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

[GXAlan]

For @pma's file

foo_abx 2.1 report
foobar2000 v1.6.12
2023-02-09 12:53:05

File A: 22_33_44.wav
SHA1: 5f36b0023887a9f1a42ec000d89258f4469e1bdc
File B: silence.flac
SHA1: 1c2d6c9cfa08d05537d33c607cc378ece6effd34

Output:
ASIO : KORG 2ch 1bit Audio Device
Crossfading: NO

12:53:05 : Test started.
12:53:32 : 01/01
12:53:48 : 02/02
12:54:08 : 03/03
12:54:14 : 04/04
12:54:23 : 05/05
12:54:32 : 06/06
12:54:37 : 07/07
12:54:43 : 08/08
12:54:49 : 09/09
12:54:54 : 10/10
12:55:00 : 11/11
12:55:05 : 12/12
12:55:11 : 13/13
12:55:17 : 14/14
12:55:31 : 15/15
12:55:35 : 16/16
12:55:35 : Test finished.

----------
Total: 16/16
p-value: 0 (0%)

-- signature --
54ced08743e8b217690dcd3512c817dca49d4a77

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My hearing for test tones is around 16 kHz to 17 KHz for a sine wave.
Setup is Sennheisser HD820 + Korg DS-DAC-10R, max volume.

To be clear, it's something "faint" but it's not silence. I don't hear it as 11 kHz in my brain. It feels like pressure but not a lot -- less than what'd you get when swimming.

Edit: I don't think the DS-DAC-10R is turning anything off when the signal is zero. I'm also not saying that it's worthwhile to get a system that reproduces these ultrasonics.
I'm just saying I've done my part for science and raising money for charity (ASR).

For me, I don't hear a missing fundamental. For me, the presence of inaudible ultrasonics are detectable from digital silence.

I dare not damage my hearing at this point with more testing if it's really playing with fire...

 

[Blumlein 88]

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).

Yes, most tweeters won't take the suggested power for the whole speaker. They expect ultrasonics to be lower level if sustained and usually short lived if high in level. Playing tones at high levels is very dangerous. Now one speaker I wouldn't be worried about are ESLs. Those you can play these high tones without worry. Any conventional tweeter you are living dangerously.

 

[Blumlein 88]

For @pma's file

foo_abx 2.1 report
foobar2000 v1.6.12
2023-02-09 12:53:05

File A: 22_33_44.wav
SHA1: 5f36b0023887a9f1a42ec000d89258f4469e1bdc
File B: silence.flac
SHA1: 1c2d6c9cfa08d05537d33c607cc378ece6effd34

Output:
ASIO : KORG 2ch 1bit Audio Device
Crossfading: NO

12:53:05 : Test started.
12:53:32 : 01/01
12:53:48 : 02/02
12:54:08 : 03/03
12:54:14 : 04/04
12:54:23 : 05/05
12:54:32 : 06/06
12:54:37 : 07/07
12:54:43 : 08/08
12:54:49 : 09/09
12:54:54 : 10/10
12:55:00 : 11/11
12:55:05 : 12/12
12:55:11 : 13/13
12:55:17 : 14/14
12:55:31 : 15/15
12:55:35 : 16/16
12:55:35 : Test finished.

----------
Total: 16/16
p-value: 0 (0%)

-- signature --
54ced08743e8b217690dcd3512c817dca49d4a77

------------------------------------------------
My hearing for test tones is around 16 kHz to 17 KHz for a sine wave.
Setup is Sennheisser HD820 + Korg DS-DAC-10R, max volume.

To be clear, it's something "faint" but it's not silence. I don't hear it as 11 kHz in my brain.

And most likely is some IMD from your description.

 

[pma]

And most likely is some IMD from your description.

IMD in headphones or headphone amp or in the ear. He says he plays it at full volume - it is like playing 1kHz sine at full volume! Only that it is inaudible.

 

[Geert]

He says he plays it at full volume

That would indeed not be necessary to perceive a missing fundamental.

 

[GXAlan]

Yes, I agree 100% there is no missing fundamental effect.
==============
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]."

Ear fullness is exactly how I would describe it.

Thankfully, the DS-DAC-10R is probably the same headphone amp as the DS-DAC-100. That means 11 mW peak output into 300 ohms.

Pma's test file appears to be -14 dB.

By the math, 11 mW for 103 dB/1V = 108 dB. That might be for 1 kHz though. The HD820 is -10dB at 48 kHz.

So I was probably anywhere from 84-94 dB of these ultrasonics.

Again, scientific experiment -- conclusion is you don't need to reproduce ultrasonics...

So to answer the original question
"Missing fundamental for a 15kHz signal - audible or not?"

The answer is that for a 11 kHz signal, it is *detectable* but not *audible* with my ears and equipment.

 

[ctrl]

This should not be a big problem, since the harmonics only produce multiples of themselves again as IMD.

There is a problem after all ...- of course there is!

I measured the test tone from @pma (22-33-44.zip) and internally with "two sine" from Arta (22kHz and 33kHz) with two different tweeters (SB21RDC and Fountek Neo CD1.0) and in all cases a severe IMD signal was generated at 11kHz:
Neo CD 1.0

SD21RDC

This would give the test a false positive result, as the 11kHz IMD tone would certainly be audible.

Not sure if it's the tweeter, amplifier, microphone, W10 or the audio interface or some combination. The IMD at 11kHz is lower with the SB21RDC.

 

[GXAlan]

This would give the test a false positive result, as the 11kHz IMD tone would certainly be audible.

Not sure if it's the tweeter, amplifier, microphone, W10 or the audio interface or some combination. The IMD at 11kHz is lower with the SB21RDC.

But doesn’t this suggest that there are some playback systems that introduce IMD?

I definitely did NOT hear 11 kHz with PMA’s generated file even though Audacity’s has all sorts of problems with IMD

 

[ctrl]

But doesn’t this suggest that there are some playback systems that introduce IMD?

Yes my guess is that the integrated amplifier generating the test tones could be the problem - it's an old Marantz PM7001.
Will use my Hypex plate amp for signal generation later.

 

[Sokel]

Yes my guess is that the integrated amplifier generating the test tones could be the problem - it's an old Marantz PM7001.
Will use my Hypex plate amp for signal generation later.

It shows similar to a simple loopback thought

(check my settings,I'm never sure!):

 

[Blumlein 88]

But doesn’t this suggest that there are some playback systems that introduce IMD?

I definitely did NOT hear 11 kHz with PMA’s generated file even though Audacity’s has all sorts of problems with IMD

More than one of us has done the files in Audacity and it does NOT have problems with IMD. Not sure what you are doing to get IMD like that, but do I need to post screenshots and files showing Audacity is not an issue?

 

[GXAlan]

Smarter people can weigh in. @pma?

What if you had “bad” negative feedback on an amp? Would that increase the likelihood of IMD in these scenarios? I have always understood that the reason to have silly bandwidth for amplifiers to get to 100 kHz is to be neutral to 20 kHz.

 

[Blumlein 88]

Smarter people can weigh in. @pma?

What if you had “bad” negative feedback on an amp? Would that increase the likelihood of IMD in these scenarios? I have always understood that the reason to have silly bandwidth for amplifiers to get to 100 kHz is to be neutral to 20 kHz.

An amp with 1st order roll offs would be -3 db at 200 khz in order to be only -.1 db at 20 khz. IMD is a result of the same non-linearity that causes THD. So if feedback caused an amp to have rising distortion at higher frequencies it would also have higher IMD.

 

[ctrl]

Update2: A refined attempt at audibility of missing fundamental with an 8kHz fundamental can be found in post#243.

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):

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):



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:

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).

 

[tmtomh]

FFS, just get a cheap ultrasonic cleaner or weight-loss cavitation machine, or a similar consumer appliance that uses frequencies in the low(ish) ultrasonic range. They operate at 30-60kHz. Turn them on and see if you hear a 15kHz tone, or anything similar, that's not produced by coil whine or some mechanical or other aspect of the unit's operation. (Spoiler alert: you won't.)

 

[Blumlein 88]

If some would watch the video link I posted a few posts back it would make it easy to visualize. They show the waveforms of combined tones and why the missing fundamental would be found by the ear. So without the ear having the harmonics there is no missing fundamental heard. One part of the video even shows how one harmonic in the right ratio can supply a missing fundamental below those harmonicaly related to the initial fundamental tone.

 

[antcollinet]

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

It is not percieved as audible BECAUSE IT IS NOT AUDIBLE. The ear has no mechanism to detect those frequencies. Look into how the cochlear works - it deconstructs signals into the frequency domain. Different parts of the cochlear detect different frequencies and send nerve impulses to the brain when they are detected. There are no parts of the cochlear sensitive to frequencies above 20Khz - no detection - no signal to the brain - nothing to be processed.

 

[ctrl]

Updated post#74.

 

[Thomas_A]

Was I long time since I read and tested, but how high up in frequency of the two combination frequencies can you detect Tartini tones?

 

[pkane]

IMD is a result of the same non-linearity that causes THD.

Right. All analog devices generate IMD, simply because none are perfectly linear. Transducers are not linear. The ear is not linear. The air is not linear. All generate IMD to various degrees. @GXAlan tried to use DISTORT to generate ultrasonic signals, except, instead, he created an extremely large, IMD-producing non-linearity (i.e., a huge distortion engine).

Let's do something a bit more realistic. Let's take the 22k/33k/44k test signal and pass it through a reasonably non-linear device simulation, such as the Rotel amp Amir reviewed recently.

First, let's approximate the distortion/nonlinearity of that amp in DISTORT (I added harmonics and mains noise, as well as a little close-in jitter):

Amir's measurement, for comparison:

Next, produce the "pure" three-tone test signal (generated by Multitone):

And now pass this pure signal through the IMD-generating non-linearity, simulating Rotel RB-1070 amp. This should be approximately what the output of the amp should look like with the input signal of 22k/33k/44k:

Cool. So the 11kHz IMD product will be at about -94dB or so relative to the amplitude of the three tones. Mostly inaudible.

DISTORT Harmonics simulating Rotel amp: