Why is a critically damped Q factor bad?

Yes typical Timbaland production where he borrowed what was done in Drum & Bass of the time ( circa 2000). That said it's way cleaner than what it's done now a days and clever layering with clean instruments preserve some transients breaking through in Nelly's track ( as well as panning / M/S processing of drums: there is a hole created in center for Nelly's voice to cut through, distorted drums on extreme L/R and clean bass hard center).

Example of up to date squared kick can be heard in Drake's tune 808 distorded and pitched lower and more general in Trap beats/dubstep.
 
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I did never have a look at the waveforms but "Say it right" by Nelly Furtado has some really ugly sounding clipping drums.
Thanks for suggesting that track. It's informative and it does introduce some distortion-like effects onto the drum kicks. These drum kicks have a fundamental peak occurring at around 45Hz. Although the drums do sound "dirty", they don't appear to be clipping as such.

Below is a typical waveform taken from that track. It's not quite in the territory of "square bass" as far as I can tell, and maybe it's more in keeping with "triangular bass".

1728049914332.png


And the results of a frequency analysis of the track are shown below.
1728050084080.png
 
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Example of up to date squared kick can be heard in Drake's tune 808 distorded and pitched lower and more general in Trap beats/dubstep.
Not sure which of Drake's tunes you were referring to.

After going ahead and auditioning a few of his tracks, I took a closer look at "Major Distribution" from 2022. Here we see a waveform that is quite triangular looking, with some embellishments added.

1728051605459.png


Doing a bit more delving, I found the following too. Is that an in-the-wild example of the elusive "square bass"?

1728052321611.png


This track has a very strong 39Hz low-frequency bass sound, as shown by the frequency analysis.

1728052542845.png
 
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@mark100 Can you please provide the time-domain response waveforms when the input is a 20Hz two-cycle toneburst, and maybe a 30Hz two-cycle toneburst as well?

Ok, to recap, sub is dual 18" reflex with f-3 around 26-27Hz.

Here is 27Hz, 0.5 cycle flat-top window
Yellow is electrical stimulus;
Blue is microphone . (Delay is due to use of a FIR filter with about 90ms of latency.)

1728051671501.jpeg



here is the same 27Hz, but 2.5 cycle and cosine windowing.
Notice the disparity in apparent number of cycles between the stimulus and measurement. About double, maybe 5 peaks vs 10-11.
1728052012118.jpeg



To get out of port contribution range, and to illustrate how then, that the number of cycles disparity goes away,
Here's 60Hz 2.5 cycle cosine windowing. Good match I think.
1728052175304.jpeg




Now back to the 27Hz 2.5 cycle cosine windowing, but with the port stuffed with pillows trying to turn it into a sealed.
About 5 peaks vs 7 now. (Can't fully close off the port it seems.)
1728053297841.jpeg



I think tone busts are a good way to explore how clean subs our are down low.
Problem with both impulse and step (which is just a function of impulse), is that they are too heavily dominated by high-frequency (given the nature of FFT linear data collection.)
Scope grabs of tone bursts are really easy with REW; I'd like to encourage everyone to try it. I still have a lot to learn about the technique, and could use some collaboration.
 
You do realise that the prerequisite for this math to be valid is that it is bad on a perfectly linear system?

I advice you to check the theory!

The theory was checked and accepted in the scientific press over 200 years ago. My checking would add nothing.

To be really clear: I have no doubt of the mathematical relation you refer to - it's perfect. It's the potential pitfall when applying to the real world that I'm raising a warning flag for.... but please do prove me wrong in this "real world meeting math theory" conundrum...

What pitfalls might these be? If you want to talk about frequencies then you have no choice but to accept the definitions of frequency which requires linearity. If you want to include nonlinearities then you must consider a nonlinear system which is fairly straightforward but requires reasoning to be based on the general nonlinear Navier-Stokes equations rather than the linear wave equation (or sometimes something inbetween depending on the relevant physics). This is required for large displacements of drivers, ports, high SPL, hot coils, etc... but linear acoustics is fine most things.
 
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I dont want to include anything - just make sure the ath is valid for the case - thats all... if you dont share my specific concern, just say so.

Ath is an input generator for the akabak BEM program? If you can wait a week or two I am the process of posting a BEM solver which will include some discussion about the sources of errors along with some test cases the majority of which will be just as relevant to ath/akabak. If you can wait a few months I should be getting onto sound from ports which is a case where linear acoustics isn't really sufficient to answer some of what we would like to know requiring the inclusion of nonlinearities to capture the relevant physics.
 
I didn't say that a step response test was invalid, and I don't think that I even implied that it might be invalid. I'm just observing that it isn't so readily available "in the wild", so to speak. It needs more careful interpretation than other available test signals and/or measurements.

And yes, critically-damped loudspeakers do have applications. Just that "tighter" bass is not one of them.
I didn’t say that you said the step response was invalid. I questioned your dismissing a test because it isn’t found in music. Step response is a valid test of a loudspeakers performance.

I don’t think you understand Q. If the Q is lower an object has less propensity to store energy. It is defined as the ratio of the initial energy stored in the resonator to the energy lost in one radian of the cycle of oscillation. A loudspeaker with a lower Q factor will store less energy and have tighter bass. It’s science!

https://books.google.com/books?id=l-AgBQAAQBAJ&pg=PA42#v=onepage&q&f=false
 
Ath is an input generator for the akabak BEM program? If you can wait a week or two I am the process of posting a BEM solver which will include some discussion about the sources of errors along with some test cases the majority of which will be just as relevant to ath/akabak. If you can wait a few months I should be getting onto sound from ports which is a case where linear acoustics isn't really sufficient to answer some of what we would like to know requiring the inclusion of nonlinearities to capture the relevant physics.
"ath" was a typo. It should have read: math. But what your say seems very interesting 🙂

//
 
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If you listen to a song with a wideband bass drum sound ie "Fear of a Blank Planet" by Porcupine Tree, on many subs you can literally hear the "thump" arrive on a later date than the "slap."
Listened to this twice on my hifi Danley SH50 replicas and twin tapped horns (60Hz -> 20Hz).
👍 Sounds just great 😃

Can't say I can hear a difference in time between slap and thump.
Just great tight drumming and pleasing bass.

I've added it to my mid bass test playlist. Thanks for the recommendation.
It's 24bit on Qobuz.
 
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A box does not "need" a greater volume to provide a lower Q.

Q is adjustable using EQ
Of course, as is bass extension. I wasn’t talking, however, about utilizing the additional design and implementation complexity of electronic EQ, only the fundamental physical-acoustical interactions of a woofer in a closed box. Just for purposes of illustration, as I had indicated.
 
Okay, my take on that: Compensating a low Q with power (probably 10+dB) is not going to solve the problem of the fidelity of reproduction. There's a thing called power compression. The more power you put in, the dimishing the return in spl, not to mention that the heated up VC increases the Qt - and so increases the decay on the Fb too. So it's often completely futile to go for a Qt of 0,5 if you need medium to high spl since you will lose that in the power compression and the Qt increase anyway. If you listen at low volume, a Q 0,5 can be reasonable but you can't ever compensate for a loss of 10+dB with power at higher levels. Settle for 0,6-0,7 instead and keep your headroom in the amp (remember what +10dB means! That's what you typically have to compensate on Q 0,5 vs 0,7 on the lower end). And don't forget to include the serial resistance of your cables and connectors/plugs (hint: it's not zero, it's typical 0,5 Ohm on + and - combined) in the simulation.

The Linkwitz transformation is mostly theoretical. I had several dispute conversations with him since he completely ignored the power compression and the contact resistances (respective their magnitude). I rather regret not comming to a conclustion about that before he died but that's one of the flaws of what he preached. Don't misunderstand me, he did some very good work but just because he's dead doesn't mean he was right about everything.
 
Ok, to recap, sub is dual 18" reflex with f-3 around 26-27Hz.

Here is 27Hz, 0.5 cycle flat-top window
Yellow is electrical stimulus;
Blue is microphone . (Delay is due to use of a FIR filter with about 90ms of latency.)

Well, the FIR filter is also adding the pre-ring. I feel that's a very important thing to mention when comparing the impulse response.
 
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Well, the FIR filter is also adding the pre-ring. I feel that's a very important thing to mention when comparing the impulse response.
That's incorrect. Those were tone burst comparisons, not impulse or step responses.

Besides, the sub's high-pass is IIR. It's low pass is acoustically complementary linear phase, with pre-ring potential canceled by the next driver's section high-pass. System impulse is free of pre-ring.
Tone bursts can be made anywhere in the speaker's full spectrum once above port contribution, and look as clean as the 60Hz example, even in xover regions.
 
That's incorrect. Those were tone burst comparisons, not impulse or step responses.

No, the pre-ring of FIR happens, no matter what what the input signal is. That's an inheritend flaw of FIR filters.

Besides, the sub's high-pass is IIR. It's low pass is acoustically complementary linear phase, with pre-ring potential canceled by the next driver's section high-pass. System impulse is free of pre-ring.

No FIR filters are are free of pre-ring. A high-pass doesn't prevent that since it's system imminent and inheritend. That doesn't mean it's bad generally but if the impulse response (or general behaviour) is imperative, that's a major argument against it. FIR is a solution to many problems but the impulse response is not one of it.

Tone bursts can be made anywhere in the speaker's full spectrum once above port contribution, and look as clean as the 60Hz example, even in xover regions.

Again, that's not an issue of the frequency, that's a problem of FIR filters itself. In most cases it doesn't matter but in some it does. That doesn't mean to avoid FIR but you have to be aware of it.