Has anyone been able to define well or measure differences between vinyl and digital?

@fair

Ref: your long tech commentary and explanation above.

This is the single best explanation I’ve (ever) heard.

Thanks for taking the time to write this here.

Some have stated here that digital sounds 'lifeless'.

The reason for this is obvious and immutable.  It arises because the analogue signal has been chopped up into billions of pieces.  It is chopped up in two dimensions: frequency and time.  Once it has been diced in this way, all the expensive gizmos in the world cannot put it back the way it was.  It will never sound like the original analogue experience.  Of the two dimensions, chopping time is by far the more damaging.  However good your clock the timing will be forever artificial.  it will never again sound like the real thing.

Digital sound could be compared with digital images.  It could be said that with sufficient resolution digital imaging can be of very high quality.  This may be so, but for imaging, the image is not chopped in the time dimension. 

@akgwhiz    I do not agree that a preference for vinyl is caused by noise and distortion being "desirable".  The preference arises not from negative attributes of vinyl being perceived perversely as positive, but from the negative consequences of digitisation that cannot be reversed.

@fair ,

There are far too many errors and misinterpretations in your post. It will be highly misleading to someone who is not familiar with digital audio.

Start off with sampling theory and window functions. The requirement for infinite time is only required for infinite precision. We obviously do not need infinite precision as our ears do not have infinite dynamic range, and audio does not extend to 0Hz. Purely practical, the inherent noise of the quietest rooms and the onset of pain sets hard limits on what we need. Hence we do not even need infinite time. The windowing function does its required job. Sampling theorem is absolutely applicable to music. These theories are tested day in and day out. All our communications are based on them.

Short term Fourier Transforms are analysis functions primarily. They make pretty graphs, and are used for signal analysis. The data that comes out of them is bounded by the window width, which defines the lowest frequency that can be represented, the sample rate, which sets the upper bound, and both which define how fine of frequency analysis can be done. They do what they do accurately, understanding their limitations.

This is exact equivalent of DSD encoding, only its frequency is 64 times lower. Correspondingly, the highest frequency that we can hope to encode with similar fidelity as DSD will be 44,100 / 2 / 64 = 344.5 Hz. Say goodbye to the "micro expression of transients and micro transients"!

I am going to highlight this last paragraph. This is 100% false. That is not how DSD works. The single bit in DSD is not equivalent to a single bit change in PCM. No direct comparisons can be made. Hence you conclusion cannot be made and can be assumed false.

There are two flaws in your statement of equivalence 11 bits and 0.03% distortion detection. More like 3 flaws. That distortion limit is at full scale. Assume your stereo is set for 100db peaks, which is fairly loud and you have low distortion playback. There is a particular distortion level evident at that volume. In your analysis, you are claiming to be able to hear distortion at the bit level, on sounds that are only 70db. Are you claiming to be able to hear 0.03% distortion on a 70db peak signal. Not average, peak. That is a low volume level. If you are a very quiet room, 25db, that is only 45db above the noise of your room. That is 8 bits. So there is still 3 bits of addition digital range below the noise floor. Further, CD is dithered. Dither improves the dynamic range where our hearing is most sensitive for added noise where it is not. That extends the dynamic range to where we are most sensitive to 110db. Your argument fails with that information.

So, for faithful reproduction of a symphony we would need 90 / 6 = 15 bits for encoding the dynamic range, and 14 bits for encoding the shape of the signal. 15 + 14 = 29 bits.

This is obviously not at all accurate. You are stacking flaws in your understanding of how digital works to come to incorrect conclusions. The digital bit depth only needs to be large enough to encompass the full dynamic range. By shifting noise, we don't even need that many bits for the dynamic range. DSD has 1 bit depth. The noise is shifted to provide large dynamic range. CD has 16 bits. The noise is shifted to increase the dynamic range.

However, in order for the quietest signal to be still distinguishable, it only needs to be 6 db, or 1 bit, above the noise floor. This leaves an equivalent of 11 bits for dynamic range, which is more than twice of the 5 bits of the usable CD dynamic range.

You are basing this conclusion on a stack of fundamental flaws. It does not represent reality. More accurate is that we can hear below the noise floor. Vinyl has a signal to noise ratio of about 70db, sometimes higher, but the dynamic range can extend 10 or 20db. CD almost beats this with a raw dynamic range over 90db. The dithering extends this to 110db far higher than vinyl.

Viewed from this perspective, LP has twice as wide usable dynamic range in comparison with CD. But higher noise and distortions.

This is also based on a stack of flawed assumptions. It is incorrect

@clearthinker ,

The MOFI debacle I think is the best counter to your argument about digitizing of an analog signal. That they could do this for over a decade, while creating some of the best rated vinyl for sound puts a hole into the argument that useful information is forever lost. Can you explain your concern with chopping time? What do you think is lost when this happens knowing we can only hear a limited range of frequencies?

Movies and video chop images in the time domain.