What is behind a "warm" or "vinyl"sound?

I found an interesting article in The Saturday Toronto Star's entertainment section on the resurgence of vinyl.

What I found most interesting in this article was a description of why people describe vinyl as "warm". Peter J Moore, the famous producer/mastering engineer of the legendary one microphone recording of the Cowboy Junkies' Trinity Sessions recording says it all comes down to the fact that humans do not like square waves - ie. when you go from super quiet to super loud at no time at all. He gives the example that if someone was to slap two pieces of wood together right beside your ear would be about the only time one would feel a square wave - and that would make you jump right out of your skin! He says digital, particularly MP3s reproduce square waves like crazy, which triggers fear which also produces fatigue. He says if those same two pieces of wood were slapped together across the room, the square wave would be rounded off by the time the sound reached our ears. Turntables cannot reproduce square waves due to through time it takes for sound to get though the length of wire and the magnet that the wire is wrapped around in the cartridge. By the time the signal gets through that the sharpness, he ugliness, has been rounded and that, he says, is what people are talking about when they describe vinyl as "warm" sounding. Interesting!

I find there are a bunch of digital manufacturers, like Lumin, that are striving for a vinyl sound. I wonder if they are somehow rounding off the square waves in the digital signal to do so? If this is the case, "perfect" reproduction may NOT actually be beneficial to the sound...at least for someone who really wants a vinyl sound experience. Better may not actually be better when it comes to digital sound reproduction!
Interesting perspective but there's one problem. There are digital sources that sound pleasingly naturally round and conversely there are some analog sources that can sound edgy, hard and sharpe (cartridge choice? ). There's definitely overlap involved with both approaches.
I'm guessing digital done well in theory is better able to "pass a square wave" than vinyl, again due to the absence of natural physical damping factors like inertia, FWIW, similar to how wave bending (as opposed to pistonic motion solely as per most dynamic driver operations) in a pure Walsh driver has historically shown itself to lend itself well to the task, but just a guess.

Maybe AL or some of our other trusted EEs out there can shed some light on that one?
Waiting for Almarg to jump in and clarify all this. But I will add that it would be that humans tend to prefer even ordered distortion or low levels of odd harmonics as that would translate most closely to the natural, live acoustics we experience. Analog and tubes and well engineered solid state equipment can achieve these characteristics even if the measured results may indicate higher levels of measured distortion. Very intriguing to see how square waves could bring out the fear reaction in humans. I know that I easily prefer the natural sound of my turntable set up, especially vocals and stringed instruments, and bass. More three dimensionality and more density of image and specificity of the performers within the soundstage. And more relaxing and less fear.
"that does not explain why digital into tube amps produce 'warm'. Any thoughts on this?"

Most tube amps sound warm because their response rolls-off lower in frequency than SS amps. Most tube amps also have rather primitive power supplies for the plate voltages, not including fast-acting regulators or fast decoupling caps. These slower reacting power systems do not provide the power needed for high-frequency transients, so it softens the sound.

There are exceptions however. I have modded some tube equipment to fix these deficiencies and the top end softness disappears. They sound a lot more like SS, but with better midrange. The best of both worlds. Bass is always a problem with tube amps however. Its virtually impossible to get the really low impedance output required to control the bass of most speakers.

The mass of the needle assembly on a tonearm will also ultimately limit the reaction time and therefore the high-frequency dynamics. Even if the cartridge measures well beyond 20kHz using a steady-state waveform, it will fail to reproduce accurately a HF dynamic waveform, thus sounding softer.

Solid-state digital can also produce the dimensionality and smoothness of vinyl, but is requires several things:

1) very low jitter in the digital signal
2) lack of digital filtering in the DAC or minimize the effect
3) very linear I/V conversion in the DAC
4) excellent fast-reacting low-noise power supplies in the DAC

With 1-4, digital can actually beat vinyl. Makes sense because the physical limits of the cartridge are eliminated.

Steve N.
Empirical Audio
if anyone thinks that they're listening to these "square waves", it's absolutely wrong.
square waves are generated to divide ("slice") recorded continuous analogue signal onto samples that represented with bits as an amplitude and samples or "square waves" per second as sampling frequency.

the digital playback has dac that decodes these "square waves" back to the analogue signal and as Steve N mentioned, most of successful digital playback depends on it. it also depends on sample frequency and number of bits per amplitude. the larger sampling frequency and resolution, the lower losses of information during an analogue conversion. 1 5min song 36bits/192kHz format may occupy the whole CD that can fit over 1hr of 16/41kHz of digital music.

in neither of cases we do not listen to any square waves and more over we do not "round" them too. all we do we convert the recorded digital information into continuous analogue signal.