Have you tried doing the blind test in the above video? 
I’ve done these before and have correctly picked emulator versus vintage. What these tests do not do is illustrate what I just said above. They stick to a limited range and pallet and avoid the extremes I mentioned.
This isn’t an analog versus digital debate, rather an observation from a critical listener that the math must be extremely complex because the emulators fall short in the ways I described. Now whether or not any of this matters for music making, well that is up to you.
Kudos to your ears because I scored 4/10… (the average was 5/10 and the best 8/10, on this particular video)
You have a point though: it’s nice that every analog synth sounds a bit different, even identical ones. Their sound also evolve with time so it’s a good starting point to have a more unique tone.
Actually, this is covered in my previous post about clipping =). Analog will give that warm distortion when you start maxing the signal, digital will just clip out, so digital synths will have a tolerance on them to not clip like hot garbage, that will affect the “power” you get out of the resonance as well. Analog will sound like a warmer fatter overdriven sound, digital will clip out, create artifacts, etc.
This is kept in check by limiting the volume output as much as possible on the digital side to make sure it will not clip. On the other hand, this overdrive can be simulated digitally, but for sake of better wording, will be too perfect. (None of the analog irregularities because its all math driven). It takes many layers of work to try to simulate analog, even with simulation it will never be ‘perfect’.
It all comes down to the world of pixies (electrons) and how they flow through the equipment. Its easy to simulate a sound, but not all the characteristics, especially at higher volumes. Add to that the components used and how they react to electricity and affect components downstream etc.
Quick example: An analog (low-pass etc) filter at its simplest is a capacitor and some type of resistor, by changing resistance value it will affect the speed the capacitor fills and releases its current. The slower the lower the filter.
The digital equivalent is normally just to allow specific frequencies to pass though while ignoring others. This is why filters are normally the easiest giveaway to know if its a digital or analog device through listening (especially high volume, high resonance). Add that to the clipping issue I mentioned and then you have the most telltale signs of analog vs digital.
Another note to mention, is digital is still limited by floating point (mathematical) calculations. In the case of a filter, say from open to close, has a finite amount of points. An analog filter is not confined by the amount of numbers (sometimes heard as steps) like digital because its more like turning on a hose, you can control electron flow, instead of controlling what number you are at. This makes it impossible to make a perfect analog simulation. But people have been able to fake things very well.
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Right, the math would be very complicated, which isn’t to say the emulation can’t be musically useful for >99% of what one might want to do. 
I’ve been pretty impressed by some of the Softube emulations I’ve had a chance to try out, with regards to how they react when overdriven a bit.
Absolutely no debate with that. I’m not getting into a Digital vs. Analog, they both have their strengths and weaknesses. Just defining what it actually means to be an “Analog” synth and how those differences convert to the sound you eventually hear.
For example, maybe 25 years ago, studios would opt for Analog recording equipment over digital, all because Digital-Analog-Converters were pretty garbage back then, and digital was truly not worthwhile. Since then the DAC’s in even low end soundcards are much much better. At that point the debate was real. Now recording analog equipment in digital domain is near exact with our higher bitrates, and they have overcome some of the clipping issues with better padding etc.
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A physical box doesn’t make it analog.
A physical box makes it a piece of hardware.
SO the fact that you like a physical box means you like hardware.
Hardware can be digital.
Just an fyi
A few examples of hardware that is digital:
Akai MPC’s
Roland Sp’s
Elektron Digitone
Elektron Digitakt
Korg Microkorg
Teenage Engineering Op-1
I could go on & on…the list of digital hardware is LONG…some of the above devices might have analog components, but they are for the most part digital.
Edit - Maybe I shouldn’t say “for the most part”…ugh… so hard sometime finding the EXACT word or phrase… especially when comparing analog with digital. But hopefully you know what I mean. The above devices are considered digital
Yes, thats true. I definitely prefere hardware, even though sometimes its not possible or useful to transfer a digital concept to analogue hardware (granular synthesis for example - but probably there are counterexamples).
Some people prefer recording over an analogue mixing desk and sometimes expensive “summing mixers” (ams, spl, dangerous…). These devices would also have their own “sound”. There are even plugins that emulate their features (slates virtual console). I ask myself what that could be. Is it only saturation/distortion by clipping (of very few tracks because otherwise the whole mix would be overdistorted) or also channel talkback and inaccuracies or more? And why would that be better? 
Edit: Not to Forget real analogue compressors that are more “transparent” (?)
Same here, I LOVE my Erebus and Nyx and whenever I’m in doubt about the difference between analog and digital, I fire up those synths and remember instantly
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I’m not really sure what you mean…but maybe someone else can chime in?
With respects to why would that make it better… I think feeling something is “better” is more of a personal preference…
Are you asking why people feel analog distortion/clipping sounds better than digital distortion/clipping?
sound generated with an analog circuit. The math or analog circuit allows for a rich abundance of harmonic overtones.
The limitations of digital only allow for as much harmonic content as the computer can generate. It will probably be many years before digital can accurately recreated the harmonic content of analog circuits.
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I don’t think this is accurate, I can get any amount of harmonic content I would like using either digital or analog. The problem I think you are referring to is when you want to overdrive that harmonic content. The limitations of digital are the sample speed and bitrate, which are so good right now it is very hard to determine a difference.
digital = made up sound
i still think, i can hear or feel this
for example i really like my uad plugins. But take the Massive Passive plugin.
Brauer, one of the most famous engineers/mixers says, he does not hear a difference to his hardware.
But there are other also very good engineers, who would swear, digital still sound a little bit more flat.
so even on this level, people hear a difference.
i do with softsynths, at least most of them. Or Lexicon native vs hardware.
It does not mean, i do not use digital. But i would love to have something analog, that makes digital signals more deep in space/3D.
Interestingly old dacs are also often given credit for why stuff like the dx7, d50, sampler/romplers can have such a good sound. That and the sample rate/bit rate giving that classic crunch. Then the stuff like the dude mixer that has line saturation and signals will fight for dominance… a bit like a compressor effect. But yeah I agree no reason to not record digital these days unless you just enjoy recording to analog because the quality is certainly there with dacs and recording gear now.
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While digital is limited by floating point calculations (or integer max value for that matter), doesn’t mean you’d be able to hear stepping. If you can hear steps at that point, they’ve been programmed and are wanted.
On the contrary, an analog synth filter can perfectly be limited by its encoders. Take the SE-02 for example. Its filter encoder is digital and applies a stepping when turned. Analog sound, though.
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Oh yes. The mk1 DX7 has mad aliasing on the DACs! Many say that is a key element of the sound.
That too may be an opinion, not a fact. Many hardware compressors are boiling over with lively character and THD.
Are you asking: What does this plugin do to the sound? To make it sound analog?