Dynamic Range

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published: Aug-23-2015, last edit: Dec-14-2019

Various aspects about Dynamic Range, noise and distortion in the real world

Dynamic range & DR ratings

The dynamic range of equipment is the difference in highest not distorted amplitude and lowest possible amplitude that does not drown in the noise floor. Such a dynamic range can easily exceed 90dB for most electronics. Higher quality (lower noise higher resolution) gear can exceed 120dB.
The dynamic range of our hearing can exceed the range of most electronics in an absolute sense but won’t in a practical sense. This is explained further below.
Then there is the dynamic range as used in the DR database.
This number shows the difference between peak and average levels but does not say anything about the small details and nuances that are embedded in the recording. I don’t think one should generalize that a higher number is better sounding but there is at least some correlation because of the recording techniques used.

In the DR database you can find out how ‘good’ the Dynamic Range (DR) of an album, (re)release, or song is and hang a ‘sound quality’ label on it. The higher the DR rating the better it sounds… but does  it ?
Sure … in lot of cases this may well be the case where ‘loudness madness‘ has been taken on annoying levels BUT when done ‘properly/tastefully’ the lower DR recordings may well sound better for some albums.

DR is determined by evaluating the differences expressed in dB (deciBell) between the average SPL and the peak SPL of a recording/song.
So if a music signal doesn’t have much peaks exceeding the average levels by much or has been ‘clipped’ or been run through a dynamic range processor (set to work as a limiter only), then the Dynamic Range number can be very small one.
This doesn’t mean per definition a low DR recording sounds bad or compressed.
This is because together with limiters/compressors the sound engineer can also play with EQ and other ‘trickery’ to mask the detrimental effects.
These dynamic range/clipping adjustments are done for each recorded ‘channel’ separately though and NOT once the album has been mixed. A normal recording consists of many tracks of individual ‘takes’ that have been done over the coarse of time. It is very possible that some of the people playing/singing on a song actually never even met.
Usually the mixing process in a studio takes much longer to complete than the actual recording sessions together, this process of ‘fine tuning’ and mixing the separate tracks of the recording to one stereo image with good sound quality takes a lot of time.
To get a small glimpse of what producers have to toy with and actually do use to ‘faff around with’ in order to change recorded instrument(s) or vocal(s) just to get it to sound ‘better’ is shown in these video tutorials.
Now try imagine how ‘real’ most of the recorded albums out there really are.

The DR number says absolutely NOTHING about the difference in level between the softest and loudest part of a recording.
The difference between the loudest and softest signal is basically the REAL dynamic range of a recording and NOT the DR rating.
So a DR8 rated recording may well have signals present as low as -80dB (random number picked here) and a DR20 recording may also have meaningful signals as low as -80dB where the only ‘difference’ expressed in the DR rating is another ‘average’ signal level compared to the peak level and NOT the dynamic range of the smaller signals.
Of course for a lot of the poorer DR8 recordings out there noise floors and compressors lifting softer signals to higher levels to reach a more ‘realistic’ sound at LOWER listening levels COULD be an indicator for poorer quality recordings.

IGNORE the higher DR values for vinyl reproductions (and those claiming they sound more dynamic because of this).
In fact often the opposite is true in order to ‘write’ the huge dynamic ranges of digital recordings in the rather limited dynamic range of vinyl (and to an extend in analog tape) tricks like compression are used to make it fit and ensure the needle isn’t ‘launched’ out of its groove.
Of course this does not mean that vinyl or tape cannot sound more pleasant to some.
In fact to a LOT (if not most) audiophiles vinyl sounds much ‘better’ (read pleasant, less edgy).
A more accurate copy of the original master recording it is definitely NOT despite what vinyl nuts claim/say.

Of course, to us music lovers, and above all fidelity whores, you can still hear obvious differences between a recording without any (obvious) processing and those that have been ‘squashed’ to satisfy the larger crowd (consumers of background music).

DR, however, has nothing to do with the differences between the smaller recorded signals (details, fine nuances) like the decay of instruments and subtle clues or soft background sounds.
Those fine nuances do not need to be ‘compressed’ at all when limiting has been applied and are thus not reflected in the DR rating at all.

I think the recording quality is more important than the numbers produced by an analyses program and also more important than the format it is delivered in.
With format is meant carriers like vinyl, tape, CD, DVD, DSD, various lossless and lossy formats.
Most of the sound quality is determined by the recording and mastering, that is when the reproduction (playback) chain is top notch quality.

clipping and compression

Limiters simply ‘clip’ (or sometimes soft-clip by rounding the signal off a bit) high peaks.
Depends on the settings and the level of the original peak(s).  This can result in  distortion levels in many degrees, ranging from inaudible to downright nasty.
Below an example of a ‘hard-clipped‘ signal overlaid by the (non-clipped) original signal. It is easy to see that the clipped signal is missing the top and bottom but otherwise looks the same.

Compressors can be set to work as a limiter too and thus only compress the louder levels.
This (non-linear) dynamic compression sounds somewhat more pleasant than hard clipping in general.
Compressors can also be used to compress the entire dynamic range. Thus lowering peak levels and amplifying the softer levels.
Below an example of ‘soft-clipping’ where the peaks of the signal are more rounded off which sounds less ‘harsh/sharp’ than when hard-clipped.

In this case, a decay after a note lingers on longer and softer passages, that would not be audible anymore as they would be below the audible threshold, will become audible again at lower listening levels.
Strangely enough most people will find compressed recordings more natural and detailed sounding than a real dynamic recording at LOWER listening levels.
The reason for that is simple… you hear more nuances as these are amplified and thus you hear it better.
So… dynamic range and how it is perceived ALSO highly depends on how loud we listen.

If recordings of a live event have had no processing (Jazz at the Pawnshop is an example) they will sound ‘more real’ at higher listening levels. Or should I say realistic listening levels of about the same magnitude as when recorded,  than at lower levels.
At lower listening levels, which is better for your hearing by the way, small details will drop below the audible threshold.
When compressed (evenly compressed, not like soft-clipping) those inaudible signals at lower listening levels now will be audible again and will contribute to the sound being perceived as more natural/better.

I should also clarify that dynamic range compression (thus making amplitude differences smaller) has NOTHING to do/in common with compression of data as in lossy audio files.
These are totally different things audibly and technically, yet many people will say MP3 sounds ‘squashed’ as in dynamically compressed, yet in reality the dynamic range of the actual analog wave-forms has not been altered at all.

dynamic range of human hearing

Then there is the dynamic range of human hearing.
There is a lot of misunderstanding and above all misinterpretation on this subject.
Yes, (young) ears can detect signals below 0dB SPL in a really silent an-echoic room… when someone has been in that room for a while and ‘climatized’. For 3kHz tones limit lies about 6dB below 0dB SPL (thus -6dB SPL).
And yes, when someone fires of a round you can hear SPL’s well above 130dB above which point it is painful in a not subtle way.
So one can actually ‘say’ the dynamic range of human hearing is around 135dB without telling lies.
There is some more INFO on listening levels HERE

Here’s the thing though… once you are in that quiet room and can hear those small signals you really don’t want to fire a gun or start to jackhammer in there.
Nope even 80 to 90dB SPL will sound extremely loud once you ‘adjusted’ to total silence.

Likewise if you have been to a really loud show or club and have been standing fairly close the the speakers for quite some time and have been enjoying the loud music (without feeling the need to plug your ears that is) and you step outside again, you may have noticed how quiet the world around you has become. Traffic noises you would normally hear quite well are MUCH softer or perhaps even be completely inaudible.

This is because the ears have made themselves less sensitive to cope with the high SPL.
In reality the dynamic range is thus smaller than the possible 130dB you will find in literature as ‘the human dynamic range’.
About 30 years ago I wanted to know and built this attenuator which can be set to -120dB, see picture below.

Reason for building it was the talk of the ‘limited’ dynamic range of the, then still rather new, CD technology which was said to be poor.
I wanted to find out about my own audible limits for dB levels for myself.

When listening to max SPL on excellent speakers at almost uncomfortable levels. You know.. when you crank up the volume to the max and can only handle that for a very short time.
I could reduce that level to the pre-set amount of attenuation by a flip of the switch.
To my surprise it turned out that when those VERY loud levels (almost clipping levels of high power amps) already became completely inaudible when the attenuator was set to -80dB.

What does this mean ? Well it means that for reproduction of music, in practice, it will be hard (impossible) to hear signals that are down -80dB above peak levels when playing tremendously LOUD. Did I not reach SPL levels exceeding 100dB SPL ?
The SPL level meter (set to register peaks) sure did and registered just below 110dB (at listening position about 2.5 meters from the speakers).
The point is that in a very quiet room you hear… well… nothing it sound quiet to me aside from a ticking clock or some of the other faint noises in a normal house.
BUT the SPL of such a room may still be around 20dB or even 30dB yet you don’t hear it as sound or noise at all.
Human hearing does have a lower audible threshold under very quiet conditions but listening to music loudly with ‘quiet’ passages is NOT the same condition as a very quiet acoustic anechoic room.

Logic tells me we should thus not be worried about noise floors of even the cheapest DAC’s nor harmonic distortion levels that remains below -80dB.

Fortunately you don’t need a calibrated attenuator you can just use this youtube video
to check for yourself. Set the volume so your system starts to distort or you dare not to go louder and then start the video. Don’t touch the volume control after you started the video.
Any distortion below that number is actually all you need (not actually true but close to it). Better numbers are not needed. When you want to know the distortion number in percentage look here.

Another interesting test is to play the start of the video at your normal listening levels and see at which attenuation you don’t hear anything any more. That is the actual dynamic range you have.

Limits of recordings

Then there is the noise floor of recordings.
Recording studios have a noise floor that appears to be quiet when in there but are quite measurable still (typical 10-25 dB SPL).
Microphones can easily pick that up and do so. Some studios use noise gates which effectively mute signals when they drop below preset levels creating a low noise floor in quiet passages. Using them wrong can result in a decay being ‘cut-off’ while still being quite audible.

Then there is the microphone pre-amp and/or mixing console that adds noise.
On top of that several tracks are mixed increasing noise BUT not as much as one would think.
The reason for that is the random nature of noise.
Multiple (audible band) noise signals will add, but also cancel out at the same time for different frequencies over the entire audible range.
When we ‘add’ the exact same signal 4 times the total signal output (which always has the same amplitude and phase) will thus increase 4x = +12dB and thus be perceived as somewhat more than twice as loud.
The noise, which is random, however does NOT increase 4x but but 2x (6dB) because the noise is NOT in phase and parts cancel out where other parts (partially) add.

This ‘trick’ is sometimes used by paralleling active (and noise introducing) components on the input of very low noise amplifiers.
The multiple input stage signals are and thus the ‘wanted signal’ is increased MORE than the noise generated by each input stage.

Anyway.. what’s important here is that the noise of the recording is usually MAGNITUDES higher than that of the actual DAC and mostly also of that of (decent) amplifiers. Certainly when microphones are positioned further away from the recorded instruments and no noise gates are used. Think live recordings, classical music etc.
Case in point … when you listen to recordings with quiet passages you can, more often than not, when noise gates are NOT used, hear noise during the softer passages. Stop the playback and the noise is gone as well, start it again and noise is quite audible in those soft passages.

Yes, the music signal is (often) physically muted in a lot of DACs but the amplifiers and analog stages behind that source will still ‘hiss’.
Obviously this is much lower than any recording (with decent equipment) and (should) be inaudible but not not measurable.
It should be below the audible threshold in your playback chain and is also often far below the background noise of an average (listening) room.
When you put your ears against the tweeter of your speaker chances are the noise floor of your system may be audible.
When you hear nothing even with the ear against the speaker and the volume control open you have a VERY low noise audio system !

The interesting thing is that some feel a noise floor is also the actual audible limit which is true in FFT plots.
In reality a noise floor of a microphone recording can be as high as -60dB when measured. Yet, tones with signal levels BELOW that -60dB noise floor (and thus still reproducible by a DAC) can still be heard by trained listeners.
A music signal is very complex though and when that is under or below the noise level nothing much can be heard though.So yes, humans can hear individual ‘tones’ below a noise floor (think Morse code decoders in the old days) but cannot detect ‘usable’ information for music any more. A noise floor of vinyl, tape etc is pretty much the end of the line for any recorded musical signal.

Those ‘small micro-dynamic’ signals you hear… those subtle clues they are not -100dB or even -130dB down in level. This seems to be a popular believe though.
Nope those just barely audible finest details are down -50dB or perhaps -60dB at the MOST.
In vinyl recordings this could be -40dB to -50dB because those small signals are ‘lifted’ in level so they don’t drown in the surface noise of the album.
This means that small details are MORE audible on vinyl pressings and thus vinyl lovers say you hear ‘more’ on vinyl and thus the dynamic range is bigger when in reality … the dynamic range is actually smaller (very lightly compressed)

Fast Fourier Transient

Another favorite piece of evidence are FFT plots.  They pop up everywhere in forums  and show when a tone is reproduced some harmonics (and when 2 tones are used also inter-modulation products) are added that reach certain levels.
For ‘poles’ up to -70dB you would expect to be able to say: well those peaks are below -70dB so are inaudible.
Even more so when the peaks only reach -80dB or lower.

The plot below shows that harmonics are added. The original tone (the spike at 1kHz), when pure and not distorted, will be the only frequency (shown a s a spike)  that would be present. Non linearity in the amplifier create (add) harmonics which are multiples of the fundamental tone which is also called the first harmonic. In this case 2kHz (2nd harmonic) and 3kHz (third harmonic) are louder than the noise floor of the ADC used. The ‘distance’ between the top of the 1st harmonic (1kHz) and 2nd harmonic (2kHz) is about 50dB. One would assume this would be audible and when listening to a pure tone it may well be.
BUT in real instruments the harmonics they create themselves are magnitudes higher and often even higher than the fundamental tones themselves so these (much smaller) harmonics are thus ‘masked’ (in other words heavily overpowered) by harmonics of natural instruments.

So harmonic distortion may be very measurable but also not audible as those relatively small harmonics are added.
Well of course there’s a little catch there…. you see music does NOT contain a single or just 2 tones in a certain ratio like test signals but has a very wide spectrum of countless signals. Even in  not complex acoustic music with just 1 or 2 instruments.

Each ‘tone’ not only has harmonics (multiples of the original frequency) being created/added by an amplifier but when multiple tones are present ‘intermodulation’ products as well. InterModulation Distortion  (IMD) products are tones that consist of the sum and difference between those signals.
Those ‘products’ are NOT related to harmonics of the recorded instrument but are ‘out of tune’ and are possibly NOT masked by real world harmonics in a lot of cases.

The added harmonics by non-linear behavior of an amplifier (harmonic distortion)  also are responsible for the IM products.

Yes, all the individual ‘poles’ that are ‘generated’ by all those different frequencies present in music will be all over the entire audible spectrum.
And yes, the music signal will mask those harmonic signals when music is played as their level is magnitudes higher. BUT the IM products will sometimes (often ?) NOT be masked by the music and may become audible in forms of noise or dissonant sounds or ‘a not natural edge’

So we assume that -70dB ‘distortion’ poles are below the audible limit we and we are home free of audible distortion.
lets add another 10 dB just to be ‘safe’ so -80 dB
Alas, here too there is this problem that isn’t very obvious from those FFT plots with test signals.

A test signal with 1 tone could show some ‘spikes’ that will remain below -80dB.
A test signal with 2 tones will show a lot more spikes which also remain below -80dB.
So one assumes those spikes (frequencies with a level of -80dB) are still inaudible.
Alas, the thing is music signals consist of many more signals than just 1 or 2 single ‘pure’ tones.
Yes, even a flute or other single instrument will have multiple signals, consisting of a fundamental and LOTS of harmonics.
All of them large amplitude signals generate lots of ‘poles’ (but each not exceeding -80dB) so we are still safe right ?
No… wrong conclusion and that’s because of the way we ‘hear’ and the frequency bands where these ‘poles’ are. The ‘sum and difference’ poles mostly.
These poles can be everywhere in and outside of the audible range and below and above the recorded frequencies.

Lets assume a lonely bass being played slapping a riff of notes.
Many different fundamentals and overtones will be there at the same time and generate a multitude of ‘poles’ all over the frequency range (harmonics will be masked, IM products NOT).
When looked at with the FFT one would see huge amounts of high amplitude poles which represent the fundamentals and overtones. The higher we go up in frequency the smaller the poles will be in amplitude.
These will surely ‘mask’ any poles generated by distortion and thus not be audible.
BUT there will be a lot of poles (all < 80dB) there that are NOT masked by the harmonics of the played bass higher up in the frequency spectrum.

All There’s the snag…. while the poles all have energy below -80dB these poles ‘add’ in the same way as the noise adds as they are not equal in phase nor amplitude.
These ‘poles’ which will be close to each other of -80dB peak all will add in the ‘noise way’ as they do not have the same frequency and phase.
They basically become an increased noise floor thus in essence, as all these ‘poles’ close to each other create a higher noise floor.
When just 4 ‘poles’ are close together and ‘add’ the total signal level will increase by 6dB
When 10 ‘poles’ close together are ‘added’ then the total signal level will increase by 10dB
When 100 ‘poles’ close together are ‘added’ the total signal level will increase by 20dB
When 1000 ‘poles’ close together are ‘added’ then the total signal level will increase by 30dB… etc.

So while individual ‘poles’ may appear to never reach audible levels, as they are all below -80dB, and thus inaudible in theory the actual ‘energy’ in a narrow frequency band is far above the the fundamentals we want to hear may have increased to -70dB or even -60dB. This is because the energy of each ‘pole’ adds like noise does.
These IM frequencies are not masked by the fundamentals nor overtones as they are too far away in frequency bands compared to the ‘wanted’ frequencies.
As our hearing ‘cuts’ the audible range up in frequency bands as acoustic energy in ‘not by the music used’ bands may become audible IF the total energy in such a ‘human band’ reaches audible limits. .
So when distortion plots show distortion spikes up to -70dB which one would assume may just be on the edge of audibility this may still be problematic as the actual amount of distortion spikes can become enormous and all add. Think -60 or even -55dB which IS audible.
Of course it also depends on how high the ‘order’ of the generated harmonic spikes go up and how many (much more audible) inter-modulation products are present.

So … let’s assume the actual system noise floor (NOT talking about the recording noise floor) can be increased by 10 to 20dB and we have a look at those nice FFT plots to ascertain what is audible we must realize that under certain circumstances the music signals will NOT mask ‘generated’ poles in certain bands and have the potential to become audible.
let’s thus build in a margin of say 20dB below -70dB which is -90dB and add another 6dB as safety margin.
That would mean that no ‘poles’ should exceed -96dB. At that point you are ‘safe’ and distortion products will remain below the audible threshold for SYSTEM generated noise and artifacts in a home hifi system setup even at high listening levels.

Also one should realize that the highest amplitudes of original signal produce the highest ‘poles’ and the amplitude of the ‘generated poles’ also lowers at lower levels so it may not be as bad as this theorizing assumes. Even -90dB poles (at 0dB) may thus be completely inaudible in real music signals unless the distortion of a DAC increase relatively at lower output levels where the MSB, 2SB and maybe even 3SB ‘topple’ in ladder (R2R) DAC chips.

Clipping will yield huge amounts of ‘poles’ and with a very high amount of harmonics as well and when multiple tones ‘clip’ at the same time things get really bad.

This can already have happened in the recording and thus NOT be removable ever again and gets worse by the reproduction chain as well. Let’s call this a poor quality recording. LOTs of those around by the way.
The reality of clipping, brick-walling , non linear dynamic compression and DAC’s being over-driven when non ‘bit perfect’ digital ‘words’ reach clipping levels of DAC’s may very well degrade the music quality more than one would expect based on FFT plots or THD/noise numbers alone.
This is because the actual waveform output is being driven outside of the DAC’s abilities and ‘hard clips’ with all its downsides being there in full glory.

Does this mean bit perfect is the only way to go ?
No, when digital EQ or volume control is used all one needs to ensure is that the analog waveform never reaches clipping levels of the DAC / output file.
Just don’t turn up your digital volume slider all the way (certainly not when using EQ or the ‘pre-amp’ function in digital equalizers and you will probably be ‘safe’.