Help me understanding Dynamic Range

[maruko]

Hello everyone, I love this forum and I am trying to learn how to read all Amir’s measurements, starting from the basics.

But nothing has caused me as many headaches as the concept of dynamic range, and I can’t seem to wrap my head around it by myself anymore. Having to also translate from English, there are still many points that aren’t clear to me.

I would like you to help me understand if my reasoning is correct and, if necessary, correct me on the bolded parts.

1. 116 dB is our best-case hearing dynamic range. Perhaps because the ear acts as a compressor of the dynamic range? Since the dynamic range of hearing is 140 dB (we can hear from 120/130 dBSPL down to -10 dBSPL) but this wide dynamic range cannot be perceived all at once. Is that correct?

2. 108 dB (18 bit) is the best-case scenario for music resolution. But, unless it’s computer-generated music, we must take into account the electronic noise from the recording microphone (16 dBSPL?), so 108-16 = 92 dB (15 bit). Is that correct?

3. The rule of thumb is that our audio devices should have a DR 10 dB higher than that of the music, so 108+10= 118 dB (19.6 bit).

4. The noise in my listening room is about 20 dBSPL, at best:

• But our ear is not a microphone, and since we perceive different frequencies at different levels, our threshold of audibility varies between 10 and -10 dBSPL, according to Fletcher-Munson curves, so some frequencies of this noise will be perceived at higher levels, and others at lower levels;
• However, shouldn't this is equally valid for the noise floor of a recording? Maybe the noise floor in a recording is made of the same frequency? So how can I calculate a difference in audibility between the noise floor of the listening room and that of the recording itself?
• Not knowing how to do it, I will consider it as 20 dBSPL, so 92-20 = 72 dB (12 bit).

5. Now that I have found that the DR I have left is 72 dB, how can I calculate an ideal maximum listening volume (meant as peaks) so that the noise floor of the recording stay at a level equal to or lower than the room noise level?
If I want to consider peaks at 110 dB (classical music), could I achieve this with a DR of 72 dB? Let’s see: 110-72 = 38 dBSPL.
38 dBSPL means the noise would still theoretically be audible, because it’s still 18 dBSPL higher than the room noise level (20 dBSPL). Unless I lower the volume of the amplifier to lower the noise floor level. Is this calculation correct?

6. However, in practice, this shouldn’t be an issue. In fact, we haven’t yet considered the masking effect of human hearing:
during peaks (loud sounds) in music, we are less sensitive to quieter sounds, therefore, the noise floor of the recording seen earlier (38 dBSPL), should not be audible when the music plays loudly. Right?

And what if the music plays at lower levels? For example, at 50 dBFS?
In this case, the remaining DR of 72 dB, at medium listening volumes like 60 dBSPL, should give us more than enough headroom, because the noise will still be at 60-77 = -17 dBSPL, well below the threshold of the room noise floor. Right?

Am I missing something?

 

[Purité Audio]

The background noise in your room is likely to be more like 30-35dB, I don’t think you have to fret about dynamic range, decent speakers transparent electronics that drives them properly, that’s it.
Spend some time acoustically measuring and make any necessary adjustments.
Keith

 

[maruko]

The background noise in your room is likely to be more like 30-35dB, I don’t think you have to fret about dynamic range, decent speakers transparent electronics that drives them properly, that’s it.
Spend some time acoustically measuring and make any necessary adjustments.
Keith

Sure, but hi-fi is my passion and I want to fully understand how it works.

 

[ZolaIII]

It's range that recorded materials go up and down from what you set as program 0 in dB or LUFS (the same). We psy perceive ±12 dB as twice as loud or twice as quiet. Anything that's in residential noise you won't be able to hear it so we elavate program 0 above it to DR negative it might go. For the music depending of layers and complexity it goes up to 16~17 (there might be something with even more but I ain't aware of it at least out of experimental territory). For most moderate complex materials even 9 is fine and 7 is really, really minimum and still compressed. Some do under that trying to justify it with being for clubs and such with huge residential noise and programe 0 at 100 dB where well you won't be able to have or want high DR but that's wrong approach and usually pushed too hard and on commercially available materials for home reproduction which neither can or will go that high SPL. Other end is very wide DR of up to 24 dB like in Cinema THX standard which is for large cinema hals with huge speakers. Again it's a problem when such not adopted properly or at all hit commercial materials for home reproduction. Dialogues being set too low to peek DR and effects being too loud and then you apply limited compression gating so it's not hard to fix on the other side you can't regain DR (in a good way at least).

 

[NTK]

There are errors in your calculations. You are mixing ranges with absolute values in your calculations, for example:

2. 108 dB (18 bit) is the best-case scenario for music resolution. But, unless it’s computer-generated music, we must take into account the electronic noise from the recording microphone (16 dBSPL?), so 108-16 = 92 dB (15 bit). Is that correct?

Let assume what you wrote about 18 bit music resolution is correct, and it is equal to 108 dB. This is a range, and it doesn't necessary mean it has to be 0 dBSPL to 108 dBSPL, but it can also be 20 dBSPL to 128 dBSPL. In the former case, if the mic's self noise is 16 dBSPL, then the dynamic range of the recording is 16 dBSPL to 108 dBSPL = 92 dB. However, in the second case the dynamic range of the recording can still be 108 dB as the mic noise is below the softest part of the music (provided that the mic's max SPL is more than 128 dBSPL and after you have perfectly optimized the gains of your signal chain).

* Note: I did not account for masking level in the above. Often, if you have a broad band noise at, say 60 dBSPL, you may still be able to discern a single tone at 4 kHz at ~20 dB below 60 dBSPL.

 

[maruko]

However, in the second case the dynamic range of the recording can still be 108 dB as the mic noise is below the softest part of the music (provided that the mic's max SPL is more than 128 dBSPL and after you have perfectly optimized the gains of your signal chain).

Ok, got it.
But, this mean we can have music with 128 dBSPL peaks?

* Note: I did not account for masking level in the above. Often, if you have a broad band noise at, say 60 dBSPL, you may still be able to discern a single tone at 4 kHz at ~20 dB below 60 dBSPL.

Can you better explain this?

 

[Keith_W]

Can you better explain this?

If you are asking about "masking", simply put - one signal can be "hidden" (or "masked") by another signal under certain conditions. For example, a softer noise will be masked by a louder noise. Or one tone may be masked by another which is close to it in frequency. Watch this video to learn more.

 

[ZolaIII]

So, we can have music with 128 dBSPL peaks?



Can you better explain this?

No you can have more on PA and in nature and God help you with that (as you really don't want to). What you want instead is properly calibrated system with equal loudness compensation under and over the calibration point so you can have full DR even on moderate listening levels in generally above the normal speach level (60 dB) comfortable at home and without neighbours burning you out publicly. If you set it to 76 dB and DR is 12 it goes up 12 dB from that. You also want sources as normalised as possible that 0 dB set doesn't change. Best is the EBU R128 as it in acceptable margin of error for it (1 dB) with up to - 23 dB range can accomplish it even for mentioned THX cinema. And no it's not absolute to stay like that you can regain what you lost to average level of +11 dB in digital FP domain without introducing any noise to signal (because noise flour is so low beyond any theoretical audible range).
Edit: but you can't apply it your self to wasp mayorit of materials that you don't own. In EU it's low but not entirely integrated across whole EU. Various streaming services implemented their own based upon it with lower max - dB trying to justify it by both how they materials won't have higher DR anyway or how targeted devices won't work satisfactory with such large - dB correction. Of course they were wrong (as explained last before editing) and as a result we again have jungle out there instead unified 0 level.

 

[kemmler3D]

But, this mean we can have music with 128 dBSPL peaks?

In theory yes, in practice it would take a completely unreasonable recording and very serious speakers to do this.

Even the Genelec 8381 only does 126dB SPL, and they cost about $65K/pair.

As an aside, it's important to keep in mind the distinction between dB, dBFS and dBSPL, and other metrics that use dB.

dBSPL refers to an absolute air pressure pushing on your eardrum. dBSPL has a specific, real-world value as 0dB is defined as the quietest audible sound.

dBFS refers to a difference between the maximum value you can represent in a digital audio file (for 24 or 16-bit files, this should be 0dBFS) and another value, which is why it's always negative. 24 bit can go further negative (-144dB) than 16 (-96dB), it has higher dynamic range.

dB is just the logarithmic scale we use to measure sound and other signals, and so without a specific context only represents a difference between two values.

However, shouldn't this is equally valid for the noise floor of a recording? Maybe the noise floor in a recording is made of the same frequency? So how can I calculate a difference in audibility between the noise floor of the listening room and that of the recording itself?

It is and isn't equally valid for the noise floor of a recording. Recording engineers do various things to keep noise out of the recording, including noise-shaping during the mastering process, which shapes the frequency spectrum of noise such that it's moved into less audible regions, as you noted, it's not the same at every frequency. So the audibility of quantization noise in a 16-bit file is less than you would expect from a simple calculation. Noise from the recording itself may be audible or may be edited out.

The real answer is that if you are turning your music up loud enough to hear the noise floor - especially the digital noise floor - you are probably putting your hearing in danger. AFAIK The practical dynamic range of most music (except for very specific classical recordings) is more like 20-40dB, not 80 or 100dB.

 

[NTK]

Ok, got it.
But, this mean we can have music with 128 dBSPL peaks?

We need to understand what sound level readings mean. The recommended settings by NIOSH for the sound level meter is A weighting and slow response. A-weighting means we'll be ignoring much of the bass in the sound level measurement. So if some says the sound level is 90 dB, is it A-weighted? If it is, our recording mic may be recording higher sound level than what the "reported" sound level indicates.

Understand Noise Exposure

Learn how to measure workplace noise exposure and how to best monitor workers' hearing.

www.cdc.gov

Also notice that NIOSH recommends "slow response". That means the sound level readings are taken using a 1-second time constant for the time weight (exponentially weighted "averaging" with a time constant of 1 second, see the MATLAB documentation "Algorithms" section for the formula). Below is an example from the MATLAB documentation. It shows 4 curves. The red one is Lpeak, the peak instantaneous SPL of each segment of the audio being analyzed. The yellow curve Lt is the sound level. The blue curve Leq is the "equivalent continuous sound level", and the green curve Lmax is the max Lt of each segment. Notice that the sound level (yellow curve) is much lower than the max instantaneous peak (red curve), which, in the example has a max difference of more than 20 dB. Therefore, even if someone reports a sound level of 80 dB(A), when using the standard settings, the actual absolute peak sound pressure levels that the mic records will probably be much higher. This MATLAB example show an "equivalent continuous sound level" Leq of about 63 dB, max Lt of ~69 dB, but with max SPL peaks at ~95 dB.

https://www.mathworks.com/help/audio/ref/splmeter-system-object.html

 

[DVDdoug]

It's hard to make hard-and-fast rules because there are so many variables, such as the relative characteristics & spectrum of the signal and noise, and the Fletcher-Munson curves,. and probably more.

Really the issue comes down to, can you hear background noise or not when there should be silence? The "specified" dynamic range or signal-to-noise ratio doesn't really come into play at low levels or silence when the signal is low or non-existent. And that depends on the sensitivity of your speakers (or headphones), how close you are to the speaker, and how much background noise there is in the room, etc.

It might be enlightening for you to do an experiment in Audacity - Open a file in Audacity and listen your normal listening level (or extra-loud if you wish). Use the Audacity's Amplify effect at -10dB (to attenuate instead of amplify). Repeat that 10dB at time until you hear nothing. By -60dB you might still hear something, but probably not at -80dB. In the analog days, 60db was considered good and the ACX audiobook is "room noise" at -60dB or better.

116 dB is our best-case hearing dynamic range. Perhaps because the ear acts as a compressor of the dynamic range?

I'm not sure if it's compression but we do get a temporary threshold shift (temporary.... hopefully temporary... partial deafness after being exposed to loud sound). Compression would be a little different because we could still hear a quiet sound following the loud sound.

(we can hear from 120/130 dBSPL down to -10 dBSPL)

I think 0dB SPL is based on the threshold of hearing. And the only place on earth that's 0dB or lower is an anechoic chamber so you're never going to hear any "signal" near 0dB.

2. 108 dB (18 bit) is the best-case scenario for music resolution. But, unless it’s computer-generated music, we must take into account the electronic noise from the recording microphone (16 dBSPL?), so 108-16 = 92 dB (15 bit). Is that correct?

Musical dynamic range (or "dynamic" contrast") can be defined in different ways. Often it's calculated as the ratio between the RMS level and the peak level. (Since decibels are logarithmic, the difference is a ratio.)

The actual sound (like a plucked string) can fade-out into pure silence and that would be infinite dynamic range, unless we consider when it fades to where it's masked by the noise or just becomes too low to hear.

Any digital audio can actually have infinite dynamic range. Digital silence is minus infinity dB. But when it's converted to analog, the DAC (and amplifier, etc.) will have some analog noise. At 8-bits you can hear quantization noise, especially at low levels, but quantization noise doesn't exist with digital silence (when there is no signal). At 16-bits or better and normal listening conditions you can't hear it.

4. The noise in my listening room is about 20 dBSPL, at best:

At best... in "soundproof" studio.

 

[kemmler3D]

Compression would be a little different because we could still hear a quiet sound following the loud sound.

I think our ears actually work a lot like a dynamic compressor with a low threshold, (I dunno, 0dB SPL?) ~0ms attack, short release (10-20ms?) and... 5:1 ratio? (10db ~ 2x perceived loudness?)... you can't hear a quiet sound DURING a loud sound but as you note, you can hear it afterwards.

So I wouldn't say the auditory system is exactly like a compressor, but what we hear does not have a 1:1 relationship with the energy reaching our ear, and garden variety dynamic compressors do provide a good analogy IMO.

 

[MaxwellsEq]

Hello everyone, I love this forum and I am trying to learn how to read all Amir’s measurements, starting from the basics.

But nothing has caused me as many headaches as the concept of dynamic range, and I can’t seem to wrap my head around it by myself anymore. Having to also translate from English, there are still many points that aren’t clear to me.

I would like you to help me understand if my reasoning is correct and, if necessary, correct me on the bolded parts.

1. 116 dB is our best-case hearing dynamic range. Perhaps because the ear acts as a compressor of the dynamic range? Since the dynamic range of hearing is 140 dB (we can hear from 120/130 dBSPL down to -10 dBSPL) but this wide dynamic range cannot be perceived all at once. Is that correct?

2. 108 dB (18 bit) is the best-case scenario for music resolution. But, unless it’s computer-generated music, we must take into account the electronic noise from the recording microphone (16 dBSPL?), so 108-16 = 92 dB (15 bit). Is that correct?

3. The rule of thumb is that our audio devices should have a DR 10 dB higher than that of the music, so 108+10= 118 dB (19.6 bit).

4. The noise in my listening room is about 20 dBSPL, at best:

• But our ear is not a microphone, and since we perceive different frequencies at different levels, our threshold of audibility varies between 10 and -10 dBSPL, according to Fletcher-Munson curves, so some frequencies of this noise will be perceived at higher levels, and others at lower levels;
• However, shouldn't this is equally valid for the noise floor of a recording? Maybe the noise floor in a recording is made of the same frequency? So how can I calculate a difference in audibility between the noise floor of the listening room and that of the recording itself?
• Not knowing how to do it, I will consider it as 20 dBSPL, so 92-20 = 72 dB (12 bit).

5. Now that I have found that the DR I have left is 72 dB, how can I calculate an ideal maximum listening volume (meant as peaks) so that the noise floor of the recording stay at a level equal to or lower than the room noise level?
If I want to consider peaks at 110 dB (classical music), could I achieve this with a DR of 72 dB? Let’s see: 110-72 = 38 dBSPL.
38 dBSPL means the noise would still theoretically be audible, because it’s still 18 dBSPL higher than the room noise level (20 dBSPL). Unless I lower the volume of the amplifier to lower the noise floor level. Is this calculation correct?

6. However, in practice, this shouldn’t be an issue. In fact, we haven’t yet considered the masking effect of human hearing:
during peaks (loud sounds) in music, we are less sensitive to quieter sounds, therefore, the noise floor of the recording seen earlier (38 dBSPL), should not be audible when the music plays loudly. Right?

And what if the music plays at lower levels? For example, at 50 dBFS?
In this case, the remaining DR of 72 dB, at medium listening volumes like 60 dBSPL, should give us more than enough headroom, because the noise will still be at 60-77 = -17 dBSPL, well below the threshold of the room noise floor. Right?

Am I missing something?

If you want to learn more, start with studying noise. It's a genuinely fascinating field and it will help you understand what's happening.

Many noise types are random. This is a very important point. As an example, if you measure the noise in your room over the space of a minute, you might get a figure like 30dB. But, instead if you measured it every nanosecond, you would discover a wild ride of level and frequency variations. As a result, a noise floor is not solid like concrete but actually a bit "translucent" (we don't seem to have a good non-optic term).

 

[maruko]

Thank you all

Another thing I still don’t understand, in the context of measurements, Amir seems to consider SNR and DR as the same thing. So, say 126 dB DR = 126 dB SNR.

Why is that? What's the difference?

From what I understand, in digital domain, DR takes into account some additional headroom (up to the point of clipping). But maybe in the context of Amir’s Analog measurements, we can consider both as the same thing?

All I know so far is:
- DR: the difference between the loudest sound (just before clipping/distortion) and the weakest sound (just above the noise floor)
- SNR: signal power over noise power
- in digital audio domain there seems to take into account a 1,76 dB constant? So say CD DR 96 dB = 98 dB SNR?

 

[ZolaIII]

SINAD is THD+N% but in dB. SNR it what it name says and theoretical range in the signal is limited by noise so that's DR in given context. Clipping is where it says don't butcher me anymore by it's name, compressing until it gives up and voltage collapses while you get toast (not really with deacent protection regarding circuits but that doesn't mean you won't blow up your tweeters for example). So you hard attend not too and it's full swap or prime tone to second harmonic depending where it is. 1 KHz is taken purposely as baseline because performance there would be best and it entirely correspond to how our hearing sensitivity is (again equal loudness compensation). Thing you need to understand badly is 0 for DR is program dB you set your self and how and with which it's influenced perceptualy, musicaly, physically... and it will take time and effort so go easy.

 

[Lambda]

But, this mean we can have music with 128 dBSPL peaks?

Live Sure.

Music: how loud is loud? (video)

Here is a much needed video on the topic of how loud we really listen to music. And issues related to hearing damage, etc. It is an argument that seems to come up twice a day since I started testing headphones. Here, I review the literature on true dynamic range of music and considerations...

www.audiosciencereview.com

116 dB is our best-case hearing dynamic range. Perhaps because the ear acts as a compressor of the dynamic range? Since the dynamic range of hearing is 140 dB (we can hear from 120/130 dBSPL down to -10 dBSPL) but this wide dynamic range cannot be perceived all at once. Is that correct?

Where you get this 116 number from?

"but this wide dynamic range cannot be perceived all at once."
but like in real live some music or can start low and become loude soddenly or over time or vice verse.

So if you don’t want another channel to automatically control volume...

Also you can easily have a 15-20Hz Signal with 130dB for a super shot time. And you won't perceive it as loud at all.

So in your example. if you want to play 2khz at -10dB SPL followed by a single 20Hz halve wave at 130dB it would need 140dB dynamic.

because it’s still 18 dBSPL higher than the room noise level (20 dBSPL). Unless I lower the volume of the amplifier to lower the noise floor level. Is this calculation correct?

Absolutely not.
Your Room Noise floor Amplitude alone dose not tell you anything.
Waht if your room noise is only at 19-20khz or between 1-10hz?

You can Hear pure tones well below the noise floor!

 

[NTK]

Another thing I still don’t understand, in the context of measurements, Amir seems to consider SNR and DR as the same thing. So, say 126 dB DR = 126 dB SNR.

Why is that? What's the difference?

From Audio Precision (the maker of Amir's analyzer):

Signal-to-noise Ratio (SNR), Dynamic Range, and Noise

Learn the differences between Signal to Noise Ratio, Dynamic Range, and Noise. Understand how these dB measurements characterize device amplitude ranges.

www.ap.com

 

[maruko]

Where you get this 116 number from?

Here on ASR, some review I don't remember which. Sometimes I read 115 dB and sometimes 116 dB. But I don't understand how it is calculated.

"but this wide dynamic range cannot be perceived all at once."
but like in real live some music or can start low and become loude soddenly or over time or vice verse.

So if you don’t want another channel to automatically control volume...

Also you can easily have a 15-20Hz Signal with 130dB for a super shot time. And you won't perceive it as loud at all.

So in your example. if you want to play 2khz at -10dB SPL followed by a single 20Hz halve wave at 130dB it would need 140dB dynamic.

So 130 - (-10) =140 dB DR. But, are you talking about single tones? What about music?
So, at the end of the day, what is our instantaneous human hear dynamic range in music? Since during loud sounds we can't hear very quiet sounds?

Your Room Noise floor Amplitude alone dose not tell you anything.
Waht if your room noise is only at 19-20khz or between 1-10hz?

Well, I can hear residential sounds, voices, cars, birds, coming from outside my home. I think what I hear should be in the 1-4 kHz range if I can hear it closed in my listening room and if we are most sensitive in this range. At least, I believe. I'm learning

 

[maruko]

From Audio Precision (the maker of Amir's analyzer):

Signal-to-noise Ratio (SNR), Dynamic Range, and Noise

Learn the differences between Signal to Noise Ratio, Dynamic Range, and Noise. Understand how these dB measurements characterize device amplitude ranges.

www.ap.com

View attachment 437391

Very nice, thanks.

And, what about this:

- in digital audio domain there seems to take into account a 1,76 dB constant? So say CD DR 96 dB = 98 dB SNR?

 

[NTK]

Very nice, thanks.

And, what about this:

Please refer to this:

https://www.analog.com/media/en/training-seminars/tutorials/MT-001.pdf