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

[lashto]

Caution - Users/Readers are to be Cautioned that some of the audio file examples and experiments contained in this Thread. Can cause Damage to either your Hearing or your Speakers if conducted incorrectly. If you don’t completely understand exactly what is being done in these tests use reasonable caution and keep volume/gain levels very low. Some of these test will destroy your Hearing and/or Speakers or both! (Added by Moderator)

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?

Spoiler: some extra details for the curious

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.

 

[fpitas]

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.

 

[lashto]

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.

good question about the IMD, I also have it in the spoiler. The answer I do not have...

 

[fpitas]

good question about the IMD, I also have it in the spoiler. The answer I do not have...

A decent hi-fi microphone will measure that. A lot of tweeters get "creative" when fed ultrasonics, especially at high levels, and generate beat notes.

 

[Geert]

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

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. Do you really expect someone to waste his time on testing this basic logic without any reason to believe it's flawed, for a lousy 50€? You should Google Brandolini's law.

 

[fpitas]

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. Do you really expect someone to waste his time on testing this basic logic without any reason to believe it's flawed, for a lousy 50€? You should Google Brandolini's law.

I had to Google that. We do see that all the time here

 

[antcollinet]

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?

Spoiler: some extra details for the curious

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?

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

Your test proposal is decidedly non trivial. Apart from the difficulty you've pointed out of sourcing kit that can do it, It is not just a case of sending some ultrasonics through that kit and then listening - you are talking about subjective perception results, so to have any validity it will have to involve blinding, and multiple test subjects, training of them, devleloping a statisically robust test method, and subsequent statistical anlysis, etc etc. An exceptionally high effort undertaking.

No-one is going to go to that level of effort when they already know what the result will be.

If our ears are not equipped to detect the harmonic frequencies you are talking about (and they are not), they cannot transmit the existence of them to the brain. If there is no signal to the brain it can't reconstruct the missing frequency from the harmonics that it knows nothing about.

And this is apart from the information provided in the other thread that the "missing subharmonic perception" only occours at low frequencies due to the different way the ears/brain detect lower frequencies.


EDIT: Ninja'd by @Geert

 

[Sokel]

A decent hi-fi microphone will measure that. A lot of tweeters get "creative" when fed ultrasonics, especially at high levels, and generate beat notes.

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.

 

[lashto]

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. Do you really expect someone to waste his time on testing this basic logic without any reason to believe it's flawed, for a lousy 50€? You should Google Brandolini's law.

Nice law. You can ~similarly apply Russel's teapot too.

It's just that I am not convinced about that missingF theory you posted. Neither by others posted in the original thread. Some pretty good ones, but none goes 100%. IMO, the missingF effect is not that well known.

Anyway, I'd like to see a direct test. Guess you don't, good for you...

 

[fpitas]

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'm not sure you need to measure the ultrasonics, but for a good test it sure would be nice. I was just thinking of measuring the inevitable intermod at 15kHz. Obviously, hearing real intermod would not be an Earth-shaking conclusion

 

[lashto]

Your test proposal is decidedly non trivial. Apart from the difficulty you've pointed out of sourcing kit that can do it, It is not just a case of sending some ultrasonics through that kit and then listening - you are talking about subjective perception results, so to have any validity it will have to involve blinding, and multiple test subjects, training of them etc etc. An exceptionally high effort undertaking.

No-one is going to go to that level of effort when they already know what the result will be.
...

fully agree with this part.

The chances for anyone to try it are quite slim. And even much lower for a proper test.
I did put it out there and offered the 'bet'. It does not look like I can do more...

 

[antcollinet]

Anyway, I'd like to see a direct test...

You're going to have to set it up then.

 

[fpitas]

fully agree with this part.

The chances for anyone to try it are quite slim. And even much lower for a proper test.
I did put it out there and offered the 'bet'. It does not look like I can do more...

Not to be facetious, but...you could do it yourself?

 

[lashto]

Not to be facetious, but...you could do it yourself?

Surely want to.
Read the spoiler and see how many things/props I am missing. Missing some answers too, particularly the IMD vs missingF question might be a showstopper

Any suggestions, highly welcome...

 

[fpitas]

Want to. Read the spoiler and see how many things/props I am missing. Missing some answers too
Any suggestions, highly welcome...

The main thing is to measure for audible content coming from the tweeter. Obviously if it's there, the test is invalid.

 

[Julf]

It's just that I am not convinced about that missingF theory you posted. Neither by others posted in the original thread. Some pretty good ones, but none goes 100%. IMO, the missingF effect is not that well known.

It is quite well known among music perception researchers.

 

[fpitas]

It is quite well known among music perception researchers.

Yes, at bass frequencies from tiny woofers it's the norm.

 

[Julf]

• transducers that can play 50+kHz are needed.

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.

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

Indeed.

 

[Julf]

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?

"Amateurs"?

 

[fpitas]

"Amateurs"?

It does seem rather rude...