Are cables additive or subtractive?

Cables can only subtract from the original signal because they are passive devices.

From a purely theoretical perspective, all audio equipment is intended to amplify, pass and reproduce the original signal unaltered.  This is obviously which results in many different approaches to achieving the best final result.

I think that noise elimination is a key.  You can obviously hear noise directly if it's significant enough, but I also think that having noise has a significant impact on the overall sound.

If a cable, for example, results in a more harsh sound, it didn't add the harshness, it either allowed noise into the signal or filtered out something else that left the harshness.

Because every cable will filter out slightly different things and/or allow different levels of noise into the signal they may all sound different.  At this point listener preference takes over and if a cable improves the sound to my ear, I will tend to think of it as additave.

Think about a cup of coffee.  Coffee is the signal and the goal of the water, temperature, process used, etc. is to make the final cup of coffee to the taste of the person drinking it.  Increasing the quality of the water or changing the amount of water used doesn't add anything to the coffee, but does change final taste.

@jasonbourne52 - My experience aligns with yours and the box somewhat because I find that differences are very small when switching back and forth. I find the biggest difference when I’ve made a change in my system after listening to it for months. In this scenario, some changes become very obvious to me while others don’t.  It’s not possible to use any system other than your own as a point of reference in my opinion when evaluating things like cables. 
 

Example: I struggled to really describe any difference between AQ Sydney RCA and Monoprice XLR in my current setup, but the move to Morrow Audio MA4 was clear and obvious to me. 

Another way to ask the original questions is:

How can a cable add anything to the electrical signal?

The scientifically perfect cable would pass the signal unaltered.

Every cable changes the signal.

Here's an over simplified example:

If cable A has a better high end than cable B then either cable B is rolling off the highs (subtractive) in comparison OR cable A is rolling off the lows (subtractive) making the highs more prominent in the overall sound.

@felixa - I think it depends on the definition of additive.

If we're talking about additive from the perspective of adding to the original signal resulting in something better, then I don't think that's possible.  I think this was the intent of the OP.

However, if we're going to consider the addition of noise then additive becomes a bad thing with the goal of the cable to not be additive.