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

[Cars-N-Cans]

Yeah, lots of young people can barely hear 15kHz. 10kHz might be more realistic. How do you control for IMD, that might reconstruct audible frequencies? Are you going to measure what comes out of the tweeter? Historically that has been why people "heard" ultrasonics.

I can still hear to 16 kHz thanks to having more petite ears, and I have done a similar test with square waves. Once the harmonics fall outside of the range of my hearing, I cannot tell them apart from sine waves with the same fundamental frequency. They sound identical. Edit: This was taking a look at our favorite cable enthusiast Dr. Kunchur's paper (http://boson.physics.sc.edu/~kunchu...olution-by-bandwidth-restriction--Kunchur.pdf). One thing I could say with certainty was the SPL levels have to be very well controlled and carefully matched, or there will be the perception of "higher" frequencies when none are present. Add'l edit: Now that I remember a bit, the directionality of the ear made this test quite hard. I can hear even higher, at least up to 17 kHz, but the ear's pattern is so narrow that I have to be at just the right position relative to the tweeter or the tone vanished. Its not reliable unless I'm at the correct orientation. This is even harder with some headphones and IEMs as the standing waves can cause nulls that will hide the harmonics some percentage of the time. I think that fact goes missing in these discussions, is that even if for some reason we could hear higher, the fact that we don't have steerable pinnae that are relatively unoccluded and narrow ear canals like dogs do means that we likely wont be able to hear it, anyway, due to acoustics since it applies equally to us as much as it does to speakers.

 

[pma]

For those who still would like to play with 22+33+44kHz "audibility", I am posting a properly generated file with fade-in and fade-out, so no audible clicks at the beginning and at the end. Again, play it at normal usual volume, to prevent hearing damage.

 

[GXAlan]

We did? Or did we find that you didn't use it properly by providing a sample file that was too short for the FFT size you picked? When you supply a very short sample and apply a large size FFT you are in effect dividing the limited energy of the noise floor in that recording across many more frequency bins, resulting in a much lower level per bin. That's not a bug, this is how this stuff works. If you were to use an 8M FFT, you would lower it a whole lot more.

Sorry to offend.

Happy to call it a problem between “keyboard and chair” although the FFT size may be helpful to include in the legend of the screenshots.

 

[pkane]

Sorry to offend.

Happy to call it a problem between “keyboard and chair” although the FFT size may be helpful to include in the legend of the screenshots.

Sure, not offended at all, just curious what you thought the bug was. If you use the camera tool to capture/save the plot image, you can include FFT size and many other settings that were used to generate the chart.

 

[dasdoing]

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.

 

[lashto]

sorry for the radio silence, busy life. And it does not look like you guys missed me much

First of all, many thanks to @AdamG247 for adding the warning. And also many thanks to @GXAlan, @ctrl, @pma, @pkane who did useful experiments & posted test files (and everyone else who tried, in case I forgot someone).

I would agree with @Blumlein 88 that the only sure test will be to use 3+ tweeters.
Even better: 3+ playback chains and play the test tones separately. That would avoid any IMD from DAC/AMP/transducers and will make sure that we only hear/feel a missingF (if anything). To be even more sure, the playback and the transducers should be time aligned to avoid any time/phase shenanigans.
But that would be even more trouble. And even I think it's too much.

 

[lashto]

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.

interesting. I do hear the sounds as that guy describes it. Also hear a pretty clear missingF in the other 9-HDs video posted by @audiofooled. And in the wiki demo and other youtube demos. Thought it was an universal effect. Guess I was wrong (and would also be interested to know why some people do not hear it)

If you look at ~4:00, the video shows how those waves combine and generate the "missing pitch". That wave-combi-effect is pretty much independent of our ears and that's another reason why I (still kinda) think that the effect might be audible .. or felt in some way as others mentioned.

 

[lashto]

I can still hear to 16 kHz thanks to having more petite ears, and I have done a similar test with square waves. Once the harmonics fall outside of the range of my hearing, I cannot tell them apart from sine waves with the same fundamental frequency. They sound identical.

quite interesting. A serious -1 for my hypothesis. But still not taking logic/analogies/etc as proof

 

[Julf]

quite interesting. A serious -1 for my hypothesis. But still not taking logic/analogies/etc as proof

So you call actual empirical evidence "logic" or "analogies" - or maybe as "etc"?

 

[lashto]

So you call actual empirical evidence "logic" or "analogies" - or maybe as "etc"?

that is still not the actual sinewave test, it's just a (very close) analogy with a square-wave test. A very good/interesting one but still no...

 

[lashto]

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).

that is a pretty strong test. Maybe it's not audible after all, although @GXAlan seems able to ABX 'something'.

A few questions/comments:

• the SB21RDC tweeter seems be linear up to ~30kHz only. Not very clear from the specs if the 44kHz will be played. A 9kHz test (i.e. HDs at 18-27-36kHz) would be fine for me too, don't think that any of us can actually hear 18kHz.
• have you done the control test to check if you can actually hear/feel a missingF with audible HDs?

 

[lashto]

==============
Looking up this paper

https://www.tandfonline.com/doi/pdf/10.1080/10803548.2013.11076978

"... according to Smith, Nixon and von Gierke, signals with frequencies over ~17 kHz and level exceeding 70 dB may cause negative symptoms among exposed workers such as excessive fatigue, nausea, ear fullness and headache [24]."

Thanks for that paper link, I was actually looking for exactly that kind of study.

Many around here post things like "either it's audible or I don't care". Or rude/unnecessary stuff like "get off my lawn with your not-audible bullshit".
That is clearly not right, inaudible sounds can still affect your body, mood or music-enjoyment. Or even kill you. Pretty much same as odorless/tasteless food ingredients can give you a stomach ache .. or worse.

 

[dasdoing]

interesting. I do hear the sounds as that guy describes it. Also hear a pretty clear missingF in the other 9-HDs video posted by @audiofooled. And in the wiki demo and other youtube demos. Thought it was an universal effect. Guess I was wrong (and would also be interested to know why some people do not hear it)

If you look at ~4:00, the video shows how those waves combine and generate the "missing pitch". That wave-combi-effect is pretty much independent of our ears and that's another reason why I (still kinda) think that the effect might be audible .. or felt in some way as others mentioned.

Let me first be sure to understand what you are hearing. at this experiment, when he removes 110Hz the lowest tone doesn't go away for you?

What I kind of here before is a sawtooth like sound and the 110Hz seperated. when he removes 110Hz the "sawtooth like sound" doesn't change in pitch but the lowest tone is clearly gone. Again, it is so clearly gone to me that I have problems believing this fenonema. I don't even have to concentrate.

 

[lashto]

Let me first be sure to understand what you are hearing. at this experiment, when he removes 110Hz the lowest tone doesn't go away for you?

What I kind of here before is a sawtooth like sound and the 110Hz seperated. when he removes 110Hz the "sawtooth like sound" doesn't change in pitch but the lowest tone is clearly gone. Again, it is so clearly gone to me that I have problems believing this fenonema. I don't even have to concentrate.

sounds like you do hear it
When he removes the 110hz wave, the sound you hear is somewhat quieter and it has a different timbre, but it's still the same 110Hz frequency/pitch. It's still same as "low".

Think about an 110Hz produced by a bass-drum and the same 110Hz produced by a piano. They do not sound the same but they are the same pitch/frequency .. and same as low, although the bass-drum will give you a much bigger chest-thump-effect and you'll probably think that it was lower.

 

[dasdoing]

sounds like you do hear it

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. and if I compare a pure 110 with the tone of the sound with 110 removed I still can't identify any trace of it.

it has a different timbre

and I would describe it as the oposite. the timbre doesn't change for me....only the base (or should I say bass? lol) is gone.

but I totally fail to understand what actually makes the timbre here, as it is not 220Hz either. but I sure hear no 110 when he removes it.

 

[dasdoing]

ok, the wiki describes it like this

we may perceive the same pitch (perhaps with a different timbre) even if the fundamental frequency is missing from a tone.

I do hear this,

but this is not the same as hearing the fundamental even if it is missing.
the term "missing fundamental" is confusing. it actually describes the fact that it's not the fundamental that dominates the percieved pitch.
As I said I actually percieve two pitches in the first one, but the fundamental is in the background.

 

[Cars-N-Cans]

quite interesting. A serious -1 for my hypothesis. But still not taking logic/analogies/etc as proof

Problem is, even if you can hear very high frequencies, the actual pitch we hear changes essentially exponentially with linear changes in frequency. With difficulty, the highest tone I can make out is 19 kHz, and by that point it sounds like a gerbil cracking a helium fart. Even more problematic is few headphones can reliably reproduce this, and speakers beam too much at these frequencies to really be useful. If we were to use square waves, this as the third harmonic would be correspond to a fundamental of just 6.33 kHz. The 5th harmonic is 31.66 kHz, and given that you have to hear at least a few harmonics for the missing fundamental to work, who do you propose to use as listening subjects? Bats? This is why I used square and sine waves, since it was much easier and more practical to hear. Even to small children, a missing fundamental test is likely to sound like silence, or induce pain from the first audible harmonic, which is likely to be the only one. Maybe two, or three if there are even/odd harmonics, if you do it for high frequencies.

 

[Cars-N-Cans]

Let me first be sure to understand what you are hearing. at this experiment, when he removes 110Hz the lowest tone doesn't go away for you?

What I kind of here before is a sawtooth like sound and the 110Hz seperated. when he removes 110Hz the "sawtooth like sound" doesn't change in pitch but the lowest tone is clearly gone. Again, it is so clearly gone to me that I have problems believing this fenonema. I don't even have to concentrate.

There is still a hint of it there, as though it sounds like somewhat hollow hum from a transformer like there is a single lamination in the core that is loose or perhaps an enclosure panel buzzing away. But the actual lowest tone does indeed disappear, leaving more of a suggestion it should be there than the illusion it still is.

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

The rest of those videos in that series are very interesting as well. Edit: I think the reason it doesn't work in the first example is that its not music, its just periodic noise. The auditory center and brain in general automatically sets out to "fill in the blanks" of recognized patterns when information is missing. If it didn't hearing speech and other things would be radically more difficult due to the fact that there is often so much missing information in some situations, like conversation in a noisy room. But with noise that we don't like hearing to begin with, it doesn't really work.

 

[dasdoing]

There is still a hint of it there, as though it sounds like somewhat hollow hum from a transformer like there is a single lamination in the core that is loose or perhaps an enclosure panel buzzing away. But the actual lowest tone does indeed disappear, leaving more of a suggestion it should be there than the illusion it still is.

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

The rest of those videos in that series are very interesting as well. Edit: I think the reason it doesn't work in the first example is that its not music, its just periodic noise. The auditory center and brain in general automatically sets out to "fill in the blanks" of recognized patterns when information is missing. If it didn't hearing speech and other things would be radically more difficult due to the fact that there is often so much missing information in some situations, like conversation in a noisy room. But with noise that we don't like hearing to begin with, it doesn't really work.

I think it is just the presentation. make a direct AB presentation of those and "most percieve as beeing present" falls into pieces. an octave will always have the same feel. First time I heard it I percieved it as beeing lower. but I can listen to it in a way that it has the same feel. hard to describe. there is an effect, no doubt. but it's the presentation that makes the ilusion.
I stay with my conclusion that a tone with it's harmonics will actually have the percieved pitch of the first overtone (octave). and that is what creates the illusion. I can't accept people distorting into "you hear the fundemantal even if I remove it"...because it's not that what is happening

 

[Cars-N-Cans]

I think it is just the presentation. make a direct AB presentation of those and "most percieve as beeing present" falls into pieces. an octave will always have the same feel. First time I heard it I percieved it as beeing lower. but I can listen to it in a way that it has the same feel. hard to describe. there is an effect, no doubt. but it's the presentation that makes the ilusion.
I stay with my conclusion that a tone with it's harmonics will actually have the percieved pitch of the first overtone (octave). and that is what creates the illusion. I can't accept people distorting into "you hear the fundemantal even if I remove it"...because it's not that what is happening

No, you you don’t hear the fundamental when it’s missing. That’s not what the missing fundamental is. It’s not like it’s literally still there. If it was, we would no longer need woofers and subwoofers

You just said it yourself, even though the fundamental is missing, the order of harmonics still means you hear the same exact order of notes, but they simply sound thin.