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Missing fundamental for a 15kHz signal - audible or not?
- Thread starter lashto
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Solid interpretation.
Here's how I see it.
my counter experiment: the H information enters the ear/skull/brain. It is not perceived as audible (because of noise masking), but the brain(?) processes it into an audible missingF.
the 15kHz missingF experiment: the H information enters the ear/skull/brain. It is not perceived as audible (because freq too high) but might still be processed into an audible missingF
anyway, I stated already that I won't take logic/arguments as sure proof. Neither mine, nor yours nor anyone else's
So ... direct test or it stays "undecided" (at least for me)
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Creating the signal is a piece of cake any number of ways. Here's an alternative. Take the low frequency signals maybe even a recording of a real instrument. Notch out the fundamental. Speed up the file in Audacity until only the fundamental would be below 20 khz. Doing all this at 192 khz for instance.
Now all you need is the adequate playback rig. Get an old Spectral amp. They had response to 1 mhz. Hard part will be a speaker. To reduce IMD, feed each harmonic separately to its own tweeter. Now how all this could possibly create the missing fundamental in an instrument that responds to nothing in the sound (the ear) is a heck of a magic trick.
I do think you need 2 harmonics. The missing tone is usually woofers, and they mainly Distort with 2nd and 3rd harmonics.
Now all you need is the adequate playback rig. Get an old Spectral amp. They had response to 1 mhz. Hard part will be a speaker. To reduce IMD, feed each harmonic separately to its own tweeter. Now how all this could possibly create the missing fundamental in an instrument that responds to nothing in the sound (the ear) is a heck of a magic trick.
I do think you need 2 harmonics. The missing tone is usually woofers, and they mainly Distort with 2nd and 3rd harmonics.
I have shamelessly stolen that !
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Also I seem to recall the reason missing fundamentals happen in low frequencies is the ears ERB is wide enough the harmonic happens in the same ERB band. Such is not remotely true at higher frequencies. But op has already said he's not listening to logic.
@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.
View attachment 263600
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Option 2
@pkane, tagged to make sure I'm doing this correctly.
Get Distort
Distort audibility tester | Distort documentation
distortaudio.org
Make a 11 kHz test tone
View attachment 263610
Add a big 2nd Harmonic. No surprises.
View attachment 263614
Add a big 3rd harmonic. There is a new IMD band in the audible range.
View attachment 263616
Add a big 4th harmonic. Now the IMD drops lower than 11 kHz
View attachment 263617
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, haven't followed this discussion and am a little lost as to what you're trying to do...
I have chosena 11 kHz tone and asked Distort to add a really high 2nd/3rd/4th order harmonic (presumably at 22 kHz, 33 kHz and 44 kHz).
A huge amount of IMD gets generated at lower values such as ~ 4 kHz when I do that..
This generation of spurious tones also seems to happen when I generate test tones inside of Audacity with 4 distinct tracks of 11, 22,33, and 44 kHz test tones which are then added.
@pkane
a) Is the resultant tone at 4 kHz an error in the way Distort is generating a 11/22/33/44 kHz test tone or doing its FFT?
b) Is the resultant tone at 4 kHz the actual mathematical result from adding those 4 frequencies together?
Thanks. That would be my interpretation too. An easy win would've been nice though
@GXAlan please post that 22/33/44kHz file. I'll try to figure out a playback chain capable of playing it.
I would suggest additional test tones for a positive proof of the "Missing Fundamental", since not all people perceive it:
So, additional test tones are needed for, for example, a fundamental at 2kHz. If the "Missing Fundamental" is perceived by the subject (with 2kHz fundamental), the actual experiment can begin.
To play the test tones, any tweeter can be used that has a reasonably linear frequency response up to 40kHz.
Spontaneously, I can only think of the SB21RDC-C000-4:
This should not be a big problem, since the harmonics only produce multiples of themselves again as IMD.
This leaves 22, 33 and 44kHz to generate the 11kHz fundamental as IMD:
IMD2: f2-f1, f1+f2
IMD3: 2*f1-f2, 2*f1+f2, 2*f2-f1, 2*f2+f1
IMD4: 3*f1 +- f2, 3*f2 +- f1
...
If you look at the possible combinations, IMD for the 11kHz fundamental is created from IMD2, IMD3. If the sound pressure of the IMD remains low at 11kHz, it should be inaudible - can be checked by measurement.
All frequencies below 11kHz can be suppressed by an appropriate high pass.
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It would be a computational error, maybe to high amplitude and clipped samples. Would you post the wav file?
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I've just generated these in Audacity and no other tones are produced. Each tone was at an amplitude of .2 out of 1.o. The combination of them gave a level of -6 db.
And of course with any distortion you'll generate IMD products.
> a) Is the resultant tone at 4 kHz an error in the way Distort is generating a 11/22/33/44 kHz test tone or doing its FFT?
The FFT has nothing to do with it. The non-linearity that's generated by specifying harmonics in DISTORT is computed in time domain, the result is then plotted using FFT, just like any distorted measurement would be when analyzing it.
b) Is the resultant tone at 4 kHz the actual mathematical result from adding those 4 frequencies together?
You have harmonics specified at 0dB, that's a very severe non-linearity. You can see the transfer function if you turn it on above the plot. Should be a straight diagonal line from -1,-1 to +1,+1:
@lashto
Before I post it, I want to make sure that we're generating the correct files. Based upon both Audacity and Distort, the simple act of generating 22,33,and 44 kHz tones leads to mathematical harmonics in the single digit kHz range.
I wanted to have a "carrier" 11 kHz -- but you don't even need that.
If this happens with the math, then the electrical signal is being asked play 22/33/44 and the resulting signal has 1 kHz tones...
That is, with 3 tracks I have this. The 3 individual signals are shown
Merge it to 192 or 384 kHz single file, and it *looks* and *sounds* like this
Export it to 358 kHz and you get this:
The question originated
1) we know that you can fake extra bass by playing frequencies at the harmonics where the bass "should have been."
2) we wondered if you took a 22 kHz sine wave (which no one can hear), a 33 kHz sine wave (which no one can hear), and then a 44 kHz sine wave (which no one can hear) and then put all 3 together, would you hear something?
And it seems like the software that isn't professional is generating a lot of IMD? PMA is able to combine those files without any issues?
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@pma, can you generate a file with no 11 kHz -- just 22/33/44?
@pkane and @pma
Does this have any implications for real-world DACs? If you feed it 22/33/44 could they generate the same problems we see with the software tools?
Before I post it, I want to make sure that we're generating the correct files. Based upon both Audacity and Distort, the simple act of generating 22,33,and 44 kHz tones leads to mathematical harmonics in the single digit kHz range.
I wanted to have a "carrier" 11 kHz -- but you don't even need that.
If this happens with the math, then the electrical signal is being asked play 22/33/44 and the resulting signal has 1 kHz tones...
That is, with 3 tracks I have this. The 3 individual signals are shown
Merge it to 192 or 384 kHz single file, and it *looks* and *sounds* like this
Export it to 358 kHz and you get this:
I'm not actually trying to test the missing fundamental with actual expected harmonics.
The question originated
1) we know that you can fake extra bass by playing frequencies at the harmonics where the bass "should have been."
2) we wondered if you took a 22 kHz sine wave (which no one can hear), a 33 kHz sine wave (which no one can hear), and then a 44 kHz sine wave (which no one can hear) and then put all 3 together, would you hear something?
And it seems like the software that isn't professional is generating a lot of IMD? PMA is able to combine those files without any issues?
--------
@pma, can you generate a file with no 11 kHz -- just 22/33/44?
@pkane and @pma
Does this have any implications for real-world DACs? If you feed it 22/33/44 could they generate the same problems we see with the software tools?
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I've just done the same thing in Audacity and get a clean result like PMA. Even if exporting to different sample rates. Do you have dithering turned off?
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Last edited:
The spectrum you show is wrong. Even then inaudible. You guys play with fire and can destroy your ears by ultrasound if you turn volume up. Bye (from this thread).
I'm afraid I'm still lost and don't have the time now to follow the conversation. What you did with DISTORT is create a huge non-linearity and pass a single tone through it, not add three tones together. If you want to just add three frequencies, use Multitone to generate this. Use this as your test signal:
Test 11k/33k/44k 1:1:1
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