That is an assumption that may not be entirely correct. But at any point, given that assumption, I see your point.
Yes, which is why I would never use a half roll in a small speaker. Accordion surrounds won't do this.
yes, it is an approximation (thought that proxy implied that). Need full FEA simulation to get the precise curve
multiroll or accordion rools have indeed less peak to peak Sd variation but the local Sd'(x) can still be high (Sd(x) is rippling) and this is what causes 2nd harmonic distoriotn/IMD. Multi rolls typically also have lower resoance frequency for the same stroke and stiffness. Al always, there are compromises.
Oldies graphs https://www.diyaudio.com/community/threads/volume-displacement-for-spl-chart.5668/post-55867 are handy 
Looks like ~150cm3 volume displacement makes ~100db ~40Hz. So ~2cm excursion with our 5" driver, or ~2mm with 15" driver give or take.
Typical 15" driver seems to have Sd ~850cm2 or so. Ten times of our example 5".
edit.
Single 15" driver has cone area of
~25x 3" driver
~17x 4" driver
~10x 5" driver
~6x 6.5" driver
~4x 8" driver
~2x 10" driver
Looks like ~150cm3 volume displacement makes ~100db ~40Hz. So ~2cm excursion with our 5" driver, or ~2mm with 15" driver give or take.
Typical 15" driver seems to have Sd ~850cm2 or so. Ten times of our example 5".
edit.
Single 15" driver has cone area of
~25x 3" driver
~17x 4" driver
~10x 5" driver
~6x 6.5" driver
~4x 8" driver
~2x 10" driver
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Oops, this one varies the whole Sd by 30% where as only the surround Sd should vary the 30%? So this sim is still extreme case.
even 10% gain variation gives AM side bands being only 26dB down. Sd modulation is causing amplitude modulation like Bl(x) and Bl(i). It has higher order products as well - especially the multi roll types. Hard to reduce IMD without fixing Sd(x). Pure 2nd harmonic distortion may be fairly innocuous but the accompanying IMD2 not so much.
Didn't Purify find that trained listeners could hear some things that people off the street couldn't hear? Are we talking about one of those types of things here?
If so, maybe there is some effect on untrained listeners even if they aren't consciously aware of it? In that regard we know that some people have claimed that certain dacs have a glossy sound and or are fatiguing to listen to for very long even if those listeners don't know why they are affected in the way that they claim. However, we have learned a lot about hump distortion in the meantime. Apparently it can have such effects on some people under some conditions.
If so, maybe there is some effect on untrained listeners even if they aren't consciously aware of it? In that regard we know that some people have claimed that certain dacs have a glossy sound and or are fatiguing to listen to for very long even if those listeners don't know why they are affected in the way that they claim. However, we have learned a lot about hump distortion in the meantime. Apparently it can have such effects on some people under some conditions.
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Nah, it's just time to do more studies!
Let's insert that that 8" Purifi driver in, that @2.83V drive does
H2:
At 20Hz is 33dB down (2.23%)
At 50hz is 49dB down (0.35%)
At 100Hz is 63dB down (0.07%)
At1000Hz is 70dB down (0.03%)
At3000Hz is 69dB down (0.04%)
Maximum H2 is 2.23%
H3:
At 20hz is 44dB down (0.63%)
At 50hz is 63dB down (0.07%)
At 100Hz >77dB down (~0.01%)
At 1000Hz is >78dB down (~0.01%)
At 3000Hz is >80dB down (<0.01%)
Maximum H3 is 0.63%
And then another 8" driver with heaps of distortion... like 11% H2 and 387% H3 in a properly designed waveguided 2 way.
(see post: https://www.diyaudio.com/community/...istortion-speaker-drivers.294787/post-7094796)
In a new era with DSP it's much easier to get the on and off axis or CTA2034A virtually identical with a very similar preference score and then compare!
Let's insert that that 8" Purifi driver in, that @2.83V drive does
H2:
At 20Hz is 33dB down (2.23%)
At 50hz is 49dB down (0.35%)
At 100Hz is 63dB down (0.07%)
At1000Hz is 70dB down (0.03%)
At3000Hz is 69dB down (0.04%)
Maximum H2 is 2.23%
H3:
At 20hz is 44dB down (0.63%)
At 50hz is 63dB down (0.07%)
At 100Hz >77dB down (~0.01%)
At 1000Hz is >78dB down (~0.01%)
At 3000Hz is >80dB down (<0.01%)
Maximum H3 is 0.63%
And then another 8" driver with heaps of distortion... like 11% H2 and 387% H3 in a properly designed waveguided 2 way.
(see post: https://www.diyaudio.com/community/...istortion-speaker-drivers.294787/post-7094796)
In a new era with DSP it's much easier to get the on and off axis or CTA2034A virtually identical with a very similar preference score and then compare!
proof only exists in mathematics.
I agree that IMD and THD are different probes of a nonlinear system. However, two systems with very similar THD can have vastly different IMD. See for example https://purifi-audio.com/2019/12/12/imd/
Sean Olive showed that non-trained listeners come to the same ratings as trained listeners, on average, but take more subjects to come to a statistically significant value.
Maybe "people off the street couldn't hear" something because it didn't actually exist. The experts just heard something that wasn't actually there. I've seen this effect in my experiments before.
Yes, have seen that too.
Yet sometimes blind tests of experts show they have essentially learned what to listen for. ESS claimed to have taught all but one of their executive team to hear state-variable settling in dac modulators. IIRC lrisbo said in another thread that Purifi did some casual research in association with a university to test off-the-street listeners verses those on the speaker design team who had learned what to listen for.
IMOE in particular, sometimes a short-term (transient) distortion/noise takes some practice to learn to notice before it has already gone by in time. Maybe similar in some ways to learning to be able to recognize certain types of regional accent subtleties in a non-natively spoken language?
Isn't learning what to listen for called creating "expectation bias"? Especially in cases where it is not even clear the phenomenon to be traced is there at all? I am not referring to the Purify research.
@ Lars: is IMD not simply to be avoided by separating bass (=excursion) and mids and taking care of limited mid excursion?
@ Lars: is IMD not simply to be avoided by separating bass (=excursion) and mids and taking care of limited mid excursion?
Thats an interesting question. Human perception discrimination is heavily influenced by training. That gives the experience and ability to be able to more accurately identify whether a phenomena is present or absent.
Expectation bias is a higher order loaded response to the phenomena being present or absent, adding predictable false responses.
So learning what to listen for does not necessarily create "expectation bias". However in a loaded setting it certainly could. Massively. Beware when "research" comes from commercial profit driven sources.
Even university researchers fail with unconscious biases.
If you want to learn how to control expectation bias, you have to ABX yourself enough and or user other methods to keep yourself calibrated. Personally, I never trust the opinion of one person. I use people that have learned to identify many small aberrations and test each person independently of the others. When they all agree they heard something and can describe it in detail, all without knowing that they happen to agree and not knowing other people's descriptions, the statistical weight tends towards a true positive. When people get experienced enough at that, they can get quite good at being skeptical and not imagining things.
This is quite true as I discovered.
In one of our tests we had a group of expert trained listeners and a non-trained group. Because we had multiple runs of the same data per person we could tell how stable their responses were. Quite surprisingly, the experts were less stable than the novices. I figured this was because the experts were listening so intensely that they imagined that they heard something when there wasn't anything.