Why Power Cables Affect Sound

I just bought a new CD player and was underwhelmed with it compared to my cheaper, lower quality CD player. That’s when it hit me that my cheaper CD player is using an upgraded power cable. When I put an upgraded power cable on my new CD player, the sound was instantly transformed: the treble was tamed, the music was more dynamic and lifelike, and overall more musical. 

This got me thinking as to how in the world a power cable can affect sound. I want to hear all of your ideas. Here’s one of my ideas:

I have heard from many sources that a good power cable is made of multiple gauge conductors from large gauge to small gauge. The electrons in a power cable are like a train with each electron acting as a train car. When a treble note is played, for example, the small gauge wires can react quickly because that “train” has much less mass than a large gauge conductor. If you only had one large gauge conductor, you would need to accelerate a very large train for a small, quick treble note, and this leads to poor dynamics. A similar analogy might be water in a pipe. A small pipe can react much quicker to higher frequencies than a large pipe due to the decreased mass/momentum of the water in the pipe. 

That’s one of my ideas. Now I want to hear your thoughts and have a general discussion of why power cables matter. 

If you don’t think power cables matter at all, please refrain from derailing the conversation with antagonism. There a time and place for that but not in this thread please. 
 I’ve seen a power cord make a difference of nearly 30% of output power out of a power amplifier. I could also see that that was caused by a voltage drop across the power cord.
You can measure differences in output power, output impedance and distortion on many power amps just by changing the power cord- and many of these differences are simply caused by voltage drop.
and finally,
There is more to it than voltage drop though. It also has to do with bandwidth of the power cord.......
 My questions are not whether a power cord can affect the sound of an amplifier (or other gear) since I have heard the differences, but rather,
1. What characteristics of a power cord would affect voltage (i.e., cause a voltage drop) - is that primarily a function of resistance and wire gauge, or something else, and
2. What characteristics of a power cord would affect bandwidth?  

There are dozens of sites that measure gear, going from budget to the best there is, find me the measurements of any competent gear that has harmonic distortion every 60Hz (or 50Hz for most non-Americans). In fact, the only measurements I have seen of mains leakage is in devices that are supposed to clean up signals/wattage, like the Wyrd4Sound Remedy Reclocker, it needs a linear power supply or else it just leaks power supply noise (shouldn’t be bought anyway as it doesn’t reduce jitter in any normal use case, only if you have like a 30ft fun and need a repeater, but even then it’s overpriced).
I've been a believer from many moons ago but my latest power cord for my subwoofer totally changed my systems SQ for the better and it wasn't subtle. Like the OP I just want to know why this happens but after reading this thread I guess the one that was on the subwoofer before was indeed letting noise through. Great info and I've learned a lot from many on this thread.  New PC was just over a c-note.
Off topic. I was looking at/interested in a Wyred for Sound Remedy Reclocker, but noted the general interest in threads was the year it came out, a few posts in the next year, then nothing. If it DID anything, there would be MORE ACTIVITY discussing it.. Seemed to have been a 'flash in the pan' and not much more.  I could maybe see buying one to allow me to add another source to my DAC...?But for the price, plus needing a real power supply? just too much money and fooling around.

What kind of difference did you hear? Bass pretty much has no timbre, that’s why matching your subs to the speakers pretty much doesn’t exist, and at 20Hz we can practically have 100% THD and it not be audible, and even 10% THD at 100Hz is about the threshold.