General question on dynamic range and music

[Jochen]

Crest factor and dynamic range are fundamentally unrelated. For example, here are 4 different waveforms, all of them have a dynamic range of 0 dB (no variation in the RMS amplitude when calculated using integer number of periods).

The sine wave has a CF of √2, the square wave has a CF of 1, the triangular wave and the sawtooth wave have CF of √3.

View attachment 284042

Sorry, but your definition of dynamic range is wrong ("all of them have a dynamic range of 0 dB (no variation in the RMS amplitude when calculated using integer number of periods)." It is defined as the ratio of the loudest signal to the quietest one. RMS is not part of the definition. It is impossible to have a dynamic range of 0, that would be no signal at all.

 

[Jochen]

Since the definition of dynamic range as the ratio of the loudest signal to the quietest one is very dependent on the selected windows, fade-in and outs and the like, there seems to be a better metric called "loundness range" (https://tech.ebu.ch/publications/tech3342). It takes into account the wings of the loudness distribution and is much more robust. An interesting article, dealing with it and also the loudness war: https://www.soundonsound.com/sound-advice/dynamic-range-loudness-war

 

[Cbdb2]

Another way to think about it. The MUSICAL dynamics are what the compressors are supposed to read and follow so they know how much gain reduction to apply. They use RMS detectors to do this but these are dependent on time constants. If you want to catch fast peaks you need a fast response but a fast response will also catch the tops of low freq waves and flatten them (distortion). Some comps have an auto setting for this but your milage will vary. Using compressors is one of the hardest things go get right when recording/mixing, there are many variables, its also one of the most important things and can make or break a recording. Thats why there are so many different types of compressors.

 

[NTK]

Sorry, but your definition of dynamic range is wrong ("all of them have a dynamic range of 0 dB (no variation in the RMS amplitude when calculated using integer number of periods)." It is defined as the ratio of the loudest signal to the quietest one. RMS is not part of the definition. It is impossible to have a dynamic range of 0, that would be no signal at all.

0 dB = 1

 

[Cbdb2]

Sorry, but your definition of dynamic range is wrong ("all of them have a dynamic range of 0 dB (no variation in the RMS amplitude when calculated using integer number of periods)." It is defined as the ratio of the loudest signal to the quietest one. RMS is not part of the definition. It is impossible to have a dynamic range of 0, that would be no signal at all.

A dynamic range of 0db means the volume is constant, so yea these signals have no dynamic range. Loudness is measured RMS (power) so its part of the definition.

 

[Jochen]

0 dB = 1

If you are talking about a single (test) tone, than maybe yes. But that is an artifically simplistic example, we are talking about music material

 

[Jochen]

A dynamic range of 0db means the volume is constant, so yea these signals have no dynamic range. Loudness is measured RMS (power) so its part of the definition.

RMS does not enter in the definition of dynamic range, which is defined as (in dB): 20 log_10 (s(t)_max /s(t)_min), s(t) being the signal loudness over time.

 

[krabapple]

You started with questions about dynamic range of recorded music. Now you just seem to be fighting anyone who has a different conception of dynamic range than you do. What is your goal?

 

[Jochen]

You started with questions about dynamic range of recorded music. Now you just seem to be fighting anyone who has a different conception of dynamic range than you do. What is your goal?

The original question has been resolved some time ago already, it was caused by different definitions of dynamic range. My misunderstanding has been removed, but it seems not of everyone discussing here.

 

[Cbdb2]

RMS does not enter in the definition of dynamic range, which is defined as (in dB): 20 log_10 (s(t)_max /s(t)_min), s(t) being the signal loudness over time.

How do you measure signal loudness? Do you think its instantaneous voltage? It isn't it has to be rectified and averaged over a significant time period ( a few milliseconds ) into a RMS voltage.
Signal loudness has been measured in studios for 80 years, its called a VU meter. Guess what, it measures RMS voltage.

 

[Jochen]

I asked autocorrect on my phone, and it came up with this counter argument:

"Dynamic range crest factor correlation coefficient of determination and I will be there in about you guys I know you are you in the office today and I will be there [...]"

Maybe you should ask your autocorrect to write running code in every computer language.

 

[Jochen]

Yep, I can see that claim.

My point is, who cares about correlation alone? What does it serve other than debates?

If there are different metrics I think it is important to understand their relationship.

 

[NTK]

The "dynamic range" of music is defined differently from purely electrical signals, because our loudness perception is not based on peak sound pressure values. "Sound level" (as opposed to peak sound pressure) is always measured as the RMS level weighted with a time constant (see formula as used by MATLAB). The time constant tau for F (fast) is 1/8 second, S (slow) is 1 second, and I (impulse) is 1/32 second.



See this article on the discussion on the complications of how to define the "dynamic range" in music (go to section "What Is The Dynamic Range Of A Piece Of Music?").

'Dynamic Range' & The Loudness War

We all know music is getting louder. But is it less dynamic? Our ground-breaking research proves beyond any doubt that the answer is no — and that popular beliefs about the 'loudness war' need a radical rethink.

www.soundonsound.com

One such measurement method is described in EBU Tech 3342, which gives the definition for the the "Loudness Range" to avoid using the confusing term "dynamic range".

https://tech.ebu.ch/docs/tech/tech3342.pdf

 

[Jochen]

The "dynamic range" of music is defined differently from purely electrical signals, because our loudness perception is not based on peak sound pressure values. "Sound level" (as opposed to peak sound pressure) is always measured as the RMS level weighted with a time constant (see formula as used by MATLAB). The time constant tau for F (fast) is 1/8 second, S (slow) is 1 second, and I (impulse) is 1/32 second.

View attachment 284054

See this article on the discussion on the complications of how to define the "dynamic range" in music (go to section "What Is The Dynamic Range Of A Piece Of Music?").

'Dynamic Range' & The Loudness War

We all know music is getting louder. But is it less dynamic? Our ground-breaking research proves beyond any doubt that the answer is no — and that popular beliefs about the 'loudness war' need a radical rethink.

www.soundonsound.com

One such measurement method is described in EBU Tech 3342, which gives the definition for the the "Loudness Range" to avoid using the confusing term "dynamic range".

https://tech.ebu.ch/docs/tech/tech3342.pdf

I mentioned this article already above in post #162

 

[Newman]

I asked ChatGPT. This is the answer I got:

"I apologize, but I cannot provide you with a specific value for the correlation coefficient between the crest factor and the dynamic range, as it would depend on the specific dataset and the distribution of the data.

However, I can tell you that in general, the correlation coefficient between the crest factor and the dynamic range is likely to be positive, since both variables measure the amplitude range of a signal. Signals with a high crest factor tend to have a larger dynamic range, and vice versa.

However, the actual value of the correlation coefficient would depend on factors such as the type of signal, the measurement techniques used, and the specific range of amplitudes being analyzed. To calculate the correlation coefficient, you would need to collect data on both variables and use statistical software or formulas to calculate the coefficient.

It's worth noting that the correlation coefficient is just one way to quantify the relationship between two variables, and it may not capture all aspects of the relationship. Other factors, such as the shape of the distribution or the presence of outliers, can also influence the relationship between the crest factor and the dynamic range."

Here is a link to a thread with many examples of garbage spewed by ChatGPT. There is no point in bringing its ‘opinions’ into a discussion unless you want to discuss ChatGPT instead of the topic.

 

[krabapple]

The original question has been resolved some time ago already, it was caused by different definitions of dynamic range. My misunderstanding has been removed, but it seems not of everyone discussing here.

And your goal now is....?

 

[restorer-john]

And your goal now is....?

See how quickly he can get banned?

 

[restorer-john]

Virtually everyone with a HiFi system is totally incapable of reproducing the full dynamic range of the 40 year old Compact Disc format. They don't even come close.

If the quietest perceivable audible signal on your loudspeakers is 1uW@8R (1 millionth of a watt), you'd need 3,981W (nearly 4kW!) of amplifier power to reproduce a 96dB dynamic range. That amplifier would need to be running rails of over +/-250V internally and could easily kill you at the speaker terminals.

 

[Doodski]

Virtually everyone with a HiFi system is totally incapable of reproducing the full dynamic range of the 40 year old Compact Disc format. They don't even come close.

If the quietest perceivable audible signal on your loudspeakers is 1uW@8R (1 millionth of a watt), you'd need 3,981W (nearly 4kW!) of amplifier power to reproduce a 96dB dynamic range. That amplifier would need to be running rails of over +/-250V internally and could easily kill you at the speaker terminals.

Those are some pretty large numbers but as you say deadly too. I've never played with the numbers as you did here and now that you have it's pretty impressive stuff the dynamic range of a CD. If peak power the DC rails would be ~+/-178.5 VDC @ 22.3A peak. If RMS power then the rail values will be 252.4VDC @ 31.5A peak. So you are right on the biscuit. Good post!

 

[Blumlein 88]

Virtually everyone with a HiFi system is totally incapable of reproducing the full dynamic range of the 40 year old Compact Disc format. They don't even come close.

If the quietest perceivable audible signal on your loudspeakers is 1uW@8R (1 millionth of a watt), you'd need 3,981W (nearly 4kW!) of amplifier power to reproduce a 96dB dynamic range. That amplifier would need to be running rails of over +/-250V internally and could easily kill you at the speaker terminals.

My question is why you chose 1 uW@8 ohms?

Seems to me with an 86db/meter speaker and peaks of 106 dbSPL the number for 10 dbSPL is closer to 25 nanowatts. Peak power for the 106 db would be around 100 watts.