jawen, Arez
It is audible. Music at 70 dB has peaks that reach 10-15 dB over that. I believe that IMD would be higher than THD when playing notes f.ex. 22 Hz and 233 Hz at the same time.
It is audible. Music at 70 dB has peaks that reach 10-15 dB over that. I believe that IMD would be higher than THD when playing notes f.ex. 22 Hz and 233 Hz at the same time.
I think that a note playing at 40 Hz would have a 2nd harmonic that is easier to detect at 80 Hz because of equal loudness?
Yes, exactly, this is what Monte wrote in 2008, at the link I attached to his design:
He writes:
"While it is widely accepted in the industry that non linear distortion at low frequency is not particularly audible I am convinced that it is audible. In fact I believe that non linear distortion is the most audible at low frequency. One look at the equal loudness curves of human hearing should convince anyone that non linear distortion is least audible above about 3 KHz and most audible below 3 KHz. Above about 10 KHz it should be completely inaudible because the 2nd harmonic is exceeding the human hearing range. At 20 Hz the human ear will hear an equal level 40 Hz tone as 20 dB louder based on a 90 dB reference level. This means the 40 Hz harmonic must be 20 dB below the 20 Hz fundamental just to sound as if it is the same level or 100% 2nd harmonic distortion.
It's very difficult to achieve low distortion at frequencies in the 20 Hz range. Consequently I wonder how test were conducted to produce the widely held belief that distortion is inaudible at low frequency?
Since most woofers produce at least 10% distortion at 20 Hz which sounds like 100% distortion at the 2nd and far higher at the 3rd, they have no clean reference to determine if induced distortion is audible. The test platform is starting with too much distortion to begin with for anyone to assess that an induced distortion is or is not audible. ...
[this is a graph] "for the distortion performance at 18 Hz with a 2.83 volt per woofer input. This measurement was made at the center of the center row with both woofer columns playing but with only two of three modules. The third modules have not yet been installed. The SPL meter was reading 103 dB for this measurement
Note that the 2nd harmonic is more than 41 dB below the 18 Hz fundamental. This is less than 1% distortion which will sound like about 10% due to the human hearing curve. The 3rd harmonic is about 36 dB below the fundamental which is about 1.5% distortion. This will sound like about 100% since at this frequency the human ear hears 54 Hz tone about 35 dB louder than the 18 Hz fundamental.
Clearly it's still not good enough! In order for the 3rd to sound like it is 1% it would need to be about 75 dB below the fundamental. We're going to need a new technology to accomplish this and to finally have a clean reference adequate for induced distortion test to finally determine if distortion at low frequency is or is not audible."
bold: my emphasis
Monte moved onto a different ultra-low-frequency approach :
https://www.mfk-projects.com/ULF/ulf.html, which aimed at even lower distortion. But I don't know if it was every completed or if it was ever measured.
Now, without major changes to the structure of one's home, in 2025, there's a few ways different ways to achieve very low bass distortion.
But like Monte, I agree that to determine if bass distortion doesn't matter, you actually have to have a low distortion bass reference.
eg. 20Hz at 90dB with H3 at -60dB = 60 Hz at 30dB, but sounding like 65dB to the human ear?
Can anyone point me to some data that shows 20Hz at 90dB with H3 of <-60dB, and suggesting that there's no audible difference to 20Hz at 90dB with H3 of -15dB (~18%), as permitted by CEA2010, CTA2034A etc)?
He writes:
"While it is widely accepted in the industry that non linear distortion at low frequency is not particularly audible I am convinced that it is audible. In fact I believe that non linear distortion is the most audible at low frequency. One look at the equal loudness curves of human hearing should convince anyone that non linear distortion is least audible above about 3 KHz and most audible below 3 KHz. Above about 10 KHz it should be completely inaudible because the 2nd harmonic is exceeding the human hearing range. At 20 Hz the human ear will hear an equal level 40 Hz tone as 20 dB louder based on a 90 dB reference level. This means the 40 Hz harmonic must be 20 dB below the 20 Hz fundamental just to sound as if it is the same level or 100% 2nd harmonic distortion.
It's very difficult to achieve low distortion at frequencies in the 20 Hz range. Consequently I wonder how test were conducted to produce the widely held belief that distortion is inaudible at low frequency?
Since most woofers produce at least 10% distortion at 20 Hz which sounds like 100% distortion at the 2nd and far higher at the 3rd, they have no clean reference to determine if induced distortion is audible. The test platform is starting with too much distortion to begin with for anyone to assess that an induced distortion is or is not audible. ...
[this is a graph] "for the distortion performance at 18 Hz with a 2.83 volt per woofer input. This measurement was made at the center of the center row with both woofer columns playing but with only two of three modules. The third modules have not yet been installed. The SPL meter was reading 103 dB for this measurement
Note that the 2nd harmonic is more than 41 dB below the 18 Hz fundamental. This is less than 1% distortion which will sound like about 10% due to the human hearing curve. The 3rd harmonic is about 36 dB below the fundamental which is about 1.5% distortion. This will sound like about 100% since at this frequency the human ear hears 54 Hz tone about 35 dB louder than the 18 Hz fundamental.
Clearly it's still not good enough! In order for the 3rd to sound like it is 1% it would need to be about 75 dB below the fundamental. We're going to need a new technology to accomplish this and to finally have a clean reference adequate for induced distortion test to finally determine if distortion at low frequency is or is not audible."
bold: my emphasis
Monte moved onto a different ultra-low-frequency approach :
https://www.mfk-projects.com/ULF/ulf.html, which aimed at even lower distortion. But I don't know if it was every completed or if it was ever measured.
Now, without major changes to the structure of one's home, in 2025, there's a few ways different ways to achieve very low bass distortion.
But like Monte, I agree that to determine if bass distortion doesn't matter, you actually have to have a low distortion bass reference.
eg. 20Hz at 90dB with H3 at -60dB = 60 Hz at 30dB, but sounding like 65dB to the human ear?
Can anyone point me to some data that shows 20Hz at 90dB with H3 of <-60dB, and suggesting that there's no audible difference to 20Hz at 90dB with H3 of -15dB (~18%), as permitted by CEA2010, CTA2034A etc)?
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In a related question, how do we know how low in frequency human hearing extends... conventional wisdom is that it extends down to 20 Hz. But those tests would have used sound sources (i.e. large woofers) with significant harmonic distortion, because that was all that was available at the time. So the test subjects were reporting on the audibility of a 20 Hz tone plus a lot of harmonic content, and maybe what they were perceiving was the harmonic content...?
Excellent question @hifijim
The closest answer I've been able to verify for myself is this:
1) Visit Stéphane's excellent Audiocheck website and look for Harmonic Distortion Test:
Stéphane says do don't need an excellent pair of headphones for measuring at 125Hz. So I just borrowed a pair of my spouse's. Luckily we have some data from ASR:
As you can see- at 125Hz ~98dB, THD is almost -70dB down - ie. 0.03% H3
Reference for harmonic calculator: https://sengpielaudio.com/calculator-thd.htm
Confirming what Stephane says: "Good headphones should add less than 0.05% THD (at 125Hz)"
But how to test at 20Hz, at 90dB at the ear, without a headphone test fixture?
We need to DIY a little... to verify what 90dB from your headphones/earphones, put it up right against your handy little smartphone. Mics that go into iPhones ARE calibrated for SPL, thank you @IamJF and accurate enough to conform to Class 2 Sound Level Meter standards.
Now you load up your favorite test suite, whether it be ARTA/STEPS or REW and start playing some test tones at 20Hz. Virtually all DACs + amps that you can connect your ear/headphones in C21 have no problems with H2/H3 < -60dB at 20Hz.
If you don't know if your ear/headphones have known low H2/ H3 performance,
eg. that is -80dB THD at 20Hz @90dB, there are available in 2025 and quite inexpensive.
Here's one:
Stéphane's own recommendation is even cheaper, the KZ ZST.
I haven't verified the KZ ZST myself. But he knows what he's doing
PS. In-ear monitors evolved from the medical industry, so they were THE reference for conducting hearing loss of pure sine waves test tones...
The closest answer I've been able to verify for myself is this:
1) Visit Stéphane's excellent Audiocheck website and look for Harmonic Distortion Test:
Stéphane says do don't need an excellent pair of headphones for measuring at 125Hz. So I just borrowed a pair of my spouse's. Luckily we have some data from ASR:
As you can see- at 125Hz ~98dB, THD is almost -70dB down - ie. 0.03% H3
Reference for harmonic calculator: https://sengpielaudio.com/calculator-thd.htm
Confirming what Stephane says: "Good headphones should add less than 0.05% THD (at 125Hz)"
But how to test at 20Hz, at 90dB at the ear, without a headphone test fixture?
We need to DIY a little... to verify what 90dB from your headphones/earphones, put it up right against your handy little smartphone. Mics that go into iPhones ARE calibrated for SPL, thank you @IamJF and accurate enough to conform to Class 2 Sound Level Meter standards.
Reference: https://www.cdc.gov/niosh/noise/about/app.html
Other phones have mics from suppliers that may not calibrate for the phone OEM, so there may be a little variation.
Now you load up your favorite test suite, whether it be ARTA/STEPS or REW and start playing some test tones at 20Hz. Virtually all DACs + amps that you can connect your ear/headphones in C21 have no problems with H2/H3 < -60dB at 20Hz.
If you don't know if your ear/headphones have known low H2/ H3 performance,
eg. that is -80dB THD at 20Hz @90dB, there are available in 2025 and quite inexpensive.
Here's one:
Stéphane's own recommendation is even cheaper, the KZ ZST.
I haven't verified the KZ ZST myself. But he knows what he's doing
PS. In-ear monitors evolved from the medical industry, so they were THE reference for conducting hearing loss of pure sine waves test tones...
Reference:
https://etymotic.com/about/
Product:
https://etymotic.com/auditory-research-assessments/
https://etymotic.com/about/
Product:
https://etymotic.com/auditory-research-assessments/
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Sorry if it was asked earlier, how does it compare with the RSS315HF/HO, which is only a bit more expensive?
No idea. I've not measured it.
My hypothesis is that because they are similar- similar volume displacement, similar motors (dual alu shorting rings) similar suspension systems eg. 12-14mm x-max, they may measure similarly to the 835017.
At some frequencies a little better, at others a little worse. But within <6dB difference. Mind you, 6dB is a lot.
Here's Purifi's best, in 2025.
See that? A 10" woofer, 20Hz at about 67dB, H2 is ~-34dB, H3 is ~-40dB
It's still a couple of magnitudes below the headphones that can muster
20Hz at 90dB, -80dB H2/H3
Purifi has the much better suspension system (neutral Sd(x) surround) and a much better motor (variable winding voice coil for neutral Bl(x) and a massive copper sleeve for neutral Le(x).
But for an larger eg. 10+ dB improvement for a single woofer, they need a much bigger cone area. Part of the problem itself is air...
The other solution system implementations eg. double reverse invert/vented/band-pass/tapped horn/current drive... a system designer consider everything at her disposal, but that's beyond the scope of this post.
My hypothesis is that because they are similar- similar volume displacement, similar motors (dual alu shorting rings) similar suspension systems eg. 12-14mm x-max, they may measure similarly to the 835017.
At some frequencies a little better, at others a little worse. But within <6dB difference. Mind you, 6dB is a lot.
Here's Purifi's best, in 2025.
See that? A 10" woofer, 20Hz at about 67dB, H2 is ~-34dB, H3 is ~-40dB
Reference: PTT10.0X-04NAB-01 datasheet
It's still a couple of magnitudes below the headphones that can muster
20Hz at 90dB, -80dB H2/H3
Purifi has the much better suspension system (neutral Sd(x) surround) and a much better motor (variable winding voice coil for neutral Bl(x) and a massive copper sleeve for neutral Le(x).
But for an larger eg. 10+ dB improvement for a single woofer, they need a much bigger cone area. Part of the problem itself is air...
The other solution system implementations eg. double reverse invert/vented/band-pass/tapped horn/current drive... a system designer consider everything at her disposal, but that's beyond the scope of this post.
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Appendix: impedance sweep attachments-
Single woofer in 28L sealed box with fiberglass fill (includes TSP parameters)Dual Subwoofer in 100L sealed box with fiberglass fill
Dual Subwoofer Reverse Inverted in 100L sealed box with fiberglass fill & DSRI + 20ohms series resistor to mimic current drive.
With particular thanks to @5th element , @DcibeL, @Juhazi , @lrisbo and Michael Zrull for discussions re: Sd modulation and soft parts non linearity, dual subwoofer reverse inverted, and current drive above 2x Fs/Fb.
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Yes, indeed, why... ?
Maybe I missed it in all the discussion, but do we have a theory on why the double reverse inverted would make H3 worse than a double standard mount woofer... and worse than a single woofer ?
A good thought. One thing is clear when comparing the two dual woofer configurations, the dual inverse has a definite H2 advantage below 100 Hz, while the dual standard mount has a definite H3 advantage below 100 Hz. It is interesting.
Only those types which can be expected to be consistent across driver variations. For example, Sd(x), Le(i), Le(x) are likely very similar across production batches, but not necessarily BL(x), Kms(x), etc. For those latter, if you can't expect them to be "same enough", running drivers in reverse wouldn't necessarily provide a benefit.
One system approach could be a dual subwoofer reverse inverted, stacked in a way that allows vibration cancellation. It may allow lighter/thinner cabinets. A few (2 or 3) of these scattered about one's room.
Ken did it:
Lay it down such that woofers fire front/rear/left/right.
Each quad stack laid along each wall of the room...
Still smaller and is at least scaleable- build one. Need more? Build another...
Still an easier build than the mighty Zod Audio M.A.U.L (40 cu ft 6th order bandpass/horn sub)
And why so big? ie. 12". Build some to hide under the couch using racetrack/oblong woofers...
I honestly don't think you need "matched" woofers. And no, I'm not going to do dual subwoofer reverse inverted with one 835017 and one 830845 to show that it can work with disparate but similar enough drivers...
... So that's what happened... I noticed your writings became strange and cryptic about a year ago... I was not sure if you were being coy, or if you were enjoying too much alcohol or cannabis or something... Ok so it is good to know that nothing is wrong, you are simply trying to thwart the big AI in the sky.
Resistance is futile, my friend... time to embrace the brave new world...