# General question on dynamic range and music

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#### Jochen

##### Active Member
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.

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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.

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#### Cbdb2

##### Major Contributor
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

##### Major Contributor
Forum Donor
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

##### Major Contributor
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.

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#### Jochen

##### Active Member
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

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#### Jochen

##### Active Member
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

##### Major Contributor
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?

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#### Jochen

##### Active Member
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

##### Major Contributor
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.

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#### Jochen

##### Active Member
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.

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#### Jochen

##### Active Member
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.

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#### NTK

##### Major Contributor
Forum Donor
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?").

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".

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#### Jochen

##### Active Member
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?").

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".

#### Newman

##### Major Contributor

"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

##### Major Contributor
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.

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#### restorer-john

##### Grand Contributor
Forum Donor
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

##### Grand Contributor
Forum Donor
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

##### Grand Contributor
Forum Donor
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.

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