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

The main thing is to measure for audible content coming from the tweeter. Obviously if it's there, the test is invalid.
not sure if that test can conclusively prove/disprove any of the missingF assumptions. Should be a good/useful try, though.

First things first: I need a (super)tweeter to play the signal. Maybe someone can suggest a cheapo/easy supertweeter (EU shop).

Also do not have a reliable mic (just an audissey thingie). I may buy an UMIK if someone clarifies how can it prove/disprove any of the assumptions.

It does seem rather rude...
rude!?
"amateur" is a latin word. Can be used as a substitute for "person interested in something". At least in some languages. No idea if that's fair usage in English (not a native)

No, they are not. If your speculation is true, you should be able to hear a 11 kHz missing fundamental even with just a 22 kHz harmonic.
Are you suggesting that a missingF can be heard from just a single Harmonic ?! That would be a much 'wilder' theory than mine :)

My current assumption is that you need at least 3 HDs (see spoiler). Don't have a reliable source for that number, though
 
First things first: I need a (super)tweeter to play the signal. Maybe someone can suggest a cheapo/easy supertweeter (EU shop).

Piëzo tweeter for sale
"amateur" is a latin word. Can be used as a substitute for "person interested in something". At least in some languages. No idea if that's fair usage in English (not a native)
In English, it is often perceived as meaning "not professional".
My current assumption is that you need at least 3 HDs (see spoiler). Don't have a reliable source for that number, though
You know what they say about assumptions.... :)
 
not sure if that test can conclusively prove/disprove any of the missingF assumptions. Should be a good/useful try, though.

First things first: I need a (super)tweeter to play the signal. Maybe someone can suggest a cheapo/easy supertweeter (EU shop).

Also do not have a reliable mic (just an audissey thingie). I may buy an UMIK if someone clarifies how can it prove/disprove any of the assumptions.


rude!?
"amateur" is a latin word. Can be used as a substitute for "person interested in something". At least in some languages. No idea if that's fair usage in English (not a native)


Are you suggesting that a missingF can be heard from just a single Harmonic ?! That would be a much 'wilder' theory than mine :)

My current assumption is that you need at least 3 HDs (see spoiler). Don't have a reliable source for that number, though
If you're broadcasting audible IMD from the tweeter, your test is no test at all. You might look at piezo tweeters.

Amateur can be somewhat derogatory, especially if someone is an actual engineer. I don't know whether Julf is, or not.

I do think Julf is right that only a single ultrasonic tone (say, 22kHz) is needed. That is the classic situation in day to day life when the poor little woofer is straining to pump out 100Hz, but can only give a huge amount of 200Hz. Nonetheless, people think it's putting out great bass.
 
A somewhat heated discussion arose in a diff thread about the missing fundamental of a 15kHz signal. 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. And increase that to €100 is someone figures out an easy test that can be done by AverageAsrJoe. Or even by me (details in the spoiler below).

I'll pay that if my assumption (missingF still audible) turns out to be wrong. @Julf already offered to take the other side of the 'bet. Any other amateurs?

And an even bigger question: anyone who can/want to actually do the test?

Sounds like a pretty complex test to me:
  • transducers that can play 50+kHz are needed. (I don't have any). @Julf suggested a $8 Piezo Tweeter. Only goes to 27kHz but maybe someone knows a better one (and ~same as cheap).
  • an amp that can reliably play 50+kHz is needed. (I might have some but no way to reliably prove/check).
  • @HarmonicTHD's suggested using Distort to generate the test signal. Seems viable, an 192kHz sample rate is needed to avoid the DAC filter (thanks @Sokel).
  • Using an analog signal generator would be my preferred way. (I don't have any but the Distort-way should be good enough).
  • An oscilloscope would be very nice as a control device. (I don't have any either).
  • Missing piece of info: how many HDs do you need to hear/test a missingF? Is 3 of them enough?
  • Let's say that one hears a by-product of the 30/45/60kHz combo signal:
    • How do they prove that it was heard?
    • How do they prove that it was exactly the 15 kHz pitch?
    • How do they prove that it's the missing 15 kHz fundamental and not some IMD product?

P.S.
a missingF test for 10kHz should be easier. I'll take that too.
Couldn’t you do a quick test using Distort and the amp and speaker (headphone) you have at home?
If you can hear it: case closed no need to dig deeper.
If not: yes refinements would be needed. Happy to spent a few bucks too if needed.
 
Couldn’t you do a quick test using Distort and the amp and speaker (headphone) you have at home?
If you can hear it: case closed no need to dig deeper.
If not: yes refinements would be needed. Happy to spent a few bucks too if needed.
Doesn't work if his speaker can't reproduce the harmonics.
 
Amateur can be somewhat derogatory, especially if someone is an actual engineer. I don't know whether Julf is, or not.
Helsinki University of Technology (these days called Aalto University), Electrical Engineering. And 40 years of professional experience. But referring to that would be appeal to authority, and shouldn't affect the outcome of discussion.
 
A somewhat heated discussion arose in a diff thread about the missing fundamental of a 15kHz signal. 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. And increase that to €100 is someone figures out an easy test that can be done by AverageAsrJoe. Or even by me (details in the spoiler below).

I'll pay that if my assumption (missingF still audible) turns out to be wrong. @Julf already offered to take the other side of the 'bet. Any other amateurs?

And an even bigger question: anyone who can/want to actually do the test?

Sounds like a pretty complex test to me:
  • transducers that can play 50+kHz are needed. (I don't have any). @Julf suggested a $8 Piezo Tweeter. Only goes to 27kHz but maybe someone knows a better one (and ~same as cheap).
  • an amp that can reliably play 50+kHz is needed. (I might have some but no way to reliably prove/check).
  • @HarmonicTHD's suggested using Distort to generate the test signal. Seems viable, an 192kHz sample rate is needed to avoid the DAC filter (thanks @Sokel).
  • Using an analog signal generator would be my preferred way. (I don't have any but the Distort-way should be good enough).
  • An oscilloscope would be very nice as a control device. (I don't have any either).
  • Missing piece of info: how many HDs do you need to hear/test a missingF? Is 3 of them enough?
  • Let's say that one hears a by-product of the 30/45/60kHz combo signal:
    • How do they prove that it was heard?
    • How do they prove that it was exactly the 15 kHz pitch?
    • How do they prove that it's the missing 15 kHz fundamental and not some IMD product?

P.S.
a missingF test for 10kHz should be easier. I'll take that too.
BBC FM broadcasts are limited to 15kHz the pilot tone frequency is set at 19kHz, no one has every complained about the pilot tone being audible.
 
Helsinki University of Technology (these days called Aalto University), Electrical Engineering. And 40 years of professional experience. But referring to that would be appeal to authority, and shouldn't affect the outcome of discussion.
Agreed about that. Still, when one consults a professional, a certain amount of respect is appropriate, I think.
 
If you're broadcasting audible IMD from the tweeter, your test is no test at all. You might look at piezo tweeters.
Unless someone offers a way to diff between IMD and missingF, yep, I have no test at all. Pretty clearly stated in the spoiler, too
I do think Julf is right that only a single ultrasonic tone (say, 22kHz) is needed. That is the classic situation in day to day life when the poor little woofer is straining to pump out 100Hz, but can only give a huge amount of 200Hz. Nonetheless, people think it's putting out great bass.
Sorry, you lost me. Even my 'amateur' brain can see that the missingF is an effect of multiple HDs playing together (either in your brain, or in your ears, or in the air or...). Don't know how many HDs are needed, but surely 2+.

I have no idea what are you guys talking about with that single HD tone. That's not even hard to test. One can play a single 22kHz all day long and will never hear a 11kHz by-product. Cause there is none. Same with a 10kHz tone .. or any other.
 
You mean the under 20Khz.
Cause I already asked if a measurement mic would measure over that in another thread and @Blumlein 88 told me we need special stuff.
I think I was referring to needing to measure beyond 20 khz. Most measurement mics don't. Some are available for 40 or 50 khz, and even some expensive ones to 100 khz. You should be able to see if a 15 khz IMD product was present. If you do, then you'll have invalidated the test. If you don't, you can't really be sure the harmonics are there without the better microphones.
 
@lashto
Please donate the 50 euro to a local charity of your choice.

Here's how to do it.

Option 1
1) Get Audacity, it's free.

2) Create a 11 kHz test tone at a low level in 192 kHz container. I chose 0.25 for the signal.
3) Export that file as a pure 11 kHz test tone.

4) Now create a 22 kHz test tone at a higher level; I chose 0.9. Export the 2 tracks as a merged file.
5) Now create a 33 kHz test tone at a higher level; I chose 0.9. Export the 2 tracks as a merged file.
6) Now create a 44 kHz test tone at a higher level; I chose 0.9. Export the 3 tracks as a merged file.

7) Merge those 2 or 3 or all 4 tracks into a new file and export that file

This will generate a lot of IMD which falls into the audible range.

1675959038860.png


-------------------
Option 2

@pkane, tagged to make sure I'm doing this correctly.

Get Distort

Make a 11 kHz test tone
1675959962318.png


Add a big 2nd Harmonic. No surprises.
1675959996684.png


Add a big 3rd harmonic. There is a new IMD band in the audible range.
1675960042572.png


Add a big 4th harmonic. Now the IMD drops lower than 11 kHz
1675960077262.png


You cannot change the view in Distort to extend beyond 22 kHz in the current version of the software, and I cannot change the FFT size up to see if the IMD is real at those lower frequencies. I certainly can hear the IMD tone when using Audacity to generate the audio, but I'm not sure if that's the limitation of Audacity.

@pkane, any comments?
 
Sorry, you lost me. Even my 'amateur' brain can see that the missingF is an effect of multiple HDs playing together (either in your brain, or in your ears, or in the air or...). Don't know how many HDs are needed, but surely 2+.
This is a large part of the problem. You "see" a bunch of things that have no basis in reality.
 
The principle of the missing fundamental is that the brain makes up the fundamental using the harmonic information it perceives. If the harmonics can not be heard then the brain has nothing to work with.
A few people have posted similar arguments/logic in the original thread. Same as you, they seem to think that's the argument.

I also posted a counter-argument. An experiment that demonstrates how non-audible HDs generate a very audible missingF
"experiments subsequently showed that when a noise was added that would have masked these distortions..., listeners still heard a pitch corresponding to the missing fundamental, as reported by J. C. R. Licklider in 1954.[4]"
This experiment is not good enough to prove my "missingF is audible" hypothesis. But it's a pretty nice +1 for it. And the main reason why I think my assumption has some chances .. not many, not the best, but surely 'some'.

The counter-experiment is also enough to prove that yours is not the argument. It's just a solid +1 for the not-audible assumption.

Anyway, don't want to repeat the "arguments" from the other thread. IMO, the only way to decide this question is a direct test.
In the meantime, I'll mark it as "undecided"...
 
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I also posted a counter-argument. An experiment that demonstrates how non-audible HDs generate a very audible missingF
Did you actually read my comment about Licks experiment. I think you don't actually understand it.
 
@lashto
Please donate the 50 euro to a local charity of your choice.

A big Thank You for the effort, highly appreciated !!!

If it works, the 'charity' was already established in the bet: it's ASR.
It was also established that €100 will be paid in this case, not €50 (because your experiment is easy and does not require extra props).
And also established in the bet: I am the one to pay if the 11kHz by-product is NOT there or NOT audible. If it's audible, @Julf pays.

Here's how to do it.

Option 1
1) Get Audacity, it's free.

2) Create a 11 kHz test tone at a low level in 192 kHz container. I chose 0.25 for the signal.
3) Export that file as a pure 11 kHz test tone.

4) Now create a 22 kHz test tone at a higher level; I chose 0.9. Export the 2 tracks as a merged file.
5) Now create a 33 kHz test tone at a higher level; I chose 0.9. Export the 2 tracks as a merged file.
6) Now create a 44 kHz test tone at a higher level; I chose 0.9. Export the 3 tracks as a merged file.

7) Merge those 2 or 3 or all 4 tracks into a new file and export that file

This will generate a lot of IMD which falls into the audible range.

View attachment 263600

Would be great if you post the generated combo-file for anyone to use/test.

Otherwise, let's hold our horses a bit and see what this proves and who pays. IIUC, you demonstrated that the 11kHz is there. And it's audible. That could mean that I was right and @Julf pays.

But is this really enough to prove me right? Is your experiment really the same as "play the 22/33/44kHz combo through a speaker and see if an audible 11kHz will be heard" ?!
And is that audible 11kHz a missingF or an IMD? (if indeed there is any diff between those two)

Opinions anyone? Did I really win the bet?

P.S.
I would let @pkane talk about the Option2, he's the Distort expert
 
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Did you actually read my comment about Licks experiment. I think you don't actually understand it.
nope, did not read. Link it again please.

Also see above, looks like @GXAlan is asking for a payment from you :p
 
If you're broadcasting audible IMD from the tweeter, your test is no test at all. You might look at piezo tweeters.

Amateur can be somewhat derogatory, especially if someone is an actual engineer. I don't know whether Julf is, or not.

I do think Julf is right that only a single ultrasonic tone (say, 22kHz) is needed. That is the classic situation in day to day life when the poor little woofer is straining to pump out 100Hz, but can only give a huge amount of 200Hz. Nonetheless, people think it's putting out great bass.
Surely you need at least 2 harmonics of a missing frequency - otherwise we'd be percieving tones an octave down from any frequency in a signal.
 
But is this really enough to prove me right? Is your experiment really the same as "play the 22/33/44kHz combo through a speaker and see if an audible 11kHz will be heard" ?!
And is that audible 11kHz a missingF or an IMD? (if indeed there is any diff between those two)
No, that is not what he showed. I think he just showed IMD happened.

It is not possible to show the "perceived" 11KHz in a chart, because it doesn't exist - it is generated purley in the brain of the listener. It can't be measured with a microphone, and it cannot be simulated (unless you create a full brain/ear simulator)
 
Surely you need at least 2 harmonics of a missing frequency - otherwise we'd be percieving tones an octave down from any frequency in a signal.
I think I've seen tests where people hear strong 2nd harmonic from an overloaded small woofer and "hear" the fundamental. But I'm not entirely certain of that.
 
I also posted a counter-argument. An experiment that demonstrates how non-audible HDs generate a very audible missingF
That's not what this experiment demonstrated. You're making the wrong conclusions. The objective of the experiment was to determine if the perception of the missing fundamental was caused by "distortions introduced by the physics of the ear". So they introduced noise to mask these distortions, to conclude they were not the cause.

The sentence following your quotes confirms my argument: "It is now widely accepted that the brain processes the information present in the overtones to calculate the fundamental frequency". No audible overtones means nothing for the brain to process.
 
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