1 bit = 6dB
so for a 16bit word you get:
1 = 6dB
2 = 12dB
4 = 18dB
8 = 24dB
16 = 30dB
32 = 36dB <------
64 = 42dB
128 = 48dB
256 = 54dB
512 = 60dB
1024 = 66dB
2048 = 72dB
4096 = 78dB
8192 = 84dB
16384 = 90dB
32768 = 96dB
So if you take 96dB as having 32768 levels (65536 levels p-p) then look back to 60dB down - or 36dB. You now have 32 levels.
CDs are linear, hearing is logarithmic. This gives an audible increase in distortion as levels decrease, especially when you only start with 16bits.
6dB per bit is too coarse. Dither only adds 1 bit of noise, which still does not stop 32 levels being too few.
Yes, it is. I think he got a bit tired of the audio magazine canards and bumper sticker slogans constantly having to be debunked, so it's a convenient way to get people to understand how digital signals actually work. Chapeau to Mr. Ogiers!
Dithering adds a couple of bits resolution at low - mid frequencies. From mid-treble dither is pure noise. It doesn't solve the issue of having too few bits.
With 24bit you don't need to bother dithering at all, in fact if CD encoding was logarithmic you wouldn't need to bother either I suspect.
Dithering actually proves my point: the last bit (bit 0) is important because you have so few quantisation steps at low levels you have to use dithering to try to synthesise more.
However dithering stops working at HF, you need a lot of points for the dither average to improve accuracy but at HF you are bound by the low CD sampling rate and run out of bits to help you and it's just noise.
The whole CD 'science' is a perpetual battle against insufficient resolution and an inadequate sampling rate. I.e. polishing the t**d.
I think there's a counting problem there.There's only a 6dB change when the largest bit changes. A 16 bit linearly encoded system distinguishes between (for example) level 31997 and 31996. That's 0.0002dB!
No, no counting problem
Sound is not linear, so one value only equals 0.0002dB with a full level signal.
With a quiet signal each value is more significant, right down to the last bit (90dB down) where each bit equals 6dB. As you state yourself in fact!
For example level 31 and 32. That's 0.28dB!
The difference between 31/65536 and 32/65536 is considerably smaller than 0.28dB. That's what we're talking about; there's no 31/32 ratio anywhere in the digitization or reconstruction.
I strongly recommend you use your ears and listen to the 4 bit demo that Werner posted (my link a few posts back). 4 bits! Music should be unrecognizable with only 16 possible levels, right?
That is completely incorrect. Both sentences.
Thanks for the link, SY. Amazing how much music comes thru, even in the undithered version. The fade out sounds rough, of course. But that's what? 3 bits and 2 bits?
A lot of guys worry about digital volume controls because you "lose bits." I have not heard a big difference, I have to admit. And just in case, my player software does volume control at 32 bits and then sends to my DAC at 24bits. No worries there. There are a LOT of fine steps in a 24 bit word.
A lot of guys worry about digital volume controls because you "lose bits." I have not heard a big difference, I have to admit. And just in case, my player software does volume control at 32 bits and then sends to my DAC at 24bits. No worries there. There are a LOT of fine steps in a 24 bit word.
So if its audible, tell me a few CDs where you've heard this 'distortion' occuring at lower levels. I'd like to listen for myself.
6dB per bit is built in to the mathematics, it has nothing to do with CD itself. In a binary system, each bit is weighted 6dB more than its neighbour to the right.
Noise is measured in bits? That's new to me - please elaborate.
What kind of dither are you speaking of here? Please explain whether its TPF, rectangular, noise-shaped or whatever. Then I might be able to understand where you're coming from.
But the issue of 'too few bits' has only been asserted, it has yet to be demonstrated.
Suspicion is a poor basis for designing a system. What do you base your suspicion on? Incidentally, nobody yet has a true 24-bit ADC, they tend to be around 20-22bits these days at best.
Please unpack 'try to synthesise more' ? Of course all bits are important, that goes without saying.
I'm lost here - do you have references for what you're claiming? I cannot follow what you're saying.
That's your opinion and you're welcome to it.
Is the 'science' of vinyl so much better in your opinion?
The 6dB steps are built into the mathematics? That must be why I posted up this mathematical table then
As for nothing to do with CDs - are you saying 16bit numbers have no place in mathematics?!
I can't find any reference to noise being measured in bits - that's a new one on me I'm afraid. Dither is however shaped noise generally applied to 1 bit. It works by statistically altering the apparent level to one between quantisation steps. Thus for a 22.05Hz waveform you get 1000 chances per cycle to get near the right answer. For a 22.05kHz signal you have one chance per cycle to get the right answer. One. Dither therefore at 22.05kHz is pure noise (the amount depending upon signal level - 1/65536 of p-p at full level, 1/32 of p-p at -66dB). If you think different then please explain how dither can improve an HF signal.
The major concept that some people seem to be blind to on this thread is that the linear steps of quantisation (1/65536 according to SY) are somehow equal throughout the whole dynamic range. While this is true for a LINEAR view of the waveform, is is NOT true for the logarithmic view.
Do our ears respond to the linear or log view?
If they respond to a log view then the resolution is not 1/65536 throughout the dynamic range but must vary. A signal 6dB down for instance must use 15bits - so the resolution is then 1/32786 and so on. OK it's quieter, but the quantisation error makes up an increasing part of the p-p level as you get quieter. With analogue you just sink into noise, but there is no loss of resolution until you get to the molecular/grain level.
SY is only correct if you only play full range p-p sinewaves through a CD. Any lesser level and you no longer have 65536 levels do you??
To hear some quiet HF stuff you may wish to listen to King Crimson - Court of the crimson king on CD.
As for all those who claim the CD is perfect (abraxalito,SY): are you are saying the people who prefer SACD are mistaken? Your view may surprise them
Hello All,
This is my 2 bits worth.
Pianissimo does not play well in my car with the windows down. However silence is golden in the music hall.
Vinyl is a mature well polished technology. CD Red Book was at the brick wall of the state of the art back when. Now with the lack of profit in hard media do you think the “record” companies will take the next step (think 78 RPM to 33-1/3 RPM) from 16 44.1 to 24 96?
I wish that they would.
DT
All Just for fun!
This is my 2 bits worth.
Pianissimo does not play well in my car with the windows down. However silence is golden in the music hall.
Vinyl is a mature well polished technology. CD Red Book was at the brick wall of the state of the art back when. Now with the lack of profit in hard media do you think the “record” companies will take the next step (think 78 RPM to 33-1/3 RPM) from 16 44.1 to 24 96?
I wish that they would.
DT
All Just for fun!
Mmmm...you blame cd's for beeing technology of decades ago...but vinyl is a crackling and prone to wear technology from ten's of decades ago!! The future is computer digital 24/96 (but even 16/44.1 is very good on a pc and the dynamic is far superior of that of the vinyl) thru a serious usb DAC + class D (i prefer class T) amp. It doesn't cost you an arm and a leg, occupies no space at all, can beat everything on this earth and doesn't need to be handled like a piece of chinese porcelain
. And you can listen to it every time you want to with the same audio quality!Obviously the mastering quality has to be good, but this is true for LP's and CD's, the majority of recordings (cd's & lp's) are of mediocre quality, so nothing to gain here. Anyway, a huge dynamic range is useful only for classical music, and if you ever listened for example to a live rock concert where the dynamic it's not correctly adjusted or compressed you know what i'm talking about
Unlistenable and irritating. The main target of a music playing system is to enjoy music and if you go overkill audiophile, you tend to miss the pleasure of listening IMHO.
32.
What might be useful for you to start with is to consider what one means by "resolution." If one can distinguish signal of a level X from a signal of X + ϵ, then the resolution is equal to or better than ϵ. Now, for that -66dB sinewave, what is ϵ? Is it 1/32 the level of the -66dB sinewave? In fact, no, it isn't. And the link I posted earlier (PLEASE listen to it) will give you a clue as to why.
It's not an easy concept to grasp intuitively, but it remains the case that the bit number does NOT limit resolution, it limits signal to noise. And a 16 bit system is vastly superior in that respect to vinyl. Take a look at my phono stage article to get a better grasp of the theoretical noise floor of a phono cartridge and associated amplification; the very best ones are 20-30dB worse than a 16 bit digital system.
That's five bits, or twice as many levels as in the audio examples you linked to. While it does work, it isn't great sounding. But -66dBFS is way down.
It's interesting that in all the nostalgia for vinyl (merited) we forget how bad we used to think vinyl was. Doesn't anyone remember the endless complaints about bad pressings, surface noise, cheap thin vinyl, bad mastering, etc?
Back in the good old days, vinyl had just as many problems as digital does today. Maybe more.
Of course I'm not saying that. What led you to think I was?
You mean it was new on you when you introduced it?
Sums are clearly not your strong suit. Since the sample rate is 44k1, there would be twice as many samples as you're saying there are. Why do you say dither is 'shaped noise' though? Do you mean your argument against dither does not apply to the more common forms of dither where the noise is not (spectrally) shaped?
I don't in fact merely think different, I can show different. A 22.05kHz signal is effectively illegal as an input to a CD system - it falls at the point where it will be aliased to DC. It however would be sampled precisely twice each cycle. I can't follow you when you say 'Dither therefore at 22.05kHz...' so please unpack what you mean. Dither does not have a frequency, its broadband and its always noise.
In terms of loudness, a doubling is equivalent to 10dB (10X as much acoustic power) I seem to recall. However loudness is a percept, so the answer to your question is : neither of them.
I'm unclear - I didn't ask about 'quiet HF stuff' I asked about distortion at lower levels that you said was audible. This disk demonstrates that distortion?
As for all those who claim the CD is perfect (abraxalito,SY): are you are saying the people who prefer SACD are mistaken? Your view may surprise them
Straw man
I don't think it is easy to say which is better, it will depend on the whole payback system, if all amps in the system is solid state amps, it will difficult to find out, but if all amps in high quality tube gear, ( some high end DAC has a tube out-put too) and also you are not too care of the noise level and only looking for more emotion and more live feeling than no CD can beat the vinyl but only reel to reel tape can
tony ma
tony ma
Exactly correct. If you record at an incorrect level and then have to crank the gain of the system to play it back, you've thrown away 11 bits of signal to noise. I think there was an article on gain structure somewhere on the intertubes that I can link you to.
Now... if one makes an LP with music at -66dB from nominal output (say, ref 5 cm/s), then crank your system gain accordingly, what will that sound like?
Digital is much more forgiving on the low end of the dynamic scale. The trade off is that, unlike tape or LP, you just can't push things on the high end of the dynamic scale- 1111111111111111 is a pretty solid wall to hit.
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