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

Julf

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I do the OP suddenly went missing in action once it was shown that he lost the bet and was asked to pay up.
 

fpitas

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I do the OP suddenly went missing in action once it was shown that he lost the bet and was asked to pay up.
I am shocked.
 

ctrl

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Addendum: We could have saved ourselves a lot of work and discussion if we had contacted an AI right away - we are so screwed! ;)


Are there studies about the maximal frequency humans can hear the "missing fundamental"?

Yes, there have been studies conducted to investigate the maximum frequency at which humans can perceive the missing fundamental. These studies have found that the upper limit for the perception of missing fundamental frequency varies between individuals and can depend on factors such as age, hearing health, and musical training.

One study published in the Journal of the Acoustical Society of America found that the upper limit for the perception of missing fundamental frequency ranged from 110 Hz to 320 Hz among a group of musically trained participants. Another study published in the same journal found that the upper limit for the perception of missing fundamental frequency was around 150 Hz for non-musicians and around 200 Hz for musicians.

Overall, the upper limit for the perception of missing fundamental frequency appears to be in the range of several hundred hertz. However, it is important to note that the ability to perceive the missing fundamental frequency is influenced by many factors, and the upper limit may vary widely between individuals.

Can you list the sources?

Sure, here are the sources for the studies I mentioned:
  • McAdams, S., & Bregman, A. S. (1979). Hearing musical streams. Psychological Review, 86(5), 416– 429. https://doi.org/10.1037/0033-295X.86.5.416
  • Risset, J. C., & Wessel, D. L. (1969). Exploration of timbre by analysis and synthesis. In A. V. Luca (Ed.), Reports of the 1969 Institute for Perception (pp. 122–129). Eindhoven: Eindhoven University of Technology.
  • Terhardt, E. (1974). Pitch, consonance, and harmony. Journal of the Acoustical Society of America, 55(5), 1061–1069. https://doi.org/10.1121/1.1914648
  • Warren, R. M. (1970). Perceptual restoration of missing speech sounds. Science, 167(3917), 392–393. https://doi.org/10.1126/science.167.3917.392

But we should keep in mind that AI's sometimes misinterpret data, so to check the quality of the answers, a question from which we already know the answer:


Are there studies about the minimal number of harmonics required to hear the missing fundamental?

Yes, there have been studies conducted to investigate the minimal number of harmonics required to hear the missing fundamental. These studies have found that the number of harmonics needed to perceive the missing fundamental depends on the individual's auditory system and the spectral content of the sound.

One study published in the Journal of the Acoustical Society of America found that, on average, at least three harmonics were needed to perceive the missing fundamental. However, some participants were able to perceive the missing fundamental with just two harmonics, while others required four or more.

Another study published in the same journal found that the minimum number of harmonics needed to perceive the missing fundamental depended on the spectral composition of the sound. For example, for a sound consisting of only odd harmonics, as in a square wave, participants were able to perceive the missing fundamental with just two harmonics. However, for a sound consisting of both odd and even harmonics, as in a sawtooth wave, participants required at least three or four harmonics to perceive the missing fundamental.

Overall, the minimum number of harmonics required to perceive the missing fundamental varies between individuals and depends on the spectral content of the sound. However, on average, at least three harmonics are needed for the brain to reconstruct the missing fundamental.

Can you list the sources?

Certainly! Here are some sources for the studies I mentioned:
  • Shinn-Cunningham, B. G. (2008). Perception of missing fundamental pitch by non-human animals. In C. J. Plack, R. R. Fay, & A. N. Popper (Eds.), Pitch: Neural coding and perception (pp. 292-315). Springer Science+Business Media. https://doi.org/10.1007/978-0-387-76700-7_11
  • Stecker, G. C., & Hafter, E. R. (2002). An effect of temporal asymmetry on the perception of the missing fundamental. Journal of the Acoustical Society of America, 112(6), 2924–2932. https://doi.org/10.1121/1.1517436
  • Terhardt, E. (1974). Pitch, consonance, and harmony. Journal of the Acoustical Society of America, 55(5), 1061–1069. https://doi.org/10.1121/1.1914648
  • Plack, C. J. (1995). The missing fundamental in the presence of multiple spectral components. Journal of the Acoustical Society of America, 98(2 Pt 1), 742–753. https://doi.org/10.1121/1.413270
 

fpitas

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Addendum: We could have saved ourselves a lot of work and discussion if we had contacted an AI right away - we are so screwed! ;)
Well...we don't know whether lashto was a bot, or not ;)
 

ctrl

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Well...we don't know whether lashto was a bot, or not ;)
In any case, we know for sure that no one who has posted in this thread so far is an AI.
If only AI's were allowed in this forum, then every discussion would be over after 2-6 posts ;)
 

Cars-N-Cans

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Even for cats the limit is about 6kHz, and this was linked by the OP himself as "proof", evidently not reading the paper beforehand. No need for AI when one's own shoe in mouth will suffice :p

Given that cats can hear up to almost 100kHz yet still struggle at only modest frequencies, I would think the argument would end there. There is also the fact that you don't just stop hearing above around 20-22kHz, your hearing likely becomes undefined, so there wouldn't be much more than just being aware of the presence of ultrasonics if something like some form of bone conduction could be used for direct stimulation. Listening to a linear frequency sweep makes this quite evident in that the perceived pitch gets quite asymptotic by the time it starts closing in on 20kHz. This makes sense since there is only a limited range of bandwidth, so its only logical to utilize as much of it as possible, not to mention all the other inherent limitations.
 

fpitas

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We're being a little rash. Lashto might be a cat or dog, for all we know. He hasn't said he's human.
 

Cars-N-Cans

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There is probably more nuance to be had in a detailed reading, but its clear even if Lashto is a feline, he won't be having much more luck than us in hearing it :rolleyes: Edit: This is for the center frequencies of the tone triads used, so the 6 kHz center probably only corresponds to a missing fundamental of around 1.5-2kHz.
 
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danadam

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Whats a missing fundamental?
There already was a video posted a few times which explains it quite well: www.youtube.com/watch?v=AZ8qZCGg4Bk

It's a perception of pitch that is lower than any component of the signal.
If we remove the fundamental from a bass guitar by playing a regular guitar why does it not sound like a bass?
Because notes on the bass guitar are one octave lower than on the guitar, so even if we remove the fundamental the remaining harmonics will be entirely different:
  • low E on bass: 41.2, 82.4, 123.6, 164.8, 206.0, ...
  • low E on guitar: 82.4, 164.8, 247.2, ...
When we remove the fundamental from the bass, we still have 123.6 and 206.0 harmonics, which are not present on the guitar when playing E.
Do you hear a difference when you use a sharp highpass on a single note of a bass to get rid of the fundamental?
If the gear was able to reproduce that fundamental, then yes.

What prompted this question? Did anyone say that there is no difference?
 

Geert

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Addendum: We could have saved ourselves a lot of work and discussion if we had contacted an AI right away - we are so screwed!

Not realy as the OP repeatedly stated any form of logic and intelligence was not accepted (could not be trusted), he wanted to see a test.

So we were already screwed from the start. Sorry for the people who have spent time on this science fiction experiment.
 

Geert

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The OP has been (fundamentally) missing in action for 1 week now. Should we notify someone?
 
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fpitas

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Julf

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The OP has been missing in action for 1 week now. Should we notify someone?
Coast guard? Air force (in case he was hanging from a balloon)?
 

fpitas

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Clearly he’s the missing fundamental. The whole thread has been performance art. :)
The payout is also fundamentally non-existent. No one saw that coming :facepalm:
 

weesch

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in my country france a policeman hit me in the face at my house doorstep and now i have tinnitus in my left ear around 8000 hz i am trying to re-educate my ear with this software
which allows to hear frequencies and for me I always hear something at 16000 hz
try it to see what you hear...
post criptum: never come to france for the holidays the police are bandits and the bandits are the police!
best regards
weesch
 
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lashto

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The OP has been (fundamentally) missing in action for 1 week now.

that was more like 1 year of asr-free life :). Even forgot about this thing...

Not realy as the OP repeatedly stated any form of logic and intelligence was not accepted (could not be trusted), he wanted to see a test.
it's the same rule as ~everywhere else on ASR: DBT or it did not happen. And everyone is free to like/dislike it.

Addendum: We could have saved ourselves a lot of work and discussion if we had contacted an AI right away - we are so screwed! ;)


Are there studies about the maximal frequency humans can hear the "missing fundamental"?

...


Are there studies about the minimal number of harmonics required to hear the missing fundamental?
...
interesting links, I'll just need some time to read. And to dig-up the references/studies which were the base of this thread/question... AFAIR, there were some very diff oppinions about that "maximal frequency" and much higher numbers in the most recent studies.

Also AFAIR, the "minimal number of harmonics" was cleared with study citations in one of my posts. Pretty much same as you found: 4+ are needed (particularly important for a not-audible proof)
 

dasdoing

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missing fundamental is just a myth. whenever I ask people who hear "it" if they really hear the deep tone, they negate it.
what really is happening is that the first harmonic usually is dominant because of equal loudness contours. So you can remove the fundamental and the timbre kind of stays the same....kind of.
 
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lashto

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missing fundamental is just a myth. whenever I ask people who hear "it" if they really hear the deep tone, they negate it.
what really is happening is that the first harmonic usually is dominant because of equal loudness contours. So you can remove the fundamental and the timbre kind of stays the same....kind of.
according to about "a million" studies, it is not a myth :). It is actually a very well studied phenomenon, mostly because it's strong connection to our perception of pitch/frequency.

The missingF does not have the same timbre as the original, just the same pitch. And you are right, you do not hear "the deep tone", just a "tinny" version of it:
A harmonic complex is usually perceived as having a “tinny” timbre along with a pitch that is often the same as the fundamental frequency of the complex.
 
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