Missing fundamental for a 15kHz signal - audible or not?

[lashto]

Sorry missed that. Will answer your questions below:



I checked some of the linked youtube videos and I can confirm that I could hear the "missing fundamental" in these examples, as others have already described, slightly distorted - checked!
....

your test looks pretty good and is high up on my 'list'. Many thanks for the big effort and hope you have a bit more patience than some others

 

[vicenzo_del_paris]

On one side we have an OP that start a thread with an unfounded claim without proper evidences and challenges the community to bring proofs against his speculations.
On the other side, we have a group of highly skilled people that engage time and effort to build scientific and reproductible experiments that show the OP claim is completely unfounded.
OP is just denying these elements without proper logical nor scientific justification, by just saying "I don't accept your proofs and I stick with my unfounded claims"

Did I correctly summarised current state of this thread ?

If so, question to the OP @lashto : what was your goal with thread (except trolling and waisting people valuable time) ?

edit: @lashto why can't you provide proofs supporting your own claims instead??

 

[Julf]

Here are quotes from the OP:

On short: considering that its 30/45/60/..kHz HDs are inaudible, will 15 kHz be audible as a missingF ?

There are many pro & contra arguments but a clear, direct test is missing: i.e. generate a 30/45/60/..kHz combo-signal and see if its 15kHz missingF can be heard.

I offered to donate €50 to ASR if someone does a (credible) test.

I'll pay that if my assumption (missingF still audible) turns out to be wrong.

P.S.
a missingF test for 10kHz should be easier. I'll take that too.

The test setups have been described. They have been performed. You have been proven wrong.
I am not "leaving" the bet. I won. You lost. Pay up.

Not only don't you seem to like "arguments" that prove you wrong, you also don't like "arguments" that show you moving the goalposts.

OK, don't take my word. How about doing a poll among the readers of this thread to see what people think - have you lost or not?

 

[fpitas]

@lashto[/USER] why can't you provide proofs supporting your own claims instead??

They never do. Always they bring the bizarre, the extraordinary or just flat nonsense, and we have to prove them wrong. Not that they ever accept our proofs.

There is a word for that kind of behavior on the internet, but it eludes me.

 

[Julf]

There is a word for that kind of behavior on the internet, but it eludes me.

Something from Nordic folklore?

 

[antcollinet]

Something from Nordic folklore?

and Nordic bridges?

 

[GXAlan]

So… @lashto, I put my ears and my equipment at risk for damage by blasting $2000 headphones at maximum volume. I have hearing somewhere between 16-17 kHz.

I made the effort of making my own test tones, ran into trouble, and got help from pma and pkane.

I ABX’d differences but 1) explained that it was not a missing F experience.

I put my equipment at risk a second time by running measurements of my $2000 headphones at full blast again. This showed that there was IMD that was not the missing fundamental that theoretically is at the threshold of audibility. PMA thinks some DC can also be detectable as a small pop.

Others have shown how sensitive home amplifiers are to IMD.

You have all of the test files at your disposal.

I am not sure what else you want? You had someone who was on your side that there may be an audible difference and I was able to figure out that there WAS an audible difference, only we discovered just how hard of a multitone signal that was to reproduce.

 

[Julf]

I am not sure what else you want? You had someone who was on your side that there may be an audible difference and I was able to figure out that there WAS an audible difference, only we discovered just how hard of a multitone signal that was to reproduce.

And just to be clear, the audible difference was not because of a missing fundamental, right?

 

[GXAlan]

And just to be clear, the audible difference was not because of a missing fundamental, right?

That is correct.

I should have heard a 11 kHz missing fundamental and I did not when listening to a 22/33/44 kHz test tone.

Adding a 4th harmonic at 55 kHz doesn’t make sense because it’s already rolled off with SACD.

With the maximum number of harmonics. 11 kHz is too high of a target missing fundamental.

 

[Julf]

That is correct.

I should have heard a 11 kHz missing fundamental and I did not when listening to a 22/33/44 kHz test tone.

Adding a 4th harmonic at 55 kHz doesn’t make sense because it’s already rolled off with SACD.

With the maximum number of harmonics. 11 kHz is too high of a target missing fundamental.

Thanks for the clarification!

 

[lashto]

so first promised, first answered: How many Hs are needed to test a missingF?

Looks like many have forgotten that giant open question in the OP. It's ~impossible to settle the bet without clarifying it. May be possible to settle for the "audible" side without an answer but the (much harder) proof for "not audible" cannot work without a clear answer.

courtesy of @kemmler3D 's nice bats & a lot of googling, we finally have some answers.

Smoorenburg (1970) developed a .. test in order to test the predominance of pure tone versus collective pitch sensations.
... for two-tone stimuli less than half of the tested subjects spontaneously classified most of the sequences according to their collective pitches ... subsequent experiments revealed that the proportion of ‘‘collective pitch perceivers’’ increases with the number of presented harmonics...

(note: the "collective pitch" is the missingF. No need to take my word, the bats-study is linked above)
The quick takeaway: two Hs are definitely not enough to test. 3 Hs don't seem that great either, particularly for the "not audible" proof. I did not find a clear "you must have xx Hs" statement but 'everything' seems to point to "4-5 or more"

Some of the bat guys used 4+ harmonics

..trained to .. classify the collective pitches of complex tones, consisting of the first four harmonics

Everyone else seems to be using 5-10 Hs and 4 is a sort of "absolute minimum":

Ritsma (1962) and Plomp (1967) conducted experiments indicating that the harmonics contributing the most to the pitch of complex harmonic sounds were in the region of the second to fifth harmonic. These second to fifth harmonics of a harmonic complex were dominant in determining the pitch of complex harmonic sounds

The encircled "dominance region for pitch" is what ~every other study uses. The number 5 looks a bit arbitrary and I find it somewhat counter-intuitive that the H6+ contribute so much less. And the H10+s have zero effects, even when they are in our "most audible" 2-4kHz range.
Counter-intuitive or not: it is how it is!

The (expected) opposite-effect is even more counterintuitive: when you start high-passing the lowest harmonics, eliminating the H2 does not matter at all:

In 1843, Seebeck made the unexpected observation that the perceived fundamental pitch is not affected when the first harmonic is removed from a spectrum

(1843 is much older than expected, this stuff seems to go back to Helmholtz, the granddaddy of all Hs)
Apparently, the H-elimination does not matter much up to the ~4th, then it starts to go down up to 10th and then it suddenly plummets to ~zero. Again, not because the 10+ Hs are too high/inaudible. Other studies used 50-100Hz fundamentals with same results:

even when components of a harmonic complex can be resolved at the periphery of both ears, pitch discrimination as an indication of pitch strength is still limited to about the 10th harmonic.

That 'strange' behavior is supposedly related to a concept of resolved/unresolved harmonics (unresolved != inaudible) and it all kinda revolves around a theory called Autocorrelation: a model for explaining the audibility of higher missingFs which has no upper limit of frequencies (no theoretical limit, practice might beg to differ). Really like that autocorrelation but it's stuff for another post. Or happy googling...

That is a bit too much digressing, back to the main Q. The short(ish) answers are:

• 2 Hs are not enough to prove anything.
• 3 Hs could be enough to prove a positive (i.e. it's audible). But not even close to enough for "not audible".
• The whole "dominance region for pitch" (i.e. 4-5 harmonics) is used as the utmost minimum by pretty much everyone and every missingF study. Even for studies involving easily audible Hs/missingFs. For a "not audible" conclusion we need (at the very least) the same "utmost minimum".

Oh well, that might be the most unpopular answer ever.

It is however pretty clearly stated in the OP that the "how many Qs" question needs an answer first. It is also hinted that this test might be impossible (particularly at 15kHz). A few initial comments also classified this test between hard and impossible.

That does not mean that I want to take the "easy way out" and declare the test impossible. I'd very much like to find a way forward and to keep the bet. Suggestions highly welcome.


P.S.
@ctrl @GXAlan & many others who helped. The above text kind of answers your posts too. Wish I had a (much) better answer, sorry for that. I can only hope that you agree with the "3 Hs is not enough" conclusion, that "dominance region for pitch" is not exactly my invention.

P.S2.
Writing this kind of giant posts is a serious pita. I am ~done for 'today' and will be out 'a while'..

 

[antcollinet]

I think the goalposts are now out beyond Betelgeuse.

 

[fpitas]

I think the goalposts are now out beyond Betelgeuse.

And, I still have no idea why anyone should care.

 

[antcollinet]

And, I still have no idea why anyone should care.

I for one do not. The answer is pretty obvious, and has been for 11 pages.

 

[audiofooled]

I think the goalposts are now out beyond Betelgeuse.

Apparently, to prove that the solar eclipse is caused by the moon you have to go to the moon itself and then prove that you actually went there...

 

[Julf]

Looks like many have forgotten that giant open question in the OP. It's ~impossible to settle the bet without clarifying it.

That is not stated in your original posting. You are just moving the goalposts.

You lost. pay up.

 

[fpitas]

That is not stated in your original posting. You are just moving the goalposts.

You lost. pay up.

I'm sure the check is in the mail.

 

[kemmler3D]

While I appreciate the discussion around harmonics and perception, that in and of itself is interesting, the initial implied question of "can we hear >20khz ...indirectly?" is not that interesting.

That would require us to have ears that can reliably pick up >20khz but a brain that filters those frequencies out subconsciously. I don't think there's ANY evidence that that's how human hearing works, there is plenty of evidence against.

Maybe we do need 4+ harmonics to do a valid test of a missing fundamental, but it's not really a worthwhile test to begin with. As OP notes, this question had been explored well over 100 years ago, and on the other hand, repeating it with ultrasonics is extraordinarily unlikely to yield anything.

 

[fpitas]

While I appreciate the discussion around harmonics and perception, that in and of itself is interesting, the initial implied question of "can we hear >20khz ...indirectly?" is not that interesting.

That would require us to have ears that can reliably pick up >20khz but a brain that filters those frequencies out subconsciously. I don't think there's ANY evidence that that's how human hearing works, there is plenty of evidence against.

Maybe we do need 4+ harmonics to do a valid test of a missing fundamental, but it's not really a worthwhile test to begin with. As OP notes, this question had been explored well over 100 years ago, and on the other hand, repeating it with ultrasonics is extraordinarily unlikely to yield anything.

In a vague theoretical way it may be interesting I guess. But at least with my system, and most others, not much comes out of the speakers beyond 20kHz. So everything discussed is only applicable in some alternate universe.

 

[Geert]

It is however pretty clearly stated in the OP that the "how many Qs" question needs an answer first.

It's not actually. In your parallel universe you're probably referring to the statement:

There are many pro & contra arguments but a clear, direct test is missing: i.e. generate a 30/45/60/..kHz combo-signal and see if its 15kHz missingF can be heard.

You want us to believe you started this thread to understand the audible effect of high frequency signals that are not produced by any music instrument (60kHz)?

I don't think so, since the whole discussion actually started with you claiming you can hear the effect of the first harmonic of 15kHz:

The first harmonic of 15 kHz is at 30 kHz. Can you hear that?

Yes I (still) can. Actually, anyone can hear that. Or more precisely anyone who can hear 15kHz. You may wanna do a bit of research on those harmonics