# Dynamic Range: How Quiet is Quiet?

#### amirm

Staff Member
CFO (Chief Fun Officer)
Dynamic Range: How Quiet is Quiet?
By Amir Majidimehr

Most people think of dynamic range as how loud something is. Mathematically though, dynamic range is a ratio. It is the loudest signal divided by “root mean squared” (essentially average) value of noise in the system expressed in decibels. Therefore the dynamic range is reduced if the noise floor of the system is increased. The purpose of this article is to investigate this lower limit.

Before diving deep let’s cover some basics. Movie soundtracks come in digital form on the Blu-ray disc. The format supports up to 24 bits of resolution per audio sample. Roughly speaking in digital systems we have 6 dB of dynamic range per sample bit. So 24 bits give us the often mentioned 144 dB of dynamic range. That is a theoretical value. In real life the system without any input will produce fair amount of noise. Due to this factor we lose about 4 bits of our 24 bit sample resolution to noise even in the best digital to analog converters (DACs). This yields an effective sample resolution of 20 bits and dynamic range of 120 dB.

In addition to DAC noise, for both live recordings and playback environments we need to consider the noise level that exists in the room. Whatever noise exists there is additive to the equipment noise. To get a sense for that noise floor, let’s run an experiment. If you have a dedicated theater or listening space and a SPL meter, go in there and close the door. Turn on the meter with nothing playing. Likely you see a number in the 50 or even 60 dB range. Taking our original 144 dB and ignoring equipment noise and subtracting this range of values from it, we now have an effective dynamic range of 84 dB to 94 dB. Since the dynamic range of 16 bit audio is 96 dB, it seems that we wasted disc space for 24 bit resolution on our Blu-ray Disc. Indeed the effective range expressed in bits is just 14 bits at the low range of that scale!

If you then argue that you are not going to play at 144 dB and knock off 10 to 20 dB due to that, our need for dynamic range shrinks another 2 to 3 bits to paltry 12 to 14 bits. Turn the volume down even more and next thing you know, you can convince yourself that we could go back to cassette tapes and still have sufficient dynamic range for our movies! Indeed there are people who argue exactly this, and conclude then that fidelity differences in our digital gear do not matter as the requirements are for so little resolution. Are they right? Is there a flaw in this analysis? Well, there is. The answer lies in psychoacoustics or how we hear.

We start with some of earliest research into how our hearing system works, namely, the Fletcher-Munson equal loudness graphs (see right). The chart is called equal loudness graphs because that is what the lines represent. The numbers on the graph are the loudness level perceived at 1 KHz in dB (SPL) with units of “phon.” As we see for example on the 40 phon line, to get the same 40 dB SPL perceived loudness level at 1 KHz, we would need to boost our 100 Hz signal by a whopping 20 dB! Our hearing is that much less sensitive at 100 Hz relative to 1 KHz. Similar thing happens as frequencies climb above 5 KHz or so.

For the purposes of this article we are concerned with the bottom line which is labeled “threshold.” As the name implies, this is the threshold of hearing. Anything below that is considered inaudible (for the average population). That line dramatically shows the “non-linear” response that the ear has. Using 1 KHz as a reference level the sensitivity at 3 KHz actually dips to a negative SPL value as the ear becomes hyper sensitive relative to the rest of the range. At the other extreme of 20 Hz, the threshold is an amazing 70 dB higher for the same level of loudness!

Given such high variability one realizes the fallacy of using a single number to describe how noisy a room is. At different frequencies, the minimum audible noise level changes. Hence we cannot use the single number given to use by the SPL meter to compute the dynamic range.

To get there we need to decompose the room noise into its frequency components and then compare it frequency to frequency to the threshold line. Only then do we know which ones peak above the threshold and hence are audible. Alas, this is not an easy exercise. The Fletcher-Munson graphs were generated by testing the audibility of test tones. In our application we are instead worried about audibility of noise. Noise is composed of many different frequencies combined so how the ear perceives it is not the same as that single tone. As a result these two numbers cannot be directly compared to each other. Fortunately there is a path there using work done by Bob Stuart (from the Meridian fame) as published in his Audio Engineering Society papers (see reference at the end of the article). It goes beyond the scope of this article to explain how he does that. But suffice it to say, using a variation of above graph known as Equivalent Rectangular Bandwidth (ERB) and some math, we can arrive at comparable values of test tones for each range of noise frequencies.

Louis Fielder, working for Dolby and former president of Audio Engineering Society, used Bob’s work to evaluate the entire playback and recording chain from equipment to listening spaces with respect to best dynamic range which can be achieved (see reference at the end of the article). Let’s review the measurements he took with respect to noise floor for a sampling of live halls and a film recording studio:

Ah, how fortuitous! The venue noise floor is high at low frequencies where our ears are least sensitive. This means that despite the noise reaching nearly 50 dB SPL, to our ears, the rooms are essentially silent relative to sensitivity of our ears at each frequency. The Skywalker Scoring Stage has especially good performance with nice margin below our threshold of hearing.

If you are wondering why the noise level goes up at low frequencies, the simple answer is that they are very hard to block. When you stand outside of your theater, it is the bass frequencies that leak out even if you have significant amount of sound isolation. Likewise, penetrations can occur in reverse direction and let external sound into the room. What might be there may include freeway vibrations from miles away! Extreme low frequency finds a way in. Heating and cooling systems are a week point as by definition they connect a noisy source (motors) to the listening space. For this reason, the above spaces were measured with these units turned off which is accepted practice for recording sessions.

Getting professional spaces this quiet with high budgets is one thing but how about home listening spaces? Fielder and his co-author Cohen surveyed 10 homes in one study, and another 27 in a second round and summarized the results in this graph:

As with professional spaces, we see elevated noise floors in low frequencies which no doubt fool our simple SPL meters and give us the high values we see on them. The average room is noisier than threshold of hearing but it seems possible to build rooms that are essentially silent as the minimum or the best performing room shows.

Fielder shows measurements in his paper for the other extreme for how loud music passages can get in live venues, registering values as high as 130 dB SPL. Using 0 dB SPL as our noise floor then for the quietest rooms we can build, that number translates into the same value of 130 dB number for dynamic range. This means we are simply limited by the DAC dynamic range of 120 dB, giving us 20 bits of effective dynamic range.

So it turns out we need high resolution audio (i.e. > 16 bits) after all if we want to make sure our distribution channel, i.e. recorded digital samples, does not add more noise than the rest of the chain. No cassette decks may apply.

By the way, much of this was probably intuitively obvious as you noticed how quiet your room was despite the high SPL numbers shown on the meter. As Dr. Toole, one of the top experts in acoustics and speaker design is fond of saying, “two ears and a brain are much more analytical than a microphone and a meter!” Indeed, your ears told the truth better than the measurement device.

References
“Noise: Methods for Estimating Detectability and Threshold, ” Stuart, J. Robert, JAES Volume 42 Issue 3 pp. 124-140; March 1994
“Dynamic-Range Issues in the Modern Digital Audio Environment, ” Fielder, Louis D., JAES Volume 43 Issue 5 pp. 322-339; May 1995

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Here is an overlay of my room noise floor (blue) and music signal (green).

Noise was 2000 averages taken around noon, PC and Refrigerator sounds identifiable, nothing noticable coming in from outside. I stuck my head outside, and could hear a golf cart and breeze rustling the leaves, along with the low buzz of suburban civilization.

Music was 500 averages at moderate level, Stanley Clarke and Hiromi and Lenny White on string bass, piano, and drums.

UMIK-1 and REW for measurement, 1/6th octave smoothing.

So, I see roughly 25-30dB between the noise floor and the tunes, add maybe 10-20dB (unaveraged) for program peaks.

Noise floor SPL was 37dBA, about 60dBZ.

I haven't figured out what the 18Hz noise is. Could be the distant interstate tire rumble, or air conditioner compressors, or even helicopter rotors. Low frequency carries so far, who knows. The 60 and 120 the cable from the preamp to the PC, the 2 and 3k spikes on the USB mic.

What's the deal with those pesky USB microphone spikes? Would one of those fancy USB regen/isolator doo-dads cleanit up?

Your music SPLs are quite low.

Should I play it so loudly I need earplugs?

Somewhere I read a Beethoven quote before he went deaf deaf: "Loud noises pain me. Soft ones escape me"

I can crank it up, 700w/4Ohm. But then I'd probably pop the breaker since it is all running off one lame wall outlet. The rack (600W when loudish and vacuuming) + vacuum cleaner (750W per label) + 8 flourescent tubes (240W) in the kitchen all at once (apparently on the same circuit) will do it.

My idea is that at some point the room stops cooperating (smaller room = lower ultimate speaker levels). That would be well above the levels shown in the graph.

The measurement I made is just daytime next-disc-in-the-rotation background while I sit here looking for the next point with which I can trip you up. I hear all the music and some of the subtleties.

I guess I like the "big" sound, room-filling, even if it is filling it gently.

A more typical loudish Beer Saturday session might measure 105dB SPLz peaks, 80-85 slow. That's about my (or my room's) limit.

The amps have 7 bias levels (I think) for their simulated Class A operation. Usually they are on level 1 (100W idle draw each) or 2 (150W), level 3 or 4 when loud loud, I may have hit 5 (maybe 500W draw) of 7, but that's a lot in a 15x19x9 room. I've seen 140F on the heat sinks at such a time. That's getting warm. Don't need it here.

I couldn't max them out, not enough wall juice.

I know, the amps aren't green. I bought shares in TECO to pay the electric bill with the dividends, now they have sold themselves to a Canadian Utility. Interestingly, the gain on that sale will pay for all of my equipment purchases. I considered Solar, which is a good idea, but did that instead. There is green, and there is green.

The next ones will probably be the new efficient things. But, these are paid for, and have sort of paid for themselves.

If you have to turn it up loud to hear "everything", something's wrong. I'm not running a disco here, anyway.

My thought on digital replay is to (often) have the room levels match the levels on the CD - stick a mic in the air and monitor that, and pull the unequalized preamp Zone 2 feed (after a little calibration - level 40 on the preamp and 25 on the soundcard gain) and monitor that, and compare.

Like this:

My Audio Philosophy (that's another thread) is accuracy (in the room at the listening position) to the source.

I'm working on it.

If something doesn't match between air (top) and source (bottom), I go hmmm... The top is the room, 50Hz dip (listening position) , 220 (dipole) dip appear above.

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USB mics (like mine) have a lot of distortion bleeding from digital section into the analog.

Is that in the mic itself, or amenable to improvement via external means - improved power or isolation? Have you tried it? I don't have anything with which to try.

I realize it is irrelevant at higher measurement levels - making that assumption using "How Decibels Add". Like 80dB + 60dB = 80.1dB

I don't think any external treatment will help but I have not tried it. My sense is that the noise is bleeding internally from USB and digital logic into the ADC/pre-amp for the mic.

Your music SPLs are quite low.

Here's today's level, a little louder than yesterday...

I don't think any external treatment will help but I have not tried it. My sense is that the noise is bleeding internally from USB and digital logic into the ADC/pre-amp for the mic.

Here's a mod from the miniDSP forum...

Before

After

Mod

OK, that was internal mod, not external . But good to know.

BTW, my problem with UMM-6 is a lot worse:

For those not familiar with this graph, I am showing the spectrum captured from the USB mike without the system playing anything. Those regular spikes after the 1K blue line are all harmonics of that frequency which tells me they are induced by the microphone circuit.

Fortunately for the typical acoustic measurements this doesn't matter.

Averaged 1/6 octave noise floor noon vs 6am

dBA remains the same at 37
dBZ drops from 60 to 50

I hope this isn't too far off topic but I have a question about DR spec. I've notice many amp manufactures list a DR spec. However I've noticed that the DR specs seems to be helped a little with lower gain amps. If that make any sense. How does the amp's gain affect the DR spec measurement. My guess is that lower gain amps can usually report a better DR spec than higher gain amps. Is there any standardized method to reporting the DR spec with regard to amps?

The ultimate dynamic range of an amp is going to be dictated by 2 things; the noise floor and the maximum output voltage. The lower the noise floor and the higher the output, the wider the dynamic range. I would typically expect that lower gain amps will have a lower noise floor, although this is a generalisation.

Obviously a whole bunch of Factors come into play here. You will get a better result if A weighted, but it might also hide low frequency issues and mains hum pick up. You'll get variable results depending on how much distortion is allowed (ie what is maximum volume?).

Interestingly my ncore amps specs also state a 2.83v (nominal 1 watt) output DR along with a high power rating.

As for testing standards I'm not sure.

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I think a good idea, and one you see reasonably often is to give a noise spec relative to the 2.83 volt. You can work out from there a reasonably close number for total dynamic range. It also is useful for comparing amps in your given system with your given speakers. If two different amps have enough or more than enough to play your speakers at satisfying volumes, your effectively realized DR will be better with the one having lower noise at 2.83 volts. A more powerful amp that perhaps never gets all of its power used might have a better total spec, but one you may never take advantage of. Of course plenty of good amps have such low noise it for the most part simply isn't a problem.

Also, I'll plug it one more time. You guys should listen to my DAC preference files. One of those DACs only has a 75 db SNR. It isn't as noticeable as you think it is. Another only has 84 or so db SNR. The remaining DACs are all over 100 db. Could you rank them lowest to highest SNR just by listening? I would do another poll just on that basis. Either by adding noise to a clean file or using different pieces of gear. Except no one bothers with listening. So I won't waste my time.

A corollary to the opposite side of how quiet is quiet would be how noisy is enough to detract from musical enjoyment?

Academic investigation (sorry don't have the info as a citation) indicate the ear has an instantaneous dynamic range of only 60 db. Other preference testing indicates that barely audible noise results in a preferred quality estimate by blind listeners for upper midrange and treble when compared to a truly quiet noise free playback. This fits with people's preference for LP.

I think of my friend's high quality LP rig. With good quality clean vinyl can you hear surface noise? Well yes, but barely at normal to slightly loud listening levels. If you ask can I hear it at the start of a disc before music starts, I can cock an ear and a couple seconds later say yes I can hear that. However, it is low enough I would never be bothered by it nor on my own comment. Once the music starts it isn't intruding on anything. So complete quiet either isn't needed for musical enjoyment or may not help versus barely perceived noise.

Now lesser LP or 7.5 ips reel tape without noise reduction is another animal. Quietly asked, "Can you hear that hiss?" and me " What did you say? You have to speak over the hiss" or something like that with the volume turned well up. Yes that detracts.

My experience with fine vs pedestrian LP, reel tape vs Dolby C cassette on a Nakamichi, and with good FM tuner listening indicate probably 70-75 db is enough music is never harmed. Plus few recordings have that low a noise in the venue. Lower noise levels aren't really a great need unless you still listen on K-horns or something similar. Even frequency response and low distortion rank higher than getting noise below -75 db.

I hear the noise floor of my Reel to Reel recordings and it has a S/N of 80 db. I also hear grove noise very frequently when it doesn't seem to be heard/bothering others.

Lots of RTR gear of old at 7.5 ips was only around 60 db for SNR and that was probably allowing for some pretty high levels to get it out of the mid 50's. 80 would be something I might hear, and yet not care about.

I think a good idea, and one you see reasonably often is to give a noise spec relative to the 2.83 volt. You can work out from there a reasonably close number for total dynamic range. It also is useful for comparing amps in your given system with your given speakers. If two different amps have enough or more than enough to play your speakers at satisfying volumes, your effectively realized DR will be better with the one having lower noise at 2.83 volts. A more powerful amp that perhaps never gets all of its power used might have a better total spec, but one you may never take advantage of. Of course plenty of good amps have such low noise it for the most part simply isn't a problem.

Also, I'll plug it one more time. You guys should listen to my DAC preference files. One of those DACs only has a 75 db SNR. It isn't as noticeable as you think it is. Another only has 84 or so db SNR. The remaining DACs are all over 100 db. Could you rank them lowest to highest SNR just by listening? I would do another poll just on that basis. Either by adding noise to a clean file or using different pieces of gear. Except no one bothers with listening. So I won't waste my time.

I have been trying for days to get round to doing your listening tests, but other things have kept me busy . Can you give another week before providing results to give me a chance to listen?

I have been trying for days to get round to doing your listening tests, but other things have kept me busy . Can you give another week before providing results to give me a chance to listen?

Sure, not like there is a stampede on this.

I worked for a company called Racal Acoustics in their research and development department many years ago. They made communications equipment for the military.
It was known then that perception of loudness was frequency dependent.
A further issues was that we come to expect particular combinations of sounds and interpret meaning from them without actually dissembling the message in our brains and extracting the information that is presented.
A popular demonstration of part of this process is the McGurk effect; this relies on visual stimulus.
In fighter aircraft and tanks for examples the visual stimulus is missing but the brain still interprets rather than analyses and in such noisy environments errors are easily made.
The bit that made me smile was remembering a procession of females arriving at the labs to have their voices recorded, appropriate noise added and these signals transmitted to various transducers set in flight and tank helmets. How a fighter pilot ever understood a word that was said to him astounded me.
I’ve often wondered if we ‘interpret’ rather than analyze when we listen to music.

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