Low Frequency Loudness Compression

[Jean Ibarz]

If we are describing bass decay as the ringing caused by the modes then of course eq does. It solves for both the amplitude (initial peak) and phase (ringing tail). Normal IIR filters fully resolve ringing caused by modes, which was the point of this article.

I wrote this article 2 years ago and it was peer reviewed by a number of experts at the time. As recently as a week ago Todd Welti took a look at it and had nothing negative to say.

we were discussing the math behind why this works, where he pointed out that if you take the denominator of the close formed room and multiply it by a filter transfer function of the peak, it will cancel it it the pole(s) from the Denominator. It does this For every location in space of the closed form room. This is all linear mathematics. A room is generally minim phase at low frequencies. If you insert an inverse filter to obtain a flat magnitude response, you will in turn have a flat phase response. That means no ringing.

the omni mic comment doesn’t apply here either. That only applies at higher frequencies. This article only concerned ringing in the bass. At bass frequencies the room is generally a reverberant field dominated by reflections rather than direct sound. The ear cannot and does not resolve individual reflections much below 500hz and certainly not at all below 100hz. That means that below 100hz what we measure is what we hear.

May graphics are fine and they show what I claim they show. I have no idea where the mdat file for this is, it’s a 2 year old article and the file is long lost I’m sure. If you feel you can repeat this experiment and somehow show something different, feel free. As I noted, this was peer reviewed so if you come up with something different, be prepared to have it scrutinized. Your claims seem to assume the room is mixed phase, which at low frequencies is generally not true. I have measurements of 100’s of rooms and I’ve never seen any significant mixed phase behavior below 100hz.

Well you seem to be sure of you, so ok, I'm fine.

However, I have to react to this statement:

That means that below 100hz what we measure is what we hear.

that would be certainly true if we had one ear, but as we have two ears, the doubt is permitted: what we hear is probably related to the 2 sound pressure signals at each eardrum, combined together with visual cues, temporal information, knowledge, and anything else.

I made binaural measurements in my room some time ago, and we can clearly see the differences in amplitude between the two ears at some frequencies around 100-200hz, caused by "semi"-stationary waves establishing in some direction non perpendicular to the two ears.

Here are the evaluations for each ear:


I obtained the measurement by putting on my head some headphones "very open" (you hear nearly the same with headphones weared or not). Then I played sinus in on line-array placed in front on me at about 2 meters, in my treated room (very absorbant: RT60 ~50-100ms for mid-high frequencies and very good absorption at low frequencies compared to most rooms), and I adjusted with a gamepad and my own custom software the amplitude and delay between each headphone driver in order to get perfect "perceived" sound cancellation. I estimated the amplitude error at about 0.1dB, which we should add the dissemetry between L/R headphone drivers that were not calibrated. In the end, the differences between what is perceived between left ear and right ear is sensitively different and it is not perceived by a single microphone.
be
In a more reverberant room, I bet you would get high sound pressure amplitude differences between the two ears.

 

[AJ Soundfield]

Suggested reading http://www.aes-media.org/sections/pnw/ppt/jj/jj_aes04_ts1.pdf

 

[DanDan]

Yes indeed, LF response varies even quite small distances apart. Thus when we get serious about exactly locating a speaker or treatment or listening position, we move in 50cm increments.

Audio Minutiae

ethanwiner.com

It is also necessary to have both single speaker and dual speakers driving.
So a full measurement at one location would be Lear, L, R, L+R speakers, Rear, L,R, L+R speakers.
I have seen Dummy Heads and HATS systems used in some of the more Academic Papers. It would be quite easy to make a Jeklin Disc Binaural rig using two Measurement mics and a simple blocking disc with foam absorbent at the both microphone sides.

 

[Jean Ibarz]

Suggested reading http://www.aes-media.org/sections/pnw/ppt/jj/jj_aes04_ts1.pdf

Very interesting paper AJ Soundfield. I disagree with at least two of these "well known" facts:

1) "20Hz is usually mentioned as the lowest frequency detected by the hearing apparatus "

I'm trying to reproduce binaural audio with externalized audio reproduction (out of the body), because I noticed that my brains "perceives" sound not only with ears, but also with body vibrations at low frequencies. My prototype is able to reproduce about 146dB SPL peak at 20hz. It can go to 7hz with lower SPL, and I was able to confirm that I can hear up to 16hz, while at 15hz the perception drops nearly instanteneously from moderate to nothing at all, no matter the SPL.

2) "At low and high frequencies, the compression is less at low levels, and the thresholds elevated."

I use this prototype (a small closed box inside which I seat, pictures here) to reproduce bandwidth <80hz, and I try to reproduce bandwidth >80hz with headphones and HRTF or BRIR. Actually, I found out that when my system is "quite correctly" equalized, the more I increase the level, the more the medium and high frequencies "hurts", while low frequencies never hurts. Also, when I was using a "usual" stereo audio system in an average size room, I used to set a flat frequency target curve when listening at low to moderate levels (up to 85dBA), while when pushing up 95dBA I was prefearing a curve with attenuated high frequencies, which in my opinion contradicts plainly the fact that "low frequencies are less compressed then high frequencies" by our hearing system. Furthermore, I am able to listen this video at ~135-140dB SPL peak without feeling pain

.

A completely unrelated observation that I would point out is that our ears make me think a lot more of a pressure-pressure sound intensity sensor, than a single omni-directional microphone.... I think this is something important to point out as some studies shows that ITD is an information that is most used at low frequencies.

 

[Jean Ibarz]

we were discussing the math behind why this works, where he pointed out that if you take the denominator of the close formed room and multiply it by a filter transfer function of the peak, it will cancel it it the pole(s) from the Denominator. It does this For every location in space of the closed form room. This is all linear mathematics. A room is generally minim phase at low frequencies. If you insert an inverse filter to obtain a flat magnitude response, you will in turn have a flat phase response. That means no ringing.

I agree with you that minimal phase PEQ may correct amplitude and decay under the assumption that the impulse response is minimal phase. I was thinking it was not the case, but you said "a room is generally minimal phase at low frequencies". I checked various measurements I made, even an extreme one with a standing wave in a 1meter length steel tube of 4mm. diameter, and yes the impulse response is nearly perfectly minimal phase, with a negligible amount of excess phase..... so your assumption seems to hold in all of my measurements: I was convinced it was not the case, but you proved me wrong: good ! ;-)

 

[Eric SVL]

on that note, have you ever tried placing subs at the front and back of the room and then eqing? That might give better results. Alternatively you could operate a subwoofer below 50hz in the back of the room with a delay applied that is equal to the time it takes for the wave to transverse the length of the room. That would cancel the length mode entirely. 35hz is well into the unimodal region where this would hold true at all locations.

This is exactly what I do and can confirm it works. Best response for the rear sub always ends up at 16 ms. The room is 16 feet long

 

[Noah Katz]

Very interesting discussion.

Perhaps some of the debate about decay is due to a bit of imprecision in its definition.

If I remember correctly from my mechanical vibrations text, it's defined as a % amplitude reduction per cycle, or perhaps more usefully for audio, dB/sec.

That would remove initial amplitude as a variable and its potential to muddy the waters.

 

[Jean Ibarz]

If I remember correctly from my mechanical vibrations text, it's defined as a % amplitude reduction per cycle, or perhaps more usefully for audio, dB/sec.

This seems a correct definition to me.

A nice visualization feature has been added in recent versions of REW beta : it allows to estimate and plot the decay rate interactively as a function of the frequency you select.

 

[Jean Ibarz]

This is exactly what I do and can confirm it works. Best response for the rear sub always ends up at 16 ms. The room is 16 feet long

A friend of mine did the experiments too and the measurements shows a great increase in the decay rate for the affected mode: seems to work.

 

[AJ Soundfield]

Very interesting paper AJ Soundfield. I disagree with at least two of these "well known" facts:

1) "20Hz is usually mentioned as the lowest frequency detected by the hearing apparatus "

I was able to confirm that I can hear up to 16hz

2) "At low and high frequencies, the compression is less at low levels, and the thresholds elevated."

my opinion contradicts plainly the fact that "low frequencies are less compressed then high frequencies" by our hearing system.

In both cases you are simply misreading the quoted statements, not contradicting them.
Like Toole's et al published works, the statements JJ made are based on rigorous controlled blind listening tests over the last century, not ad hoc self administered style experiments.
Needless to say, I agree with Mathews original statement EQ reduction of amplitude will correspondingly reduce decay.
Of course I care only about audible-perceptual results, not pretty visual ones for selling pillows etc. That's why I interjected JJ as a reminder.
So I may "view" the same thing a bit differently.

cheers

 

[DanDan]

How We Hear Pitch

When two sounds happen very close together, we hear them as one. This surprising phenomenon is the basis of musical pitch — and there are lots of ways to exploit it in sound design.

www.soundonsound.com

 

[Jean Ibarz]

In both cases you are simply misreading the quoted statements, not contradicting them.
Like Toole's et al published works, the statements JJ made are based on rigorous controlled blind listening tests over the last century, not ad hoc self administered style experiments.
Needless to say, I agree with Mathews original statement EQ reduction of amplitude will correspondingly reduce decay.
Of course I care only about audible-perceptual results, not pretty visual ones for selling pillows etc. That's why I interjected JJ as a reminder.
So I may "view" the same thing a bit differently.

cheers

Oh yes, that's true: Fletcher and Munson curves seems to indicate that at high levels, the low frequencies are more compressed (because it requires a higher increase in SPL to increase one phone) than high frequencies. I think I was not looking at high enough SPL, and this seems to correlates with my auditive experiences ! Probably another thing better understand, thanks !

 

[Jean Ibarz]

Why are these graphs indicating different compression at high SPL between low frequencies and high frequencies ?

1) This one indicates higher compression at low frequencies compared to high frequencies at high SPL:

(source: https://www.kmuw.org/post/loudness-and-fletcher-munson-curve)

2) this one it is unclear:

(source: https://line6.com/support/page/kb/g...live-tone-and-the-fletcher-munson-curve-r448/)

3) and this one indicates the opposite trend (lesser compression at low frequencies than high frequencies for high SPL):

(source: https://en.wikipedia.org/wiki/Equal-loudness_contour)

or I am still misinterpreting one or all of these graphs ?

does anyone have the original reference of graph 1) ?

Edit: graph of my previous post is from the 1933 article of Fletcher and Munson, derived with a speaker placed in front of the listener: it seems good to me.
1) I don't know, but seems good to.
2) is from Stevens and Davis, and are derived with earphones, seems not good to me.
3) ISO-curves, don't know much about them, seems not good too.

Here the authors says that there exists numerous studies that show different results, and conclude that "there is no absolute threshold-of-hearing curve that is independent of the way the sound gets to the inner ear". Well, maybe it is plausible that we are not measuring the right "thing" ?

 

[DanDan]

Some random points. I wouldn't infer compression from those curves. But it depends on what you mean by compression. I would take a guess that those spectral changes in sensitivity take a while to kick in.
There are protective physioacoustical protection mechanisms that mechanically inhibit the ear's response at high levels. Again I doubt they are have fast enough attack and decay to be called compression. Also there are psychoacoustic factors, e.g. hearing is less susceptible to damage from sound which we like. Lastly, the 3-5K bag experiences resonant amplification. I think that needs to be considered separately from the rest of the spectrum.

 

[Noah Katz]

... I would take a guess that those spectral changes in sensitivity take a while to kick in.

... Again I doubt they are have fast enough attack and decay to be called compression.

That raises the question of what duration tones are used to develop the loudness curves.

I would have guessed steady state, but your statements imply otherwise.

 

[Jean Ibarz]

There are protective physioacoustical protection mechanisms that mechanically inhibit the ear's response at high levels. Again I doubt they are have fast enough attack and decay to be called compression.

Yes, the acoustic reflex (or stapedius reflex), I know very little about it. In wikipedia it is stated that : "The acoustic reflex mostly protects against low frequency sounds.[13] ". It may explains the higher compression at low frequencies. What I called "compression" is the fact that when you play a music at some high SPL, like 80dBA (or equivalently about 90-95dBC), when you raise the level to 95dBA (or equivalently about 105-110dBC), the perceived increase in medium/trebles is higher then with low frequencies. Hence, you have to adjust the response of your system to perceive the music with the same "neutrality": either you increase the level of the low frequencies (low shelf 100hz), or you decrease the level of high frequencies (slope from 2-3khz to 20khz). At least, this is what I do.

 

[AJ Soundfield]

Why are these graphs indicating different compression at high SPL between low frequencies and high frequencies ?

Ok, I think I understand what you're asking now Jean...and I suspect, the answer is different groups of human test subjects have slight differences in frequency dependent thresholds (what's being measured), hence the slight differences in spacing at the extremities.
I was a bit confused by your use of the term "compression", which the ear does at high levels. But I think you may have mean "compressed" spacing of the thresholds? Regardless, there will be some slight variability due to human physiology, possibly in the test methods also, or a combination.
Like the 20hz thing, those are not "absolutes", but "very close" guidelines.
At least I hope I'm addressing what I think you meant ;-)

ooops, see you posted while I slooowly typed!

cheers,

 

[Jean Ibarz]

Yes. But my guts are still telling me that there is something more then individual differences: I think you all haved been to concerts and noticed how the bass seems "a lot too much" when the sound level is moderate, and how it becomes "neutral" when the sound becomes very loud, at nominal concert level. And I think we all notice this, not just some individuals. At least, my friend and I does, and I am not aware of any of my friend that does perceive the opposite !

 

[DanDan]

Maximum Bass at All Frequencies, Jah Bless..... Don't know where I read that, Reggae dude no doubt, but word. It appears we can not alone tolerate but actively like lots of Bass. DBX did make some products, including for Hi Fi, which generated what they called SubHarmonics. Certainly some of my live acts have benefited from this. Sometimes we want the solo act with just a guitar to sound Godly. I do think Fletcher Munson is probably too simplistic. It may have been done with Sine Waves or such, dunno, haven't really looked into it. But I think we all know that the feel good hormones which come with high volume also come with the warnings of harshness and sting from loud medium to high frequencies. Again I think that the 3-5K resonant amplification seen in Fletcher Munson is at play. NIHL typically sees most damage in this region. Our bodies may know what they are doing better than our brains do.

 

[DanDan]

"... I would take a guess that those spectral changes in sensitivity take a while to kick in.

... Again I doubt they are have fast enough attack and decay to be called compression.

That raises the question of what duration tones are used to develop the loudness curves.

I would have guessed steady state, but your statements imply otherwise."

I would guess any old research, eg. the development of the third octave, used Sine Waves, steady state. I am suggesting that it may take quite a while for a FM sensitivity curve to kick in after a change from a different one.
Much longer than musical events. As I said earlier, depends on what one means by compression. I really don't think the hearing system reacts quickly enough to compress music.

 

[Noah Katz]

I would guess any old research, eg. the development of the third octave, used Sine Waves, steady state. I am suggesting that it may take quite a while for a FM sensitivity curve to kick in after a change from a different one.

I'd guess sine waves are used for convenience, not because a lot of time is needed.

If I turn up the bass I can hear the difference instantly.

 

[DanDan]

It was 1933 Noah, I wonder if anything other than Sines were available. I am suggesting that it takes a while for the curve of sensitivity to establish when the overall volume is changed. But I an reconsidering even that now, due to finding the following. To be honest I hadn't taken any notice of this until just now.
It appears a lot of our assumptions that we hear best and flattest at high levels are probably mistaken.
Fletcher Munson's work has been improved on with very different results. This graph suggests to me that the spectra we hear at different volumes, particular at commonly occurring levels, don't vary much at all.

 

[Noah Katz]

Dan,

I am suggesting that it takes a while for the curve of sensitivity to establish when the overall volume is changed. But I an reconsidering even that now, due to finding the following...

I gave my reason for thinking otherwise.

What are your reasons, and why are you (I think) making a connection between the shape/spacings of the curves and the revisions thereof, and the time it takes to hear something?

 

[Jean Ibarz]

On wikipedia it is said the following about the acoustic reflex (or stapedius reflex) : "the latency of contraction is only about 10ms, but maximum tension may not be reached for 100 ms or more.[13] According to the article Le traumatisme acoustique, the latency of contraction is 150 ms with noise stimulus which SPL is at the threshold (ATR), and 25–35 ms at high sound pressure levels. Indeed, the amplitude of the contraction grows with the sound pressure level stimulus.[17] "

I don't think it takes "much time" to adapt to level variations too, more than 5 seconds seems unlikely to me.

I agree with Noah Katz: "What are your reasons, and why are you (I think) making a connection between the shape/spacings of the curves and the revisions thereof, and the time it takes to hear something?".

You say "Fletcher Munson's work has been improved on with very different results." : what makes you thing this is an improvement ? and not just a different result that may be better or poorer ? are they produced under the exact same conditions too ?

 

[DanDan]

Thanks Jean, I guess 'much time' is undefined, but I am assuming we are both talking about the same kind of Compression? In Mixing and Mastering I would call more than 500mS slow, so I think say 2-4 seconds to adapt to a level change is very very slow. We would use the term 'Levelling' with such long time constants. I take it you concur as you said ? "more than 5 seconds seems unlikely to me"

Thinks are often more complex than some Wiki think. This reflex you refer to is almost certainly an automatic reflex to a sudden noise. But I suggest it quickly changes behaviour once the brain accepts the new stimulus as music.

Generally science develops over time, increasing in understanding and accuracy. Although current world events suggest a return to the Flat Earth...... So I think it reasonable to accept the current International Standards Organisation data as improved on the work 80 years ago. https://ledgernote.com/columns/mixing-mastering/fletcher-munson-curve/ Also e.g. the third octave standard was widely used for a long long time. But now we know that the ear/brain can readily discern anomalies or other factors with much narrower bandwidths.

Noah, it is as if we share a misunderstanding of a common language. As you see Jean and I both think it would take a few seconds for the ear/brain to adapt to noticeable level change.
"What are your reasons, and why are you (I think) making a connection between the shape/spacings of the curves and the revisions thereof, and the time it takes to hear something"
I am not at all. I went along with it for a while but the gaps between the lines in the ISO graph seem equal?


Why do I assume it is not instantaneous or fast? Well I guess a lifetime working in sound means one has kind of seen it all. But specifically, I note that it takes up to 10 minutes to adapt to a really quiet space. Gradually one hears blood flow, and eventually the hissing of molecules hitting the eardrum, or neurons firing, or both. Also, I am living in a Recording Studio and I have a mix up right now. I tried dropping the master 20dB, and there is no immediate loss of Bass and Treble.