Acoustic Horn Design – The Easy Way (Ath4)

Here is an interesting AES convention article by Regina Smitt on audibility of nonlinear distortions in compression drivers.

Causes of Nonlinear Compression Driver Distortions and Their Audibility


Here is conclusion:
The resulting thresholds of hearing of nonlinear distortions were evaluated with respect to the structure of test signals. It was obvious that nonlinear distortions with an amount of 2% are already audible even for music signals (see figure 17).
In comparison with usual woofer loudspeakers these values reach significant lower amounts. A reason therefore might be the lower degree of masking of the arising distortions by the original test signals. Typical spectrograms of musical signals show a decreasing frequency response for higher frequencies (see figure 10,11,13). By contrast the resulting nonlinear wave propagation distortions have an increasing frequency response to higher frequencies.
For sinusoidal signals a threshold of audibility of 0.7 % was calculated. The amount of 0.5% was also attained by the threshold for the chord. This effect'causes probably in the perceptance of intermodulation distortions especially of difference tones. The produced frequencies are not a part of the transmitted frequency range of the horn loaded compression driver. According to the dependence of the thresholds on structure of the test signals it seems to be obvious that the temporal structure influences the audibility more intensively than spectral structure, Using temporal stationary signals the thresholds of audibility reach significant lower values. Generally, the dependence on test signal reaches a lower value than in investigations at woofer loudspeakers·

The graph below is from the same paper. It partially confirms the Earl findings, that audibility threshold of nonlinear distortions at some complex signals may be quite high (or may be strongly depend on the listening experience, in my understanding)
 

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My conclusion was simply that: The audibility depends highly on the statistics of the signal.

But what was said above about masking is also a relevant fact. And there are always going to be highly audible test signals. In fact, for any given nonlinearity there will be a specific test signal that will be most audible.

I would love to read the paper, but I am not interested enough to actually buy it. But thanks for the link.
 
I meant to get back to this earlier.

Alex specialty is in nonlinear acoustics. When we first met I too was doing a lot of nonlinear work as well. At that time we both believed that nonlinearity was a major aspect of sound design.

Then I started to study the perception of nonlinearity and found, much to my surprise, that they really weren't very audible. Alex became quite interested in our work and, as I said, told me that he had duplicated it at JBL. He admitted to duplicating our results.

Why it now appears that he has changed his mind, I can't explain, other than to say that maybe he hasn't - I have not talked with him for a long time. Many of those papers are old, back when even I myself believed in the high audibility of nonlinear distortion.....

This recent (June 2020) amateur study is interesting...
Archimago's Musings: BLIND TEST RESULTS Part II: "Is high Harmonic Distortion in music audible?" Respondent Results

"Looking at the results here, I believe the data supports the idea that in a blind test, of those who reported hearing sonic differences, lower harmonic distortion did correlated to "better" sound...."
 
If one looks at each and every sample in a signal, then one can compile the statistics of this signal. The most obvious is the mean, or really the DC term. This will virtually always be zero, or nearly zero, since the audio system cannot propagate DC. The next is the Standard Deviation (SD) which tells use what the signals level is (the RMS) - loud or soft, etc. But there are many higher order moments in statistics. The third moment is the skew, which tells us if there are more or less positive points than negative ones. The fourth moment is the kurtosis, which tells us how "peaked" the signal is, i.e. how points tend to lie beyond the norms implied by the SD (i.e. a Gaussian distribution, which has no moments higher than SD.)

Consider a signal with a high skew going through a system with clipping on one side and not on the other. If this signal is one way then the THD will be higher, if it is the other way then the THD will be lower. The skew, in this case, shows use that different signal skews and system nonlinearities affect the signals very differently.

I noted this when after a discussion with Sean Olive he mentioned that they found the works of Tracy Chapman the most revealing of poor sound quality. When I looked at the stats of her songs they had extremely high values of skew - far higher than any other artists.
 
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...I noted this when after a discussion with Sean Olive he mentioned that they found the works of Tracy Chapman the most revealing of poor sound quality. When I looked at the stats of her songs they had extremely high values of skew - far higher than any other artists.
That sounds as if nonlinear distortion was a significant factor in subjective assessment of sound quality then (?).
 
That sounds as if nonlinear distortion was a significant factor in subjective assessment of sound quality then (?).

Yes, one might say this is a possibility, but hardly the only hypothesis that one could make. Perhaps the skew and kurtosis of a signal makes the frequency response aberrations more apparent. Nothing nonlinear about that. It's probably a blend of both, an interesting study, but at this point it could be either way.

If you haven't realized it yet, the PDF (Probability Density Function) differences between the input and output will define the system nonlinearities to the extent the signal excites them - mostly level.
 
If you haven't realized it yet, the PDF (Probability Density Function) differences between the input and output will define the system nonlinearities to the extent the signal excites them - mostly level.
This seems as too complicated thought to get my head around it at the moment. Wouldn't a phase distortion (all-pass behaviour of the system) alone change the statistics of the signal?
 

TNT

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Yee, I'm not sure they are neutral. But are they fun and engaging - yupp. When I first heard them at Munich, I was startled. It was like live, the real thing compared to all other rooms there. A woman singing Lieder, it was fantastic. No hint of horn. But probably it was the total impression that was so overwhelming (also visually!) that neutrality wasn't on the "agenda" ;-) I cant recall to have seen any measurements ever. But I assure you, its not like you are listening to something that is produced by a lorry signal horn.

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