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Borealid 2 days ago

You are correct, and that "high enough fidelity" is the rate at which music has been sampled for decades.

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LouisSayers 2 days ago | parent [-]

The problem I'm mentioning isn't about the fidelity of the sample, but of the samples themselves.

There are an infinite number of frequencies between two points - point 'a' and point 'b'. What I'm talking about are the "steps" you hear as you move across the frequency range.

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kazinator 2 days ago | parent [-]

Of course there is a limit to the frequency resolution of a sampling method. I'm skeptical you can hear the steps though, at 44.1 kHz or better sampling rates.

Let's say that the shortest interval at which our hearing has good frequency acuity (say, as good as it can be) is 1 second.

In this interval, we have 44100 samples.

Let's imagine the samples graphically: a "44K" pixel wide image.

We have some waveform across this image. What is the smallest frequency stretch or shrink that will change the image? Note: not necessarily be audible, but just change the pixels.

If we grab one endpoint of the waveform and move it by less than half a pixel, there is no difference, right? We have to stretch it by a whole pixel.

Let's assume that some people (perhaps most) can hear that difference. It might not be true, but it's the weakest assumption.

That's a 0.0023 percent difference!

One cent (1/100th of a semitone) is a 0.058% difference: so the difference we are considering is 25 X smaller.

I really don't think you can hear 1/25 of a cent difference in pitch, over interval of one second, or even longer.

Over shorter time scales less than a second, the resolution in our perception of pitch gets worse.

E.g. when a violinist is playing a really fast run, you don't notice it if the notes have intonation that is off. The longer "landing" notes in the solo have to be good.

When bad pitch is slight, we need not only longer notes, but to hear it together with other notes, because the beats between them are an important clue (and in fact the artifact we will find most objectionable).

Pre digital technology will not have frequency resolution which is that good. I don't think you can get tape to move at a speed that stays within 0.0023 percent of a set target. In consumer tape equipment, you can hear audible "wow" and "flutter" as the tape speed oscillates. When the frequency of a periodic signal wobbles, you get new signals in there: side bands.

I don't think that there is any perceptible aspect of sound that is not captured in the ordinary consumer sample rates and sample resolutions. I suspect 48 kHz and 24 bits is way past diminishing returns.

I'm curious what it is that Deadmau5 thinks he discovered, and under what test conditions.

	▲	kazinator 2 days ago \| parent [-]
		Here is a way we could hear a 0.0023 difference in pitch: via beats. Suppoise we sample a precise 10,000.00 kHz analog signal (sinusoid) and speed up the sampled signal by 0.0023 percent. It will have a frequency of 10,000.23 Hz. The f2 - f2 difference between them is 0.23 Hz, which means if they are mixed together, we will hear beats at 0.46 Hz: a little slower than once in every two seconds. So in this contrived way, where we have the original source and the digitized one side by side, we can obtain an audible effect correlating to the steps in resolution of the sampling method. I'm guessing Deadmau5 might have set up an experiment along these lines. Musicians tend to be oblivious to something like 5 cent errors in the intonations of their instruments, in the lower registers. E.g. world renowned guitarists play on axes that have no nut compensation, without which you can't even get close to accurate intontation.