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post #1 of 18 Old 10-19-2015, 11:38 AM - Thread Starter
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Decibels: Sensitivity to different frequency ranges and to perceived loudness differe

I've read that we are more sensitive to midrange frequencies than bass frequencies yet also that 10dB higher sounds twice as loud for midrange but somewhere around 3-6dB is twice as loud for bass. It seems odd that bass needs to be higher in dB to sound as loud as midrange yet it takes fewer dB to make things twice as loud. Also, if 75dB is twice as loud as 65dB (in midrange), is 85dB 4 times as loud and 95dB 8 times as loud? Not sure I understand the math exactly...

Also, how does treble stack vs. midrange and bass?
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post #2 of 18 Old 10-19-2015, 11:40 AM
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https://en.wikipedia.org/wiki/Equal-loudness_contour

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post #3 of 18 Old 10-19-2015, 11:46 AM - Thread Starter
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Originally Posted by beaveav View Post
That image at the top of the wiki helps somewhat but I was hoping for a simplified explanation so I can make sense of this stuff better than my current limited understanding of it.
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post #4 of 18 Old 10-19-2015, 12:01 PM
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Power = 10 * log10(Pout/Pin)

1 dB is barely audible and takes 1.26 times the power.
3 dB is a slight increase (e.g. "bump the volume a hair") and takes twice (2.0 times) the power.
10 dB sounds twice as loud and takes ten times the power.

If 75 dB is your reference, then 85 dB is twice as loud, and 95 dB is twice as loud as 85 dB or four (2 x 2 = 4) times as loud as 75 dB. Every 10 dB increase doubles perceived loudness.

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post #5 of 18 Old 10-19-2015, 12:17 PM - Thread Starter
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Originally Posted by DonH50 View Post
Power = 10 * log10(Pout/Pin)

1 dB is barely audible and takes 1.26 times the power.
3 dB is a slight increase (e.g. "bump the volume a hair") and takes twice (2.0 times) the power.
10 dB sounds twice as loud and takes ten times the power.

If 75 dB is your reference, then 85 dB is twice as loud, and 95 dB is twice as loud as 85 dB or four (2 x 2 = 4) times as loud as 75 dB. Every 10 dB increase doubles perceived loudness.
This is for midrange frequencies, right?

(Regarding perceived increase in loudness vs. increase in dB, not amplifier power required)
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post #6 of 18 Old 10-19-2015, 12:33 PM
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Yes. The curves compress at very LF and very HF as show in the equal loudness contours previously linked.

Note the power ratios per dB are independent of perceived loudness. 10 dB takes 10x the power no matter the frequency.

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post #7 of 18 Old 10-19-2015, 12:39 PM - Thread Starter
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Originally Posted by DonH50 View Post
Yes. The curves compress at very LF and very HF as show in the equal loudness contours previously linked.

Note the power ratios per dB are independent of perceived loudness. 10 dB takes 10x the power no matter the frequency.
Ok; at 20Hz, how many dB sounds twice as loud? At 80Hz? At 120Hz?
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post #8 of 18 Old 10-19-2015, 12:55 PM
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The response of the human ear is not linear across the frequency range, and, worse yet, at lower volumes it processes sound differently than at higher volumes. The basic answer is that at low volumes you'll see a big dip in the midrange which is less pronounced at higher volumes. That means your question is not so simple to answer.

Much of the work on the acoustics of the human ear is old and done with equipment that was pretty primitive, yet the work remains valid. The two major studies are Fletcher-Munson (1937) and Robinson-Dadson (1956). The Robinson-Dadson work is generally considered to be more accurate, and when the ISO for Normal Equal-Loudness Level Contours (ELLC) was established this data was used. Searching on these should turn up more work than you could read in a week.

A quick search turned up a few guides which have charts which ought to explain the relationships. I can't post the links, but try searching for Robinson-Dadson at the Audioholics Website and you should find a decent one.

You'll see terms "sones" and "phons" which are different than db because they deal with perceived loudness at various frequencies, not actual loudness.
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post #9 of 18 Old 10-19-2015, 02:34 PM
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Quote:
Originally Posted by DonH50 View Post
10 dB sounds twice as loud
I've always had a problem with this, everyone knows that hearing sensitivity is not linear with frequency, but I would suggest it varies a lot from person to person too. Even if it didn't how can you possibly assign a comparison like "twice as loud" to something that is entirely subjective and cannot be measured quantitively.

Testing the threshold of hearing is fine, its easy to determine at each frequency for each individual, same for threshold of pain. But testing how many dB gives a perceived doubling in loudness, how do you even approach that? Surely it has to be more complicated than just asking people to say "when" once they think a tone increasing in amplitude has reached twice its initial perceived loudness? And whatever method is chosen must give a huge range of results between individuals, much bigger than threshold of detection or threshold of pain because they are easily definable even in the context of subjective audio perception.

More simply, the equal loudness contours are an average from a very large sample size, many individuals will have a perceived frequency response quite different from the graph found on wikipedia.
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post #10 of 18 Old 10-19-2015, 04:18 PM
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@PlasmaPZ80U : The curves are equal loudness curves, so as you move along the curve you can see how much louder or softer sounds need to be at different frequencies to have the same perceived loudness. Jumping from one curve to another you can see how much is needed to move to a different perceived loudness. If you are really interested read the Wikipedia articles and/or pick up something like Everest's Master handbook of Acoustics. Some things require a bit of research and don't have a real simple two-second answer.

@Ormy : The equal loudness curves have been with us for a long time. They were updated quite a few years ago and the updated versions are in use today. (There have been some other tweaks but I think the '56 Robinson/Dadson curves are generally accepted.) You may disagree, and of course there is variance, but they are the standard used around the world. The methodology is described in the papers (original and the update most often cited):

Fletcher, H. and Munson, W.A., "Loudness, Its Definition, Measurement, and Calculation", J. Acous. Soc. of Am., Vol. 5, 1933, pp 82-108.
Robinson, D.W. and Dadson, R.S., "A Re-Determination of the Equal-Loudness Relations for Pure Tones", British J. of App. Physics, Vol. 7, 1956, pp 166-181.

They do note that the curves are subjective, but are better than nothing IMO. I am not sure the variance among individuals is as large as you imply; what do you base your conclusions upon? That said, I know the proper relationship among SPL, sones, and phons is an on-going matter of debate since sones are indeed subjective. Most texts (at least the ones I have, lay and professional) do include disclaimers about the subjective nature of the curves.

In any event, this is not my primary field, so I am not really qualified to debate you or the writers of the papers.

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post #11 of 18 Old 10-19-2015, 06:39 PM
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Quote:
Originally Posted by DonH50 View Post
The equal loudness curves have been with us for a long time. They were updated quite a few years ago and the updated versions are in use today. (There have been some other tweaks but I think the '56 Robinson/Dadson curves are generally accepted.) You may disagree, and of course there is variance, but they are the standard used around the world.
Very true. Robinson-Dadson is considered to be the most accurate study, and formed the basis for the "Normal Equal-Loudness Level Contours" of the International Standards Organization in ISO 226.

It specifies SPL combinations of continuous pure tones which will be perceived as equally loud by human listeners on a statistical basis. So, yes, while there may be some minor statistical variation between human listeners with normal hearing, these are so small as to be insignificant.

I use "normal" not as a value judgement, but what a human would have without hearing damage. I can't say "typical" or "ordinary" as earbuds are now creating hearing loss in younger people that we can't say is "normal" (i.e. undamaged human hearing as from the factory) although it is, alas, now "typical". Anyway, someone with hearing loss would typically have a bathtub curve for frequency response (dropout at particular frequency bands) which would alter the response curve. Such people use hearing aids to restore the frequency response to a more typical curve.

As an aside, I went through this with a hearing-impaired family member, so I'm familiar with the hearing aid issue, including the problems with them, and, yes, I am simplifying here for purposes of discussion, and no, I'm not making a value judgement about hearing impairment being abnormal in a bad way. My point is how the statistical analysis of typical humans reflects what is hopefully undamaged hearing. This makes me wonder what "normal" hearing will be after a generation of earbud users alters their hearing for the worse.

Anyway, the interesting ramifications of the curve is that countour filters for loudspeaker drivers can be helpful because our ears detect small humps in SPL and read them as more significant than their magnitude would otherwise suggest depending on the frequencies involved. These humps can arise from additive/subtractive effects from multiple drivers in close proximity, the relative efficiency of those drivers, driver/cabinet resonance, and crossover overlaps. This is why computer modeling and simulation for speakers is so useful. So a Zobel network can squash that hump resulting in a more linear perception of the sound, at least for the statistically average listener.
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post #12 of 18 Old 10-20-2015, 07:37 AM - Thread Starter
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Originally Posted by Retrovert View Post
The response of the human ear is not linear across the frequency range, and, worse yet, at lower volumes it processes sound differently than at higher volumes. The basic answer is that at low volumes you'll see a big dip in the midrange which is less pronounced at higher volumes. That means your question is not so simple to answer.

Much of the work on the acoustics of the human ear is old and done with equipment that was pretty primitive, yet the work remains valid. The two major studies are Fletcher-Munson (1937) and Robinson-Dadson (1956). The Robinson-Dadson work is generally considered to be more accurate, and when the ISO for Normal Equal-Loudness Level Contours (ELLC) was established this data was used. Searching on these should turn up more work than you could read in a week.

A quick search turned up a few guides which have charts which ought to explain the relationships. I can't post the links, but try searching for Robinson-Dadson at the Audioholics Website and you should find a decent one.

You'll see terms "sones" and "phons" which are different than db because they deal with perceived loudness at various frequencies, not actual loudness.
I think I found those charts... though it does seem there are no easy or simple answers to my question.
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post #13 of 18 Old 10-20-2015, 08:09 AM
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Originally Posted by PlasmaPZ80U View Post
I think I found those charts... though it does seem there are no easy or simple answers to my question.
Iirc most equal loudness curves are ten dB apart from curve to curve at 1000 Hz. So that is roughly twice as loud from curve to curve. Equally true, if you had gone to high school, for the curves in the bass. The spacing is closer but subjectively the change is twice as loud because the curve, you see, indicates the levels at which the various frequencies seem equally loud, at least to a theoretical average listener.
You can look at lower frequencies and see both what spl it takes for, say, 40 Hz to be as subjectively Loud as 1KHz at any given spl level. You also see that at the bass end the curves get closer and closer together. For those who were awake in ninth grade, that means that the added relative loudness to seem twice as loud becomes less and less as you get louder and louder at any given lower frequency. There just is no single simple answer to "how many added spl sound twice as loud at 40 Hz?" The answer is "it depends." You cannot, no matter how hard you wish, make the answer simpler.
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post #14 of 18 Old 10-20-2015, 10:54 AM
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Originally Posted by DonH50 View Post
The methodology is described in the papers (original and the update most often cited):

Fletcher, H. and Munson, W.A., "Loudness, Its Definition, Measurement, and Calculation", J. Acous. Soc. of Am., Vol. 5, 1933, pp 82-108.
Robinson, D.W. and Dadson, R.S., "A Re-Determination of the Equal-Loudness Relations for Pure Tones", British J. of App. Physics, Vol. 7, 1956, pp 166-181.
I'm aware of the papers but I haven't found anywhere to access them for free (my university logins for various journal aggregators have long been expired). I was lazily hoping someone might be able to provide a link to free copy or maybe summarise the methodology if they happen to know it (both pretty unlikely I know). The abstract doesn't mention anything beyond "new techniques have been introduced".

Quote:
Originally Posted by DonH50 View Post
They do note that the curves are subjective, but are better than nothing IMO. I am not sure the variance among individuals is as large as you imply; what do you base your conclusions upon? That said, I know the proper relationship among SPL, sones, and phons is an on-going matter of debate since sones are indeed subjective. Most texts (at least the ones I have, lay and professional) do include disclaimers about the subjective nature of the curves.

In any event, this is not my primary field, so I am not really qualified to debate you or the writers of the papers.
I'm sure the papers are clearly outlining the limitations of the data as most respectable research papers do. But I suspect sound mixing staff (on movies etc) are implementing them with a rigidity and confidence that isn't warrented (what else are they supposed to do? I have no idea haha).

I base my conclusion on a small test I did with a friend a few years ago. Using a DSP and test tones, we each took turns to sit in the MLP of his system and perform the following steps:

1) turn off all auto EQ and other processing, using 'direct' mode on the AVR
2) Play test tone at 4KHz, adjust master volume till a calibrated SPL meter showed [x]dB.
3) Reduce test tone by 1/6 octave
4) adjust volume at that frequency using PEQ on the DSP* until it sounded equally loud as the previous tone, ignoring the SPL meter (move your head enough to find a peak and a null to account for comb filtering)
5) Repeat step 3 and 4 until you get to 40Hz.
6) Make a note of all filters on the DSP and delete all filters
7) Repeat steps 2-6 with a different value of 'x' on the SPL meter.

*I can't remember what we used for Q-value on the filters.

We knew his sytem wasn't flat but it doesn't matter since we only wanted to see the differences between our results, it was quite large, as much as 6dB at some points, and usually 2dB or more (my sensitivity to 40-300Hz seemed much lower for example, but with a strong peak in sensitivity at 120Hz compared to my friend). I know its far from rigorous, I don't actually have the data anymore, and its only one data point, one or both of us could be edge cases for hearing but it does suggest...

I even repeated it by myself on my own system (far less capable) a few times and found that my own response seemed to vary across different days. I'd repeat it a few times in one sitting/day and get repeatable results, a week later; wildly different results. I realised it was mostly dependent on if I had been in a noisy environment (say at work) earlier in the day and also on my mood, e.g.tension and anxiety would increase sensitivity above 1KHz. I guess I should try it again at some point, see if my hearing has changed in the intervening years (which it well might, I'm still a young man)

I guess I envisage a future auto-EQ technology that performs RoomEQ before some equivalent of this test for you a few times to create a more tailored frequency response for your individual equal loudness contour. Maybe even for multiple people just like current system use multiple measuring positions for RoomEQ. If anybody does this and makes money, I hereby claim 20% of all profit

Last edited by Ormy; 10-20-2015 at 11:04 AM.
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post #15 of 18 Old 10-20-2015, 11:28 AM
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Hmmm... I have not looked for them in my piles or online. Copyrights may still be in force, at least for the second:

"For works made for hire and anonymous and pseudonymous works, the duration of copyright is 95 years from first publication or 120 years from creation, whichever is shorter (unless the author's identity is later revealed in Copyright Office records, in which case the term becomes the author's life plus 70 years)."

I strongly suspect physical condition, mood, phase of the moon, and other physical and emotional factors dominate perceived differences in sound for most of us. That is one reason for ABX testing, to eliminate (or at least greatly reduce) some of those variables since the test time is short enough that we don't change much. Long ago I remember a test where different foods and smells were presented to listeners with resulting significant differences in the perceived sound even when nothing about the audio system was changed. And no I don't know where that one is either, alas.

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post #16 of 18 Old 10-20-2015, 12:25 PM
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Twice as loud.

Difficult to 'measure' sensations.

Like twice as bright, or

... twice as heavy
... twice as sweet
... twice as hot (heat or peppers)
... twice as rough
... twice as salty
... twice as long (time)

Even more difficult when varying the level of the initial circumstance.

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post #17 of 18 Old 10-20-2015, 02:12 PM
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Quote:
Originally Posted by DonH50 View Post
Long ago I remember a test where different foods and smells were presented to listeners with resulting significant differences in the perceived sound even when nothing about the audio system was changed. And no I don't know where that one is either, alas.
Makes sense, let us know if you find it. Don't get me started on copyright extensions, I just found out the TPP (Trans-Pacific-Partnership) which I thought was just about copyright, is somehow raising the cost of mackerel (one of my favourite foods) in my country, the UK. Seriously, WTF?

Anyway, thanks for your input DonH50.

@RayDunzl My point exactly. Its similar to the idea of simultaneous events in special relativity; just because two events happen simultaneously for one observer, does not mean they will appear so for another observer in a different reference frame. Just because two sounds at different frequencies sound the same loudness to one person, does not mean they will be the same loudness for another. Replace 'loud' with the (subjective) adjective-sensation of your choice.
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post #18 of 18 Old 10-22-2015, 05:55 PM
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Quote:
Originally Posted by PlasmaPZ80U View Post
It seems odd
6db is acoustically, twice as loud, so no it doesn't seem odd; more like the reverse, it seems odd that it takes 10db to get twice as loud treble.

Quote:
Originally Posted by PlasmaPZ80U View Post
Also, if 75dB is twice as loud as 65dB (in midrange), is 85dB 4 times as loud and 95dB 8 times as loud? Not sure I understand the math exactly...
Correct. (If you believe them that 10db is twice as loud. )
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