I like the way that you have approached the question. What are the electrical differences that could account for your results?

There are various ways of describing an electrical signal, a commonly used one is the Fourier series. You describe the signal as being composed of the summation of many periodic sine waves.

In the case of the electrical signal in the home, you can think of the signal as a sine WAV with a period of 60hz and with an amplitude of ~120v rms with lots of other smaller signals added to it. The 60hz part will not vary much at all, this is due to the fact that you are tied to a vary large utility grid that is kept in sync for the purpose of multiple power generation facilities. The frequency it regulated to such an extent that many clocks simply use the frequency of the outlet to keep time. The amplitude varies noticeably due to the power needs of your neighborhood and the power companies generation sources.

It is the small additional signals that are difficult to express mathematically for a household signal, the Fourier series is a useful concept generally, but is it used the describe a summation of signals that do not change with time. The signal varies is shape, but the components going in to the signal are the same. It is a useful model, but the small additional signals that are summed for a household signal are constantly changing as neighbors turn lights and appliances on and off randomly.

If we assume that the best sound from our system would be obtained from a pure sine wave with no added noise. And we know that the signal we get from our outlet has a pure sine wave with a summation of noise. How would the addition of a special power cord change the signal to more closely approximate the pure sine wave? The perfect power cord would need to eliminate the noise.

This idea conflicts with the sales pitch of the ultimate power cord, the ultimate power cord would be of the highest quality and would be completely transparent and not change the signal at all.