*WHITE PAPER* The Sound of Music - How & Why the Speaker Cable Matters

The main reason for the test in the first place was to find a simple measurement that quantified the difference between different geometries. The easiest way is to see what the voltage drop was across a single conductor. There is no sleight of hand or skullduggery going on here. I am an engineer and engineers only work with the truth, because everyone can see when your bridge falls down. (doctors bury their mistakes, lawyers suggest better luck next time, accountants can come up with any figures they like). What fascinates me, is the imagination of the trolls who don't want to know.

I know there is a difference between cables and the is not down to a slight frequency variation at 20kHz, there is something more going on and I have tried to identify it.

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What you are attempting to do is bury your mistake.

Townshend audio

Lets talk frankly. 
Any capacitance on a speaker cable (stand alone, just vs. a measurement equipment), is the fact there are two cables in parallel, for all the length, at a close distance.
Such a capacitance can be fixed easily by building such a cable, from two separates. Capacitance is gone!
Do you thing that now all cables will sound identical?
No!
The factor to build a speaker cables, is custom built, per the Amp's DF and length required. This would effect the cross section (in gauge or sq. mm).
Such a cable can be calculated. 
I did.
Not only that, but I conducted a test on multiple participants and found it works 100% of cases. 
I also figured, that if a cross section is calculated, adding thickness, will not make any improvement.
So I have the formula. 
It was tested.
None of the sound characteristics can be measured by any of the methods of the tests you conducted.
It is about controlling a speaker, that is a coil moving in an electromagnetic field. None of the AP tests apply.
 

BTW.

1.  Has anyone heard a difference between speaker cables?

2. Has anyone heard a difference in the sound on the clip https://youtu.be/v11hmOE1Vcc.

3. I have tried to explain it, but some are not happy. Is it just coincidence that the traces track characteristic impedance quite closely?