Can someone please explain to me why and how a 24bit/44.1kHz file is considered high resolution

Yes, if you need to repackage.

Absolutely, but as far as I can understand he is using a signal level close to 0dBFS. What would it look like if the level was around -50dB? -70dB? Or to use @Peter_Comeau’s example of 40dB dynamic range. How would the weakest signals at -40dB look (and sound)?

They’d be fine. Why wouldn’t they?

A dithered CD has >96dB of range to play with (due to maths). Don’t forget these scales are logarithmic.

Let’s take your example of information at -70dB. So first I assume you’re listening in an anechoic chamber because in a domestic setting that’s already below the noise floor. Then also look at the real world recordings. The most dynamic recorded classical CDs have around 24dB of range.

To be fair you wouldn’t want much more in a domestic setting anyway.

So where’s the problem? “High res” is just the usual marketing industry tactic of chasing higher numbers and oneupmanship. It makes no practical difference to your listening.

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I don’t know! That is what I’m trying to understand. In John Atkinson’s measurements of CD gear he some times show graphs of a sine wave at 16 and 24 bit down at -90dB. Now this is without dither and extremely low in level, but clearly shows a difference which corresponds to my understanding of digital resolution:

Would dither help the 16bit reproduction here?

Those plots would be much more understandable as power spectra (i.e., plotted in the frequency domain, rather than the time domain).

You’d see a sharp peak at 1kHz, surrounded by broadband noise. In the first plot the level of the noise would be much higher than in the second.

Noise-shaping dither would change the frequency-spectrum of the noise: lowering it through most of the audio band, while raising it at high frequencies.

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Thanks! Yes, that would show where the noise is. If I understand this right the resolution remains the same so John Atkinson’s curves would be just about the same with dither or noise-shaping dither applied.

Please, please watch this video. In it (starting around 8:41), Monty Montgomery addresses exactly your question. But watch the whole thing.

I’ve seen this video. Like John Siau, Monty Montrgomery focuses on high level digital. His square wave talk is more like it as a square wave has lots of harmonics - just like music, but I’d like him to display a square wave at (for example) -48dBFS at 16 and 24 bit. If there is a practical difference it should show up here…
Intelligent use of dither seems to be the recipe to make 16bit digital good

No. he does something better than that: he shows what happens when you decrease the sample ratebit depth. (With dither) the sine wave stays a sine wave; it’s just that the level of the noise goes up. Even at 2 bits/sample, you can still hear the pure sine tone (though it’s almost drowned out by the noise).

Square waves are not band-limited. How well those are reproduced depends on the sample rate (since you need to include arbitrarily high frequencies to get a true square wave).

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Not wanting to pick nits as you linked to that most excellent video, but: did you mean to say “he shows what happens when you decrease the bit depth”?

Thank you !! Corrected.

That sounds reasonable, but music is not sine waves, It’s more like the square waves Monty Montgomery talks about. Do you think a square wave would ‘survive’ a bit depth reduction to 8bits (i.e. -48dBFS in a 16bit system)?

A square wave is just an infinite sum of sine waves, though. (It won’t survive as a true square wave in a sampled system, as the sampling requires limited bandwidth.)

How so? Music is band-limited (has little to no utrasonic content). Square waves are not.

He explained exactly what happens to square waves.

  1. The band-limited “approximation” to a square wave is a superposition of sine waves for all odd harmonics up to the Nyquist frequency (half the sample rate), where the amplitude of the nth odd harmonic falls like 1/(2n+1).
  2. Each such sine wave is faithfully reproduced (as he demonstrated).
  3. Superimposed on top of those sine waves is the noise, whose level depends on the bit-depth.

That I did not expect either!

N Y Q U I S T

Thanks for your patience! I’m slowly getting it now…

Nicely explained and demonstrated starting at 17:22 in the video.

Since there is no defined standard …blue book, black book, therefore anything > Redbook qualifies!

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Why not discuss 96 KHz vs 88.2 KHz while we are at not concluding 16 vs 20-24 bit?

Record companies decided to archive their analog master libraries to DSD64 back in the 90s, these masters could only properly reproduce a format that was divisible by 44.1KHz. So any modern 96KHz or 192KHz recording created from DSD64 master files have quantization errors.

Then why did they start using multiples of 48KHz??? It has ONLY to do with optimal synchronizing to video - sound tracks from movies recorded in a 48KHz multiple, such as the 24-bit 96KHz format embedded into DVDs and Blu-Rays. But because ignorant consumers demand 192Khz falsely believing it is better than 176.4KHz, that is what they market.