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

[Cars-N-Cans]

And this is why doing the “missing fundamental” test at high frequencies is a fool‘s errand. There are no musical notes that practically correspond to extremely high frequencies, only the harmonics. That means that any missing fundamental test will be restricted in how high up it can be. Can’t use 15 kHz, or even 10 kHz as the fundamental since it’s so shrill. My approach to ”how high” was to use a sine and a square wave with the same fundamental energy. Once the two sound indistinguishable, which was around 7 kHz for me, then all the harmonics are outside of human hearing. I think that or something similar is a better way to test whether ultrasonics are audible.

 

[danadam]

This is a much better demonstration of it (its actually pretty trippy):

Here's another one. 4 samples:

• A: 100 Hz + harmonics
• B1: 150 Hz + harmonics
• B2: like B1 but with fundamental removed
• C: 200 Hz + harmonics

spectrum:


In "missing-fundamental.flac" the samples are played in 4 phrases:

• A, B1, C
• A, B2, C
• A, C, B2
• A, C, B1

Even though the first frequency in B2 is higher than in C, the first two phrases both sound ascending and the last two phrases both sound as moving up and down (at least to me )

 

[lashto]

And this is why doing the “missing fundamental” test at high frequencies is a fool‘s errand.

This is just something I am curious about. You & many others are probably not, feel free to ignore the thread.
("my argument is the decider" seems to still be quite a trend. Sorry, the thread rules haven't changed: only direct tests count).

There are no musical notes that practically correspond to extremely high frequencies, only the harmonics.
That means that any missing fundamental test will be restricted in how high up it can be. Can’t use 15 kHz, or even 10 kHz as the fundamental since it’s so shrill.

Sounds like a half-truth to me. Yes, there are (almost) only Hs above ~10kHz, but why you think it's ok to not care about them?!
Many instruments have Hs at the same volume or even higher than the fundamental. E.g. brass instruments are considered to be examples of missing fundamental and their Hs count the most (some gigantic Hs from a trumpet)

More generally, this chart shows ~all acoustical info above 10kHz. And synths can easily produce fundamentals over 10kHz.
Quite a lot of 'music' up there, not buying your "forget about it" argument. Some of us can still hear over 10kHz and care about that stuff.

My approach to ”how high” was to use a sine and a square wave with the same fundamental energy. Once the two sound indistinguishable, which was around 7 kHz for me, then all the harmonics are outside of human hearing. I think that or something similar is a better way to test whether ultrasonics are audible.

Mentioned already that yours is an excellent example of an analog experiment. Might just be the best/closest.
Few reasons why it's not even close to "the decider":

• not familiar with square vs. sinus wave tests and not going to just take anyone's word for that stuff. You should at least include some details: e.g. how to listen for those diffs, at what levels are they audible etc... Even better, post your test files so anyone can check and/or link some study that confirms what you (supposedly) hear.
• by definition, the square waves only include half of the Harmonics (i.e. the odd ones). That will make em much harder to hear than a full H spectrum (especially relevant to this case with the already tough high freq limitations). The missingF effect is quite feeble and hard to hear, making it ~50% less audible is not exactly the best way to decide.

Long story short: you may think/say that your argument is "the proof", but that does not make it so.

 

[lashto]

not sure man. I can imagine what is meant here. hard to describe. the "loud base" doesn't change, but the lowest tone clearly goes away.

someone else already had a pretty good description: the missingF just sounds "thinner", it's still same as "low" in terms of freq/pitch.
And no worries, that is not an easy/obvious thing to hear. Apparently less than 1% of people have perfect pitch and can easily hear such differences (and before someone asks, I am not one of those)

 

[Julf]

not familiar with square vs. sinus wave tests and not going to just take anyone's word for that stuff.

So you are not familiar with it, but aren't going to take the word of those who are?

Long story short: you may think/say that your argument is "the proof", but that does not make it so.

Short story apparently made very long: you won't accept anything that conflicts with your belief, so this debate is about as pointless as a debate with a flat earther or conspiracy theorist.

 

[tmtomh]

So you are not familiar with it, but aren't going to take the word of those who are?

Short story apparently made very long: you won't accept anything that conflicts with your belief, so this debate is about as pointless as a debate with a flat earther or conspiracy theorist.

Sadly @lashto 's attitude here is all too common, not only in audio discussions but also in the culture in general: too many people have a blanket refusal to believe anyone who's knowledgeable or an expert, AND also refuse to look up the information themselves. They don't realize that indiscriminate skepticism is just as silly as blind faith (and in fact both are flip sides of the same coin). Both are forms of willful delusion.

This behavior can be relatively harmless in many hobbies: IMHO almost every hobby, and pretty much all forms of human play, rely in part on the artificial maintenance of mystery and possibility, so we can explore, feel wonder, have the enjoyment of discovering things ourselves even if they are already known in general, and so on.

But this behavior becomes harmful (whether just in messing up discussions like here, or in other situations by making the world a worse place in serious ways) when people insist on doing it in arguments and debates with others about what the fundamental truth of reality is, as lashto is here.

As you say, Julf, the purpose of lashto's approach and comments is obvious: to preserve that artificially large zone of the supposed "unknown" so they can smuggle in their own fantasy about what the facts of reality are.

It would be infuriating if it weren't such a tired and boring tactic.

 

[fpitas]

Sadly @lashto 's attitude here is all too common, not only in audio discussions but also in the culture in general: too many people have a blanket refusal to believe anyone who's knowledgeable or an expert, AND also refuse to look up in the information themselves.

This behavior can be relatively harmless in many hobbies: IMHO almost every hobby, and pretty much all forms of human play, rely in part on the artificial maintenance of mystery and possibility, so we can explore, feel mystery, have the enjoyment of discovering things ourselves even if they are already known in general, and so on.

But this behavior becomes harmful (whether just in messing up discussions like here, or in other situations by making the world a worse place in serious way) when people insist on doing it in arguments and debates with others about what the fundamental truth of reality is, as lashto is here.

As you say, Julf, the purpose of lashto's approach and comments is obvious: to preserve that artificially large zone of the "uknown" so they can smuggle in their own fantasy about what the facts of reality are.

It would be infuriating if it weren't such a tired and boring tactic.

I'll add, it also got a large group on a pointless snipe hunt.

 

[danadam]

Sounds like a half truth to me. Yes there are (almost) only Hs above ~10kHz, but why you think it's ok to not care about them?!
Many instruments have Hs at the same volume or even higher than the fundamental. E.g. brass instruments are considered to be examples of missing fundamental and their Hs count the most (some gigantic Hs from a trumpet)

More generally, this chart shows ~all acoustical info above 10kHz. And synths can easily produce fundamentals over 10kHz.
Quite a lot of 'music' up there, not buying your "forget about it" argument. Some of us can still hear over 10kHz and care about that stuff.

It's not about which harmonics are important, only about which fundamentals. No one argues that there are no harmonics above 10 kHz or that they are not important. But fundamental is limited. Quick googling shows that highest note on violin is A7 and on trumpet C8. This is 3520 Hz and 4186 Hz respectively.

 

[lashto]

The rules for this thread and the 'bet' were stated quite clearly: direct and reproducible tests are highly welcome but lalala does not count as proof. No matter who's and no matter how good it is.
You may or may not like the rules but complaining won't help you much ... or anyone else.

Do a real test, post test files, describe your controls: all ok! I'll be more than happy to settle the question and the bet.
Otherwise, I do not expect anyone to just take my word if I say "I heard crickets" and the exact same is valid for everyone else. Nothing special or 'original' here, the same applies to any other statement about sound.


P.S.
quite a few people had very useful contributions and just for that I'm thinking about an extra ASR donation. Even if the Q is not settled. Your 'noise' however is not very encouraging.
That aside, be my guests, it surely helps the visibility of the thread.

 

[kemmler3D]

The rules for this thread and the 'bet' were stated quite clearly: direct and reproducible tests are highly welcome but lalala does not count. No matter who's and no matter how good it is.
You may or may not like the rules but complaining won't help you much ... or anyone else.

Do a real test, post test files, describe your controls: all ok! I'll be more than happy to settle the question and the bet.
Otherwise, I do not expect anyone to just take my word if I say "I heard crickets" and the exact same is valid for everyone else. Nothing special or 'original' here, the same applies to any other statement about sound.


P.S.
quite a few people had very useful contributions and just for that I'm thinking about an extra ASR donation. Even if the Q is not settled. You 'noise' however is not very encouraging.
That aside, be my guests, it surely helps the visibility of the thread.

Looks like someone has actually done a very similar study to this... on bats. https://www.researchgate.net/figure...damentals-in-the-low-middle-and_fig4_13680570

 

[MRC01]

missing fundamental never worked for me and I sometimes suspect it's a psychological suggestion.
none of the "ilusions" in this video have any effect on my for example:

I even had to laugh at the 3:54 minutes mark. It's hard for me to believe that this realy works for others.

It's an audible illusion which involves how we interpret what we're hearing. That's why some people hear the missing fundamental, others don't. I can hear each sound either way: with or without the missing fundamental. It's like the 2-D representation of a cube, one can see it either way you want. Or at least some people can.
A possible contributing factor is that I'm a life-long amateur musician.

 

[lashto]

It's not about which harmonics are important, only about which fundamentals. No one argues that there are no harmonics above 10 kHz or that they are not important. But fundamental is limited. Quick googling shows that highest note on violin is A7 and on trumpet C8. This is 3520 Hz and 4186 Hz respectively.

looking at the trumpet H spectrum the fundamental, what we actually seem to hear are the 3 & 4 Hs (and presumably some after). For 3-4kHz fundamentals, that would be all above 10kHz. All very important, more important that the fundamental (at the very least for similar brass instruments with missingF spectrum).

P.S.
according to my googling, trumpet fundamentals do not seem to go much above 1kHz. But there are many other instruments which do. Anyway, just a tangent argument and I guess it's fair to argue using your own googled numbers

 

[Julf]

The rules for this thread and the 'bet' were stated quite clearly: direct and reproducible tests are highly welcome but lalala does not count as proof. No matter who's and no matter how good it is.
You may or may not like the rules but complaining won't help you much ... or anyone else.

Indeed. Lalala does not count as proof. But still you keep maintaining your beliefs based on pure speculation and lalala.

 

[pma]

looking at the trumpet H spectrum the fundamental, what we actually seem to hear are the 3 & 4 Hs (and presumably some after). For 3-4kHz fundamentals, that would be all above 10kHz. All very important, more important that the fundamental (at the very least for similar brass instruments with missingF spectrum).

Highest fundamental note is 7902.13 Hz.

 

[MRC01]

... according to my googling, trumpet fundamentals do not seem to go much above 1kHz. But there are many other instruments which do. ...

That sounds about right. Yet trumpet is one of the instruments that has a lot of very high frequency harmonics, so a good trumpet recording can have energy > 20 kHz depending on the mic used, how far away, and the trumpet player.
Piano might be a better choice, the highest note fundamental is just above 4 kHz.

 

[Geert]

Do a real test, post test files, describe your controls: all ok! I'll be more than happy to settle the question and the bet.

The result was already in a month ago:

https://audiosciencereview.com/foru...5khz-signal-audible-or-not.41848/post-1480670

I suggest you pay the donation and move on.

 

[danadam]

Here's a series of files (96k sampling) for fundamentals 1, 2, ..., 7 kHz. Each file plays twice a sequence of three samples:

1. the fundamental with harmonics,
2. harmonics without the fundamental,
3. just the 2nd harmonic.

Each sample is volume normalized to around -6 LUFS. Example spectrogram for 6 kHz file:


I still can hear a difference between 2. and 3. sample on the 4 kHz file. I could maybe even describe it as a change in pitch. But I stop hearing any difference between them on the 5 kHz file. In other words a mix of 10, 15 and 20 kHz tones sounds like pure 10 kHz tone to me. Not surprising, as my limit is around 16 kHz, so this 15 kHz already has little to no effect.

I have no problem saying that the "missing fundamental" effect ends for me there

 

[Julf]

I have no problem saying that the "missing fundamental" effect ends for me there

Problem is that lashto probably won't accept that as evidence either - basically asking us to prove the non-existence of Bigfoot, and dismissing any evidence we bring up.

Just as with Bigfoot, the burden of proof is on the person making the claim.

lashto, can you think of a way to prove the effect you claim exists, and then go ahead and do it? I am sure we would all be happy to verify and try to replicate your results, as well as pointing out any problems with your experiments.

 

[tmtomh]

The rules for this thread and the 'bet' were stated quite clearly: direct and reproducible tests are highly welcome but lalala does not count as proof. No matter who's and no matter how good it is.
You may or may not like the rules but complaining won't help you much ... or anyone else.

Do a real test, post test files, describe your controls: all ok! I'll be more than happy to settle the question and the bet.
Otherwise, I do not expect anyone to just take my word if I say "I heard crickets" and the exact same is valid for everyone else. Nothing special or 'original' here, the same applies to any other statement about sound.


P.S.
quite a few people had very useful contributions and just for that I'm thinking about an extra ASR donation. Even if the Q is not settled. Your 'noise' however is not very encouraging.
That aside, be my guests, it surely helps the visibility of the thread.

As @Geert notes above, test was run some time ago:

Update:
In my first version, the volume levels were not adjusted, the 11kHz test tone was way too loud compared to the 22-33-44kHz test tones.
So I had to increase the 22-33-44kHz multitone from -15dB to -3dB in Audacity, which created some IMD at 11kHz.

So I switched to my hypex plate amp and the 11kHz IMD was nearly gone (IMD at 11kHz is -60dB down - reason see above):
View attachment 263720
As suspected, the SB21RDC tweeter does not produce significant IMD at 11kHz, only the expected test tones at 22, 33 and 44 kHz.
Without the test tone boost in Audacity, the IMD at 11kHz was very low (about -71dB down compared to the 22kHz test tone):
View attachment 263723


Next I used a sine generator to create a 11kHz tone and level matched with the 22kHz tone, second image is the 11kHz test tone alone:
View attachment 263721 View attachment 263722
The tweeter generates some HD2 and HD3 - nothing to worry about. I could clearly hear the 11kHz test tone.

Then I switched to the 22-33-44kHz test tone and could only hear dead silence from the tweeter.
Even when I held my ear very close to the tweeter, I couldn't hear any sound.

As has already been suspected, the brain cannot reconstruct a "missing fundamental" if the harmonics can no longer be perceived by the ear - or I cannot perceive the "missing fundamental" (to be absolutely sure, I would have to do a positive test with, for example, 2kHz fundamental).

So you can pay up and then kindly take a seat.

 

[Cars-N-Cans]

Mentioned already that yours is an excellent example of an analog experiment. Might just be the best/closest.
Few reasons why it's not even close to "the decider":

• not familiar with square vs. sinus wave tests and not going to just take anyone's word for that stuff. You should at least include some details: e.g. how to listen for those diffs, at what levels are they audible etc... Even better, post your test files so anyone can check and/or link some study that confirms what you (supposedly) hear.
• by definition, the square waves only include half of the Harmonics (i.e. the odd ones). That will make em much harder to hear than a full H spectrum (especially relevant to this case with the already tough high freq limitations). The missingF effect is quite feeble and hard to hear, making it ~50% less audible is not exactly the best way to decide.

Long story short: you may think/say that your argument is "the proof", but that does not make it so.

Due to all the potential issues with pre-ringing and such with digital sound when dealing with sampling rates and very high frequencies, there are no files to post. I used an analog signal generator that I had set up before-hand with marking the controls on where they needed. Also I did it with triangle waves as well. My recollection was it was the same. My hearing has a firm cut-off at 19 kHz. Nothing higher can reasonably get thru. Divide that by 3, and we have roughly the point where the square and sine waves sound the same, which is just over 6 kHz.

And the reason I can say what I said is I have already done said errand and tried such tests myself. There's nothing to hear. Its simple physics.

Again, you are free to repeat such tests as you propose ad-nauseum as so many have done before, only to either get false-positives, or simply nothing when the test is set up properly. The false-positives are the huge pitfall since there are so many things to watch out for. Even relatively small changes in amplitude will cause the same waveform to sound substantially different.