Audibility of Non-Linear Distortion: A Practicum

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I'm a real measurements person, but I like to keep things practical. After looking at enough graphs of harmonic distortion for different drivers, I decided to try a simple experiment - can I actually hear a 5th harmonic at -xxdB down from the fundamental?

I devised a relatively simple method of doing this. Using a digital audio 'workstation' (Cocko's Reaper), I set up a series of pitch shifters, one each producing a 2nd, 3rd, 4th, 5th and 7th harmonic. I patched in a stereo input (from my CD player), and also sent out the unprocessed 'fundamental'. I then patched everything out on one channel to my amplifier. I checked that the results with a FFT and a microphone, to make sure I was on target for my harmonics.

I also created an 'IMD' test, but taking two pitch shifters, and setting their output to +15% and -15% of the fundamental frequency. For a single tone, this produces a warble tone, often used in speaker testing. Watching a FFT of the output of a speaker, it was obvious this induces a lot of IMD.

Here is a screenshot of my setup:
An externally hosted image should be here but it was not working when we last tested it.

So using the volume control on the various harmonics/IMD tracks, and the 'solo' buttons, I could listen to specific levels of each harmonic/IMD. The volume slider lets you set a specific -dB relative to the fundamental/source signal.

The results were surprising. Here is a chart of the point where I could no longer hear a difference between just the original, and the original plus the harmonic/IMD:
An externally hosted image should be here but it was not working when we last tested it.

All listening was done on a single Pluto loudspeaker, my head 18" from the speaker, at a 90dB SPL level.

The warble tone was of a 100Hz sine wave. All other tests were done with music. I can provide reference to the specific albums if people really want.

A few things were surprising - the biggest was that with music, for the most part, I couldn't hear differences below -40dB down. Particularly with the IMD test, which was particularly noxious at high levels, below -30dB, it was basically inaudible.

I noticed that music with lot of HF content made it easier to hear (Vivaldi). Music with lots of bass, and/or lots of compression made is harder to hear differences (Nujabes). Contrary to 'common knowledge', complex music (orchestral) masked differences while simple (singer/acoustic guitar) made it easier to hear differences. So the point at which difference could be heard changed depending on the music, but still within what I would call a small window- ie, somewhere between -30 and -40dB.

I've zipped up the file I made to do these sort of examinations, so other people can try it. Reaper can be downloaded for free, and then use the file I've attached. People will have to route their hardware I/O (on each track), but other than that, it should be relatively straightforward. Use the solo button of the harmonics/imd to turn them on or off. Keep the 'fundamental' solo on. Change the level of the harmonics/imd with the track's respective volume sliders. Don't change the level of the track labeled 'fundamental'. To change the volume of the IMD tracks, use the volume slider and solo button of 'IMD1' - 'IMD2' is slaved to it. Be careful where you click, you may disrupt some of the internal routing.

Feedback? I, for one, am less worried about non-linear distortion now.


  • Harmonic
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Very cool, thanks for this. I've searched a lot for a software that would do this very thing, but had not found one that was practical or easy to use.

One question for you: Did you measure the harmonic levels at the Pluto itself? Or did you just chart the digital signal harmonic levels?
Reason I ask is that lower order harmonics can mask the higher orders to some extent. Much of that was mapped out in research in the 1930's 70's and 80's. So it would be nice to know what was actually coming out of the speaker itself.

The levels you've found tend to agree with what is generally considered a "good" roll-off of harmonic.

EDIT: Oh, I see. You did measure at the speaker itself, good!
I am not certain but I think you are confusing IMD with non-linear distortion. There may be a relationship, but non-linear distortion typically will vary with amplitude.

Also much discussion has revolved around the 7th and 9th harmonics...

Then too one needs to know the baseline IMD of the speaker itself, minus the added (synthesized) distortion signal...

Complex orchestral recordings can't be lumped into a single category. There are some very well recorded ones, and some that are not. On a very low distortion system I have found that the better the recording, the better the listening experience and also the detail, whereas on systems that have "difficulty" with complex passages one gets the result that you reported.

Just opinions. Mine. :D

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