This video should help you if you've not already seen it. Very well worth the watch, and fully answers how that question has already been answered - since before digital audio existed:
As an EE, I would like to offer an editorial. This video is a great explanation of dither. A best example is when we used it in the 1980’s insurance headquarters where 50 desks were typing. The noise was unnerving at times, especially with migraines or poor sleep. The solution was to inject white noise. This white noise reduced the difference between the loudest typewriter noise and the ambient noise which is best described as nothingness. Of course, truly it isn’t nothing because even ventilation fans make some noise. If dithering is injected into the room such as speakers playing some off-radio station hiss then the floor noise (not to be confused with the building floor) then the difference between the maximum sinusoidal peak (volume) and the perception of the lowest volume is decreased. At the end of the day people could not hear as well when they got home but what did we care.
The pro’s of this video is a great presentation, a convincing educator with a bunch of cool stuff every geek would want in his garage. There are con’s when this video gets outside of dithering and I will save the best for last. So, the cons: (1) where does the stair step in a digital sinusoidal wave come from. It comes from 0 and 1. If we take everything in terms of digital 0 and 1 there are stair steps. But with an old analog oscilloscope it cannot be seen due to the resolution of the machine. Without the sinusoidal wave being high enough (loud enough) our typanic membranes would not move. The ossicles of the middle ear would not vibrate and the 8th cranial nerve that transmits impulses to the temporal lobe would be silent.
In this analog scope the frequency can be seen relative to time. However, there is a third dimension, a Z dimension that is not measured and just like all background noise (e.g. cassette tape hiss) this interferes with the “hearing” of the whole sinusoidal signal. More of this in the end.
Of most worthy comment is that the scope is meant to show the rough shape of the wave per unit time. It does not show what makes up that wave. There are harmonics, studio noise, instruments out of tune and farther away (minimal time delay) that all go into making what the analog scope can only show as a sinusoidal wave. It does not rise to the level of digital resolution.
The true genius is not in our measurement and blending of source signal and dithering but the applied mathematicians who can use quantization, 1 and zero and create the mathematics that end up being manipulated by mixing and recording machines. Quantum physics sound simple, where is the electron most likely to be in the electron cloud at any one time. This is undergraduate level science. To be able to use that to make lock and key encryption or Google and IBM quantum computers, with their added software, is so much beyond a bachelors degree as it gets. In this video the man, and myself, are at the bachelors level. As Dr. Neil de Grass famously says, “The danger is knowing a bit about something but not enough to know you are wrong”. Probably, these applied physical mathematicians are too busy than to comment on audio forums.
So far, we have spoken about floor noise and how dithering affects it. Next bit count. The video author is quite right on all explanations. The higher the bit count the cleaner the signal and the less floor noise we need.
Ok, I promised the best for last. What is noise, sound, music to our ears? Is it sound waves that can be seen on an analog scope that is meant for broad strokes of an electrical signal all the way up to hundreds of incoming volts? Is sound a nice pair of speakers? Is it listening to recordings that are recorded prior to 1978 when digital remastering went into use? Why do some people like listening to records, tube amplifiers and their older McIntosh amps. Why are some of the class d amps good sounding but the music just becomes irritating after a while. U may notice that u loved the Eagles. Bruce or Rhiana. Perhaps u can only listen to Rhiana for so long. I can. Some days yes and some days no. It digital, those days are more. Do u expect to see a digital signal on an analog scope that displays an overall sinusoidal (or square wave)? The resolution needs to be thousands of times more. So more that it takes a computer program to see.
Enter into my long awaited piste. Music and sound is only important with perception in the temporal lobe of the brain and one of 4 types of brain waves we have, theta for relaxation being the most applicable here. If digital vs analog were measured in 1,000 subjects, we call this number N, then regression analysis could tell us which one of the 4 waves is varied and by how much, multifunctional analysis and regression towards the mean. There is a really interesting phenomenon. When two people are touching, such as holding hands, their brain EEG signals change time to go in-sync. I’ve often wondered if this same occurs in some animals more than others such as humans petting dogs. It is relaxing and the dogs love it too. When was the last time you called a car out, by name, amongst a group of cats and it came to be pet All 5 minutes?
In summary, digital cannot be measured on an analog scope. It just doesn’t have the resolution. I am now a spine surgeon and not smart enough to speak about applied mathematics. Einstein was one of those people along with Maxwell, the folks at Fermi Lab and the quantum computer manipulation scientists of today. Sorry, there are other people today in similar and dissimilar professions that I do not know enough about to give proper credit to. An audio engineer just takes their work and mixes their products. No offense intended to audio engineers. Take, “Take me to church” by Hooser. Look at how a radio station audio engineer changed that song. Look how the engineer made that Diamonds on your Maybeck song did for that singer whose name I cannot remember.
Mark Levison, a great audio designer who hires good electronics engineers around him. In any hi-fi world we all know the name Levinson. Of the current generation, how many know who Neil Armstrong was and how many would say it is the elliptical orbit of the earth that creates seasons.
Measure brain waves and not oscilloscopes for the truest measure of digital vs analog signals.