Why the analog sound is fat
Analog recording has its own particular sound. Some say that it is the sound that defined modern recording techniques, and if you want your recording to sound 'like a record', then if you don't have the analog sound, you're in trouble. There is a certain amount of logic in this.
There are many digital simulations of the analog tape sound - hardware units and plug-ins - but most simulate only the distortion characteristics of analog, and sometimes a little of the noise. But analog recording is far more complex than that. For instance, there is modulation noise.
Modulation noise is noise that changes in level as the signal level changes. This is a separate effect to the constant background hiss that is audible in any analog recording. Modulation noise has two main causes...
One is Barkhausen noise which is produced by quantization of the magnetic domains (quickly glossing over a complex technical phenomen in five words...).
The other - more significant - cause of modulation noise is irregularities in the speed of tape travel. These irregularities are themselves caused by eccentricity and roughness in the bearings and other rotating parts, and by the tape scraping against the static parts.
We some times hear of the term 'scrape flutter', which creates modulation noise, and the 'flutter damper roller', which is a component used in better machines to minimize the problem.
If a 1 kHz sine wave tone is recorded onto analog tape, the output will consist of 1 kHz plus two ranges of other frequencies, some strong and consistent, others weaker and ever-changing due to random variations.
These are known in radio as 'sidebands' and the concept has exactly the same meaning here.
Modulation noise, subjectively, causes a 'thickening' of the signal which accounts for the fat sound of analog, compared to the more accurate, but thin sound of digital.
It has even been known for engineers to artificially increase the amount of modulation noise by unbalancing one of the rollers, thus creating more stronger sidebands containing a greater range of frequencies.
Don't try it with your hard disk!