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Dynamic range question, Dynamic range of hearing vs. equipment
thesurfingalien
post Jun 8 2011, 01:16
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Hi All,

I am having problems understanding the concept of dynamic range, and more specific how the dynamic range of human hearing relates to the dynamic range as specified for audio equipment.

What I have read on the Net is that the dynamic range of human hearing is, on average, 135 dB (the pain limit / threshold?).

I also understand that the dynamic range of a CD (16 bit) is limited to 96 dB, and for HD (24 bit) recordings 144 dB. This dynamic range is calculated by the bit-depth.

For playback of music (I use 44.1/16 flac only) I use a E-MU 1820 that has a dynamic range of about 115 dB (or so). I am not sure what my amp can do...

However, when I play music I hardly pass 80 dB (or so) listening volume, so the 96 dB CD data (if the recording makes full use of the range that is) gets "compressed", while the relative dynamic range remains.

After the long intro my question in essence is:

Does the human hearing have a similar "resolution" that is comparable to the resolution defined by the bit-depth in (digital) audio? Or am I just comparing apples and pears?

Regards,
Peter

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Canar
post Jun 8 2011, 01:44
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QUOTE (thesurfingalien @ Jun 7 2011, 17:16) *
However, when I play music I hardly pass 80 dB (or so) listening volume, so the 96 dB CD data (if the recording makes full use of the range that is) gets "compressed", while the relative dynamic range remains.
I think this is where the problem in your reasoning lies. Your 96dB of CD dynamic range is kind of wasted. You hear the "top" 80dB while the lower 16dB is lost beneath the noise floor. Realistically, playing at 80dB, there's maybe 30-40dB of noise in your room, so you get maybe 40dB of dynamic range in your environment.

This post has been edited by Canar: Jun 8 2011, 01:45


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pdq
post Jun 8 2011, 01:51
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...and with proper dither the dynamic range of 16 bits is considerably more than 96 dB.
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Woodinville
post Jun 8 2011, 02:28
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In most any modern room, the lower limit of masking noise is well above 0dB. The greatest output level you get from most speakers is under 115dB. For most circumstances, 16 bits is good enough. 20 bits is more than enough to accomodate atmospheric-noise levels to speaker-overload levels. 24 bits is usually wishful thinking.


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knutinh
post Jun 8 2011, 09:20
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Given that background noise can have all kinds of distributions, frequency range, etc. How should one measure background noise to arrive at some level reading that can be compared with the dynamic range of recording medium and the maximum SPL of your loudspeakers to be assured that the noise level of the room dominates the noise level of the recording medium at all times, all frequencies etc?

If room noise was some white noise source rated at 20 dB A-weighted, and the noise level of the recording medium (at some sensible playback level) was similar to a white-noise source rated at 20dB A-weighted, I think that it is fair to believe that _some_ perceptual gain might be expected by lowering the noise level of the medium by 3 or 10 dB?

-k
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Woodinville
post Jun 8 2011, 09:30
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QUOTE (knutinh @ Jun 8 2011, 01:20) *
Given that background noise can have all kinds of distributions, frequency range, etc. How should one measure background noise to arrive at some level reading that can be compared with the dynamic range of recording medium and the maximum SPL of your loudspeakers to be assured that the noise level of the room dominates the noise level of the recording medium at all times, all frequencies etc?

If room noise was some white noise source rated at 20 dB A-weighted, and the noise level of the recording medium (at some sensible playback level) was similar to a white-noise source rated at 20dB A-weighted, I think that it is fair to believe that _some_ perceptual gain might be expected by lowering the noise level of the medium by 3 or 10 dB?

-k


You need to know the noise spectrum, there is no simple answer. If you're talking noise on noise masking, 3dB is about the limit.


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knutinh
post Jun 8 2011, 10:15
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QUOTE (Woodinville @ Jun 8 2011, 10:30) *
You need to know the noise spectrum, there is no simple answer. If you're talking noise on noise masking, 3dB is about the limit.

That was kind of my rhetorical point: simplistic claims about acoustic noise floor masking medium noise floor may well be practically correct, but they must be making some assumptions that are seldomly communicated clearly.

-k
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DonP
post Jun 8 2011, 10:50
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For listening to high dynamic range material (say, 80 dB) turn off any nearby PC's, turn off the heat, unplug that fridge in the kitchen. I've had no luck requesting that the passenger jet 20 miles away cut it's engines for a few minutes.

So what steps would you need to take over that in a home environment to hear another 20 dB and talk about needing more than 16 bits?
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knutinh
post Jun 8 2011, 11:19
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QUOTE (DonP @ Jun 8 2011, 11:50) *
For listening to high dynamic range material (say, 80 dB) turn off any nearby PC's, turn off the heat, unplug that fridge in the kitchen. I've had no luck requesting that the passenger jet 20 miles away cut it's engines for a few minutes.

So what steps would you need to take over that in a home environment to hear another 20 dB and talk about needing more than 16 bits?

I am not claiming that 16 bits is not enough, and I am certainly not claiming that I have heard its limitations. I still think that claims from a sceptic/scientific forum like this should be subject to some dissection before being broadcast as a bullet-proof advice.

Question is: is 20dB room-noise/recording-noise headroom enough to say with certainty that recording does not matter in any perceptual way? I think that perceptual mechanisms as well as pdf/frequency distribution are needed in that argument, knowing your way around log10(x1/x2) is not sufficient.
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thesurfingalien
post Jun 8 2011, 12:29
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@All:

Thanks so far for your replies, but it's not actually what I am looking for (or I just don't understand).

I am having trouble with the relation between bit-depth (the resolution) and the dB scale. I know the formula for calculating this, but what is that based upon.

The second question is if there is any relation between this dB-scale, and the sound pressure dB-scale.

Thanks,
Peter



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knutinh
post Jun 8 2011, 13:37
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QUOTE (thesurfingalien @ Jun 8 2011, 13:29) *
The second question is if there is any relation between this dB-scale, and the sound pressure dB-scale.

dB is just that - a scale. It says how large something is compared to some other thing using a non-linear scale that is appropriate for many applications.
QUOTE
I am having trouble with the relation between bit-depth (the resolution) and the dB scale. I know the formula for calculating this, but what is that based upon.

Not knowing what formula you are talking about, it is hard to comment.

The rule is that for e.g. 16 bits you have 2^16 = 65536 discrete levels available. Any continous signal that is directly discretized as 16 bits will have an error that is limited by a half stepsize in each direction. We are sometimes interested in the power of the full-scale signal compared to the power of the corresponding error. Given some assumptions this turns out to be approximately 6*#bits, or 96dB in the case of 16 bits.

-k
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drewfx
post Jun 8 2011, 17:05
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QUOTE (thesurfingalien @ Jun 8 2011, 06:29) *
@All:

Thanks so far for your replies, but it's not actually what I am looking for (or I just don't understand).

I am having trouble with the relation between bit-depth (the resolution) and the dB scale. I know the formula for calculating this, but what is that based upon.


I'm not sure which formula you are referring too, but assuming it's the "simplified" ~6dB per bit formula, the long explanation is it works like this:

A dB is just a logarithmic way of expressing a ratio of 2 values. For digital audio we use the ratio of the squares of the amplitudes, which equates to:

dB's = 20*log10(ratio of amplitudes)

So for a ratio of "2" (twice the amplitude), you get 20*log10(2) = ~6dB

And since each added bit doubles (a ratio of 2) the the maximum value you can store, that's where you get the ~6dB per bit. Or to put it another way, using the ratio of the largest number at a given bit depth to 1, for 16bits:

dB's = 20*log10(65536/1) = +96.3dB

Sorry if you already knew this.
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[JAZ]
post Jun 8 2011, 19:04
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Like others have said, the key is knowing that talking in dBs is just talking about ratios (difference between two values).

Then, dBs are used to calculate different things, which can be compared. The two that matters to us are these ones:

dB SPL (dB Sound pressure level), which is a reference scale from no pressure (no signal) upwards.
I.e. 0db SPL is the minimum signal possible.

db FS (dB Full scale), which is a reference scale from the maximum level of the media downwards.
I.e. 0dB FS is the maximum signal possible in the medium (or in some cases, like with floating point math, the value that represents the physical maximum, when it is to be converted to integer and/or analog).


As such, a non-dithered CD has the noise floor at -96dB FS, which means that has a SNR of 96dB. (How to calculate this and why is explained in the thread by drewfx.)

Like others have said, the minimum (reasonable) noise floor of a quiet room is 30dB SPL (An anechoic chamber might have lower levels, but that's not an usual room). (An office room is said to have a noise floor around 50dB SPL, with people talking and machines running). On big discotheques, the music can reach values around 100dB SPL. (or sometimes 110dB SPL). I can't comment on concerts, but concerts are reallly different from each other and big ones use to be on open spaces.

One can say that if you were to hear the noise floor of a CD in this quiet room, the strongest signal of this CD would be reproduced at 30+96 = 126dB SPL. (At least. Intersample peaks could be higher, but that's another subject, just like the comment about dither).


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saratoga
post Jun 8 2011, 19:15
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QUOTE (knutinh @ Jun 8 2011, 05:15) *
QUOTE (Woodinville @ Jun 8 2011, 10:30) *
You need to know the noise spectrum, there is no simple answer. If you're talking noise on noise masking, 3dB is about the limit.

That was kind of my rhetorical point: simplistic claims about acoustic noise floor masking medium noise floor may well be practically correct, but they must be making some


The assumption is generally that room noise is white. I don't think one needs to communicate this, its fairly obvious.

I don't think the assumption is all the relevant though. Given the equal loudness contour, and that quantization noise is effectively white, the only part of the quantization noise at 16 bits really contributing to the noise floor would be about 2k-4khz, which incidentally is the only part of the room noise spectrum that really matters. So unless your room is an anechoic chamber with a perpetually running tuning fork, the exact distribution of noise doesn't matter too much smile.gif
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DVDdoug
post Jun 8 2011, 19:37
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QUOTE
The second question is if there is any relation between this dB-scale, and the sound pressure dB-scale.
Yes. There is a one-to-one relationship. (But, the exact conversion factor isn't usually known.)

Let's assume you are playing a -6dBFS test-tone file on your computer, and the sound is coming out of your speakers at 80dBSPL. If you boost the digital signal by 6dB (to 0dBFS), you'll get 6dB more from your speakers (86dBSPL). ...Assuming your amplifier is not clipping, and that your speakers are linear, etc, etc, etc.

But since, we usually don't have a calibrated system, we can't make conversions between the two. Obviously, when you adjust the volume control, or move closer to the speaker, you change the acoustic SPL level without affecting the data in the file. Movie theaters are calibrated, so if everything is set-up correctly and you are sitting in the "right" location, etc., you can know the approximate SPL level in advance.

Oh... SPL measurements get a little more complicated with things like "A weighting" and averaging. (SPL is often measured in a way that corresponds with human perception of loudness.)


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Woodinville
post Jun 8 2011, 19:38
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QUOTE (saratoga @ Jun 8 2011, 11:15) *
The assumption is generally that room noise is white. I don't think one needs to communicate this, its fairly obvious.


Room noise is almost never white. In fact, I don't think I've seen such a thing.


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Northpack
post Jun 8 2011, 20:15
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I guess room noise usually has the least amount of energy in the 2kHz range - we naturally build our accommodation in a way that we allow higher noise levels in those frequency domains we are less sensitive to (we're instinctively "noise-shaping" our environment). Think of all the noise emitting devices and how walls filter the sound from outside. Either we have low frequencys which pervade the walls or we have high frequency noise generated by all kinds of electric gear.

This post has been edited by Northpack: Jun 8 2011, 20:18
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knutinh
post Jun 8 2011, 20:49
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QUOTE (Northpack @ Jun 8 2011, 21:15) *
I guess room noise usually has the least amount of energy in the 2kHz range - we naturally build our accommodation in a way that we allow higher noise levels in those frequency domains we are less sensitive to (we're instinctively "noise-shaping" our environment). Think of all the noise emitting devices and how walls filter the sound from outside. Either we have low frequencys which pervade the walls or we have high frequency noise generated by all kinds of electric gear.

If your theory on acoustic room noise tending to follow perception, and dithering of digital quantization follows the same general curves, then measurements of both should be comparable?

I'd think that some major mechanisms are:
1. The tendency of thick, heavy housing materials to attenuate high frequencies more than the very low frequencies.
2. The 50/60Hz powerline frequency and any in-room equipment that generate noise at it or one or more multiples
3. Temporal fluctuations - passing cars may influence long-term averaged mesurements but in-between passing cars, the noise level could dip significantly

For "harmonic" noise sources (e.g. mechanical AC), what spacing is needed between harmonics before measuring them as if they were dense stochastic noise will lead to very wrong conclusions as to human perception in our context?

-k
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saratoga
post Jun 8 2011, 20:58
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QUOTE (Woodinville @ Jun 8 2011, 14:38) *
QUOTE (saratoga @ Jun 8 2011, 11:15) *
The assumption is generally that room noise is white. I don't think one needs to communicate this, its fairly obvious.


Room noise is almost never white. In fact, I don't think I've seen such a thing.


I didn't say it was white, just that by comparing it based on total energy to a white noise source, you are assuming its white smile.gif

Given the modes that fit into a typical room, I doubt its all that white. But as I argued before, I also doubt it matters much unless you've got some loud fan or something next to you in an otherwise quiet room.
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DonP
post Jun 9 2011, 00:17
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QUOTE ([JAZ] @ Jun 8 2011, 13:04) *


dB SPL (dB Sound pressure level), which is a reference scale from no pressure (no signal) upwards.
I.e. 0db SPL is the minimum signal possible.


dB is a logarithmic ratio of power, 1/10 of a bel. A bel is a 10:1 power ratio, so a dB is the tenth root of 10 power ratio.

no signal would be negative infinity dB. Ratios, remember?

0dB spl is nominally the minimum volume a human can detect. About as accurate as "the width of the king's thumb" if you don't know which king. So they've standardized the reference at 20 micropascals.

There are other 0dB references for other contexts like dBm (reference = 1 milliwatt) and the mentioned dB FS.
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greynol
post Jun 9 2011, 00:32
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Let's not forget dBu and dBV.


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Woodinville
post Jun 9 2011, 02:02
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QUOTE (saratoga @ Jun 8 2011, 12:58) *
QUOTE (Woodinville @ Jun 8 2011, 14:38) *
QUOTE (saratoga @ Jun 8 2011, 11:15) *
The assumption is generally that room noise is white. I don't think one needs to communicate this, its fairly obvious.


Room noise is almost never white. In fact, I don't think I've seen such a thing.


I didn't say it was white, just that by comparing it based on total energy to a white noise source, you are assuming its white smile.gif

Given the modes that fit into a typical room, I doubt its all that white. But as I argued before, I also doubt it matters much unless you've got some loud fan or something next to you in an otherwise quiet room.


Actually, the world nowadays is annoyingly noisy, when you get right down to it. (sigh)


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drewfx
post Jun 9 2011, 02:17
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And to further clarify the use of "dB" vs. "dB SPL"/"dB FS"/"dBu"/"dBV"/...

The thing to remember is "dB" alone is always used to compare 2 values - it's an expression of the ratio between the 2 values. "Signal A peaks at -7dB relative to signal B".

But "dB with a suffix" is used to compare a single value to a predefined reference value specified by the suffix. As previously noted, "dB FS" defines 0dB FS as "the maximum value that can be represented (Full Scale)". So if you use "dB FS", it means you are comparing your value to this predefined value. "Signal A is -22dB FS" means "Signal A is -22dB compared to the predefined value of 0dB FS".
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MichaelW
post Jun 9 2011, 04:42
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QUOTE (Woodinville @ Jun 9 2011, 13:02) *
Actually, the world nowadays is annoyingly noisy, when you get right down to it. (sigh)


Yes, but when I spend time in the country I'm struck by how very noisy birds can be. Not to mention the time I was having a cup of coffee on the sidewalk in urban Adelaide, and the parrots in a nearby tree were drowning the traffic noise. Real quiet is hard to find (and rather freaky when you do).
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WernerO
post Jun 9 2011, 10:12
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QUOTE (MichaelW @ Jun 9 2011, 04:42) *
when I spend time in the country I'm struck by how very noisy birds can be.


Last week we spent a lot of time in the garden (agricultural village, meaning detached houses on plots sized 500 - 1000 square meters each, lawns lined with trees, ...) and it struck me too what a racket the few remaining birds here make. So I went and measured ~60dB (C-weighted), with excursions to 70dB.

We need more cats.

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