Differential Balanced Sound Quality


I've read where running a true balanced (differential) amplifier as such sounds much better than running it single ended (I'm assuming the same amp has both balanced and single ended inputs here).

Why would that be the case? Is it merely the improved SN ratio, etc. from being balanced, or is it something circuit related with running each channel's plus and minus through separate amplification stages?
greg7
Also, I took the opportunity to read the article I linked. It has lots of good information about the 2nd harmonic, but none about the 3rd. Here’s some more Pass writing that discusses both:

https://www.passdiy.com/project/articles/audio-distortion-and-feedback

And here in the introduction (on p3): https://www.firstwatt.com/pdf/art_ba_3.pdf
I'm just a newbie compared to most here if not all. I recently converted to what I believe are true AES48 supported pre-amp and amp (wyred4sound both units) and can say that the noise floor and transparency have never been greater in any system of mine in 30 years. The noise floor is basically inaudible. I am currently using "simple" balanced cables with Neutrik ends and mogami wire between the gear and quite happy. I have other weak links in the system but this is not one of them.  

Thanks to the knowledge freely shared here. 
Here is a quote from the late Charlie Hansen in The Stereophile, talking about their Ayre Codex, their cheapest electronic component having a linear power supply: "remember that every circuit is a modulated power supply....When you run balanced, it is like making the best power supply 1,000 times better."

@oldears Great quote.  There's someone over on diyaudio who's posting tag is "The power supply of my power supply is my FRIEND!"
Alternatively, the balanced equipment discussed above separately amplifies the positive and negative parts of the electrical signal. This requires double the circuitry because you have to amplify two signals (0-to-positive and 0-to-negative) instead of one (negative-to-positive) as in single-ended equipment.  If you imagine music as a sign wave, then balanced equipment is separately amplifying the upper and lower halves of the wave. The benefit of this added complexity is that any noise introduced into the signal by your equipment will be cancelled out when these two "half" signals are re-combined to make the full-wave signal that drives your speakers. This is because any injected noise will appear positive going in one amplification circuit and negative going in the other... add them together and you get automatic noise-rejection because they'll be in exact opposition.

@cal3713 The bit about positive and negative parts is problematic. Usually for balanced operation differential circuits are used, and its probably easier to understand that they amplify **opposites** rather than 'halves'. And it does not require double the circuitry- this is because in a differential circuit, the cathode (or emitter, or source) circuit has all the parts used in it in common. As far as noise or distortion goes, the benefit of cancellation accrues with each stage, not just at the loudspeakers. Finally, for a given single-ended gain stage, if done differentially will have theoretically 6dB less noise generated. This can be significant from one end of a circuit (like a preamp) to the other. Two stages, each with 6dB lower noise, that makes 12dB... So you don't need as many gain stages. In our full function preamps there are only three stages of gain from phono input to main output and they can work with LOMC cartridges; contrast that with a typical single-ended preamp which will have at least 4 stages of gain (unless an SUT is employed) or more to do the same thing and you can see that the parts count myth is just that.