Digital vs. Analog
When looked at from a certain perspective, digital recording predates analog, that is to say, sound represented by ones and zeros or more to the point ons and offs, and in this case, I am referring to the player piano. Now one might argue that music boxes are digital devices, but they are more akin to digital sequencers than digital recordings, whereas piano rolls exist that were recordings of actual performances, my Dad’s Uncle had a piano roll that was an actual recording of a performance by George Gershwin. One could argue that sheet music represents the original digital recordings, but they lack the performance aspect that denotes a recording as opposed to a record.
On the other hand, one could argue that PCM is more in the way of a reproduction or recreation than an actual recording, in fact, it is possible to create digital music out of whole cloth without an actual performance having ever been done, I have done this in the studio, and there is a great deal of computer-generated music in the modern electronic music genre (EDM tends to be bits of sound samples cobbled together to match a computerized drum beat). Furthermore, some DAC manufacturers have claimed that they built up a library of prerecorded waveforms for given instruments that they would substitute for the originals to create a higher resolution more accurate representation (how they could possibly do this I have no idea).
Before we get into the blasphemy of which format is better we need to take a slightly closer look at the technologies involved. There are two forms of digital recording currently in common use Pulse Code Modulation (PCM) and Pulse Width Modulation (PWM, also referred to as Sigma-Delta, Direct Stream Digital [DSD], or single-bit digital). Oddly enough a Sigma-Delta DAC can be used to decode PCM though not as accurately as a multi-bit PCM DAC, and as far as I know, the reverse is not possible.
Since PCM is the more complex, and the more common, we’ll start our discussion with that. When looking at PCM there are two significant numbers to consider, Bit-Depth (not to be confused with Bit-Rate which is a measurement of compression, IE: how much of the original file still exists) and Sample Rate. If one thinks about a graphic plot of a sound wave, the Bit-Depth is how finely the sound wave is sliced vertically (dynamically) and each bit represents about 6dB of dynamic range (so higher Bit-Depths are capable of more dynamic range), and Sample Rate is how finely the sound wave is sliced up horizontally, IE: over time, and since the Sample Rate is measured in Hz the standard unit of time is one second. So in a 16-bit/44.1kHz file, 44,100 sets of 16 numbers are produced for every second of music, and since in stereo half are dedicated to each channel that means a frequency cap of 20kHz (10% of the samples are used to store other information necessary to the process). To make things a bit more arcane and to allow for things like quantization the 16 numbers aren’t a simple stack to create a plot point but are hierarchical, going from what is termed the “most significant bit” to the “least significant bit”. If I understand the process correctly, the most significant bit determines whether we are on the positive side of the sweep or the negative side, the next bit in order of significance determines if you want the top half or bottom half of that half of the sound wave, with each subsequent bit cutting the previous in half, which means in terms of fidelity the least significant bit is the most important bit as it determines overall accuracy. Also as you can see, more bits means not only more dynamic range but a more accurate placement of that point on the plot. This is why many refer to 24-bit/44.1kHz as being Higher Resolution than 16-bit/44.1kHz, though in terms of musicality, soundstage, and imaging, Sample Rate is really what we are looking for.
Which brings us to DSD, remember as a kid putting playing cards in the spokes of your bicycle? Remember how when you went faster the sound got louder and the pitch higher? Now imagine a wheel with 2822400 spokes with missing spokes at key intervals, moving at one rotation per second, that is Sigma-Delta. It is a much more analog approach to digital recording, in fact, it is not much different than how magnetic tape works.
Which in turn brings us around to analog. Like digital, there are two common forms of analog recording, records which we affectionately call vinyl and magnetic tape.
Weirdly, if you take a needle and attach it to a diaphragm and run that needle across a soft surface, the diaphragm will pick up all of the surrounding sound and transfer it to the needle which will etch it into the soft surface, and even more weird, if you then run the needle through the resulting groove that sound will be accurately played back through the diaphragm, and that is essentially a record. Of course, over the years we have inserted electronics into the chain in order to make the process more efficient and in some ways more accurate, but the process is fairly unchanged.
Take a long strip of mylar and coat it with a thin layer of ferrite particles and you have magnetic tape, subject that tape to a modulated magnetic field moving across its surface, and the magnetic fields of the particles will align with the modulated magnetic field. As result, you have a strip of north or south poles which can in turn be read by a magnetic pickup, hence why I noted the similarity to Sigma-Delta. Actually what I find to be truly amazing is the long lifespan of magnetic tape given the fact that induced magnetism fades over time (advanced aging tests stipulate 35 years or twice that of a CD, of course, practical experience has shown those life spans to be short of the mark as tapes from the ‘50s and CDs from the ‘80s are still playable, on the other hand, Edison’s first recordings made over 120 years ago are still playable, so the victor in longevity is still vinyl).
All of which begs the question, “Why Digital?” The answer is Noise Floor, Dynamic Range, and Bandwidth. In analog playback systems impurities equal noise whereas in digital systems they represent a loss of resolution or in extreme cases dropouts or skipping (which is true of both digital and analog).
Bringing us back to our initial subject, which is better, analog or digital; and to enter the world of sacrilege the short answer, in the long run, is digital. That is to say, given a sufficient Sample Rate, there should be no audible difference between analog and digital except for Dynamic Range and Noise Floor, both of which digital excels at. The pertinent question is what is a sufficient Sample Rate, and according to people whose ears I trust, that is around 400kHz, though I would probably hang my hat on 768kHz or Quad DSD.
Of course, the other key phrase in the above statement is “in the long run”. When the recording industry adopts high-resolution (again DSD 256 or 24-bit/768kHz PCM) as the norm, then digital will have come into its own, there is a reason most DSD and high-resolution PCM tracks are of old recordings dating back to the ‘60s, ‘70s, and early ‘80s, very few recordings are actually made in high resolution digital, it is something equivalent to direct to disc records, only the tweaks are doing it. My guess is, that it will be quite a while before that changes significantly since the recording industry is not likely to see a financial benefit to it. And for the record, transferring digital recordings to vinyl will most likely not make them sound better (unless the DAC they are using actually sounds better than the one you are using, and remember the audiophile community tends to be ahead of the curve, whereas the pro community is more interested in consistency and reliability than absolute fidelity).
Finally, the answer to the question, “why did the initial digital revolution fail so miserably?”, is that the audio engineers involved in its development, focused on a single aspect of human hearing, frequency response. The original sample rates of 44.1kHz, 48kHz, and 50kHz were based on the tape head speeds of video recording equipment (the only recording equipment with sufficient bandwidth to record digital signals reliably), and they felt that since few people could hear over 20kHz that was sufficient, despite the fact that many audiophiles could hear the difference between even those sample rates. Soundstage and imaging are all about time domain, so it is not about the frequency response of the ear but the processing speed of the brain, even those with limited hearing (under 10kHz) can locate a fly buzzing around their head.
So in conclusion, until the demand for high-resolution recordings becomes a reality or more likely, the progression of the hardware makes low-resolution recordings obsolete, vinyl will rule the day, though sadly it will be mostly old recordings as modern analog recordings are even more rare than high-resolution digital recordings.