smells suspect) Frequency resolution being dependent on the number of samples is a very well known property of basic sampling theory and signal analysis. In fact, one can interpolate the frequency spectrum by zero-padding the time samples. This increases the resolution in an artificial way because it is after all an interpolation. However, a longer song has more natural frequency resolution than a shorter song. Note, this frequency resolution is not related to fidelity which is some messy human related thing that is over a sliding window of shorter duration that I don't pretend to understand. BTW, the opposite is also possible. You can zero-pad the spectrum as a means of resampling (interpolating) the time domain. This is slower but more spectrally correct than say time-domain linear or cubic interpolation. These techniques require an FFT and so are somewhat expensive to apply to long signals like an entire song, as I did for the plot. Daft Punk's HBFS takes about 8 seconds on one CPU core with Numpy's FFT.