Visualizing the effects of distortion in measurents (a suggestion)

I find myself not quite able to mentally "auralize" distortion measurements, even though I understand what it is.

So I'm thinking of a way to visualize the distortion in an FR graph.
So let's assume we are looking at one particular harmonic, which just for the ease of mental math, is an octave above the fundamental. You see a bump at 500Hz, it will translate to an added frequency at 1KHz if you play a 500Hz sine wave. Basically this distortion is always creating a frequency at double the frequency as where ir's showing up. So a 1.5KHz distortion here amounts to a 3K hiss. Ew.

But how do we SHOW this in a useful way? Well, we are able to show just the distortion "material" by itself in the same graph. We can place it visually at the correct relative volume. But I still can't tell what that MEANS in terms of perceived FR. So what if you were to transpose the distortion measurements up so the peaks aren't where the distortion occurs, but where the harmonic is added? So everything is pushed up, and that 500Hz distortion bump now shows as a 1KHz bump.

Now what if we could somehow add it to the FR curve itself, literally "distortion graph + FR graph", and overlay that with like 50% opacity over the pure FR graph, giving you a "phantom view" of where troublesome spots can be heard?

This is just me playing with some thoughts ans concepts that could help ME personally, and I think it would be pretty interesting to see.

Another idea, perhaps more useful, is to take the transposed distortion graph, perhaps summed together, and colour grade it so the higher the %THD, the more red it is, then it goes towards green, blue, and perfect 0 is just gray. Then you add the colour to the FR plot itself so areas with more distortion artifacts BEING HEARD are hotter in colour.

Visualization is a field worth looking into, so we can get more intuitive and useful measurements for the less technically minded, IMO

 

Some distortion measurements use a test tone because it makes it easy to see and measure the harmonics. It isn't that 1 KHz or some specific frequency is a particular problem, it's that it's one of the common frequencies used for measuring. Music is broadband (20 Hz - 20 KHz); whatever is playing will have that whole curve shifted up at the frequencies and lower levels of whatever harmonic distortion exists.

I guess you could mathematically generate what that would look like using pink noise, but I think the overall effect is quite small given that THD is commonly such a low value.

Edit: the above applies to DACs & amps, where the THD doesn't vary that much if at all by frequency (AC line frequency excepted). Transducers are a different ballgame, moving parts have resonances, etc; so meaningful results require a sweep measurement. That measurement already includes the distortion, it's part of the total output. But again, except for very low frequencies, it's small, typically less than 1% or 0.04dB. So while it can be audible, it's hard to visually differentiate even if you partitioned the FR by splitting out distortion products.

Said the MechEng. If you need someone to explain the 2nd Law of Thermodynamics, give me a shout. The above is based on 2 pretty elementary EE classes and there are a bunch of folks on this forum who live and breathe this stuff who can correct whatever I effed up.

 

Might be useful:
http://www.pmillett.com/file_downloads/ThesoundofDistortion.ppt