Phase offset audibility, particularly with mixed cabs

[HaphAsSard]

Sorry bro,
If I had more of ideas for car analogies just to explain with more comprehensibly words, for sure I'd do it

Nah, I hate car analogies.. And as I said, it's not just you but everyone who posts here in TB:Amps.


(Hm, OK, it's me. )

 

[fast_frank_d]

@ThisBass Here are some plots of the 2 cabs that sound very good individually, but very bad together. I thought phase was what I should be looking at, but maybe not. My goal in this thread (other than general knowledge) is to know what quantity (or quantities) have the largest impact on muddy bass and allowable limits. Then I will be sure to model them so I can select or create cabinets that will play nice together.

 

[agedhorse]

I'm not convinced those phase plots are accurate. There should be more of a difference given the very different Q of the filter model.

 

[fast_frank_d]

There is definitely something I am not understanding. I would not have expected the maximum difference in group delay between the 2 cabs (4ms at 50Hz) to be at a frequency when the transfer function phases are nearly identical. Clearly I have more reading to do.

Regardless of my lack of understanding here, maybe the 2-4ms group delay difference in the bass region is the real culprit in the muddiness of these 2 cabs operated together? 4ms seems like a lot to this ignorant fool. Not sure if it's relevant, but just thinking about my 5.1 home theater speaker calibrations as a reference, and the audible effect of a 4ms delay to the rear channels.

 

[agedhorse]

Just a caution, sometimes models are not all that accurate (or even remotely accurate).

To get a phase difference of greater than 45 degrees it pretty tough UNTIL you start mixing different TYPES of cabinets (sealed with ported with folded horn with bandpass), and sometimes with different driver types (large diameter, heavy cones with high inductance motors can rapidly depart from phase coherency as frequency increases. The problem won't necessarily be in the low bass but more in the mid bass to midrange. I don't think these models address anthing except the lower frequencies. I typically will listen to cabinet pairings, and if something doesn't sound right, I will run phase coherency testing (it's harder and more time consuming than it sounds, because mic placement and any acoustic boundaries come into play)

There's more to it than purely phase response, but having coherent phase response between two cabinets generally improves the odds of the cabinets working well together over the same bandwidth.

 

[fast_frank_d]

Yes, agreed. The models have to be assuming some value for cabinet rigidity (system stiffness or spring rate), box air leakage (damping/loss), and also port efficiency/air friction (more damping plus some non-linearities I don't understand) which will all affect actual Fb vs the modeled Fb and actual phase vs modeled phase. However, these must be relatively small variances or the modeling software would be completely useless without the ability to input these values.

For me, I think of these things as external variables I can't control like humidity or room acoustics. Obviously, garden variety bassists (*cough* like me) don't have a unique rig for every season and venue. But it would be great to know what plot values to target to have a reasonable expectation of a good match between cabs, rather than things just being a total crap shoot when you hook 2 cabs together. Maybe it's group delay, or phase, or whatever, but I bet there is some number that shows the difference between 2 cabs that sound good together and 2 that sound horrible.

 

[ThisBass]

The frequency response characteristic shape looks quite different which is an indication of different damping respectively filter Q. Same is for the group delay deviation which shows a relativ "conversion" between the two cabs, see the range 40..70Hz versus the range of 70..150Hz.

By default I'd expect different Q (damping) for these two cabs which will lead to sound issues by running both cabs together.

The phase charts are (quite) meaningless. Even for a matching design that shows just the same filter alignment, if cab A) was designed to show a lower f3 versus cab B) then the phase charts can't exactly match any more.


Here you are with a design for the 3012HO in a rather large net volume just to get some additional f3 low extension.
The response shows already some indication of ringing, the roll off shows a marked "hard knee" shape. Of course there are better options just to design for a "smooth" roll off but, as there is no free lunch there are (almost always) trade offs we have to consider with every design.

The following chart shows a design for the 3012LF with a smooth roll off characteristic.

Phase chart

I think its very easy to notice phase "anomalies" of white versus yellow. At 50Hz the phase difference equals about 47 degree, the loss in SPL at 50Hz caused by the phase "anomaly" equals (rather smallish) -0.75dB. IMO that's a reduction which is too small in number to be (well) audible noticed. And as "phase shift" acts immediatelly without any delay there is no way to derive "muddy" sound caused by phase anomalies.


Frequency Response chart of yellow versus white modelling

The roll off shape looks quite different which is an indicator for different filter alignment which results in different filter Q (respectively damping, step response). By default I would be very sceptical to run both cabs together. I don't think these cabs would accomplish well.


Another design for the 3012HO but modelling is for "smallish" cab volume and higher f3 versus the modelling above.

Response of both cabinets, the 3012HO for rather smallishc chamber versus the 3012LF

The roll off of each cab looks very similar "shaped"

So even does the "shape" of the group delays

Some (still noticeable" deviation is of no concerne. Its more of an interest that the "shape" indicates "similar" filter alignment.
Same of course is for the frequency response consideration which also "indicates" a "good supplementary" filter alignment in this case.
At least on paper (modelling) both cab alignments predict a good chance to get two different cabs but good accomplishing characeristic in practice.

I neglect the phase charts. These still show "noticebale" deviation but, I think there is no serious interest to discuss things which are of no meaning.

If you take into account desired f3 each cabinet and total cab dimension, supplementary SPL each cabinet, personal sound goals, distinct voicing of diffrent drives, so it all can be lead into kinda skunk work to design on paper what shall accomplish well in pratice. I'm afraid you don't hold the budget and also are not willing to spend lots of time into (trial and error) prototyping till the finished products show the best result.

It might be helpfull to chose drivers of the same driver family and same sub-family. For example Kappalite non LF series drivers. In this case the phrase "size means nothing but size" is no longer valid but, it might help a lot to design cabs that accomplish well soundwise.

 

[DukeLeJeune]

View attachment 2970408

View attachment 2970811

One thing I couldn't help but notice in the charts showing frequency response of the 3012HO and 3012LF together is, their relative SPL's aren't accurately portrayed. The 3012HO's broadband efficiency is 3.4 dB higher than that of the 3012LF, based on the T/S parameters, which are dominant in the absence of cone break-up peaking, which apparently isn't modelled by this program and which doesn't affect the bottom end anyway. The shapes of the curves are good; it's just that the white curve should be moved upwards by about 3.4 dB.

Not sure how that would effect an analysis of their respective phase responses and group delays, except maybe to give correspondingly more "weight" to the 3012HO when estimating how the two would sum.

 

[agedhorse]

Using normalized amplitude plots can quickly lead to misleading conclusions. Phase response (along with group and propagation delays and absolute amplitude plots) are all different glimpses into the summed system response.

 

[morebass!]

subscribed. I’d like to understand why sealed and ported don’t mix well.

 

[agedhorse]

subscribed. I’d like to understand why sealed and ported don’t mix well.

Generally, because the filter equations that describe each type of cabinet response is different enough that the combination of amplitude/phase response, group delay and propagation delay are far enough apart not to work well together. There can be exceptions, but as a rule of thumb I would not recommend mixing dissimilar TYPES of cabinets.

 

[morebass!]

subscribed. I’d like to understand why sealed and ported don’t mix well.

 

[morebass!]

Ok, sorry about double post.

 

[fast_frank_d]

@ThisBass, I read your post several times, digested it, and then did some modeling iterations. If I understand your perspective, transfer function magnitude shape and group delay shape are the most important things to look at for cab compatibility, phase doesn't matter so much, and is really just a downstream symptom of the first 2 things.

Using this approach, I looked at a real-world example of adding a Kappalite 15 to a Kappalite 2x3012LF. Interestingly, I could get the 3015 plots to align very nicely with the 2x3012LF. The 3015LF did not look as good no matter how I tuned it. I could optimize magnitude shape or group delay shape, but not both (see plots). With the 3015, magnitude and group delay come into alignment nicely with a single unique tuning. I have not included the phase plots to keep the clutter down, but basically the 2x3012LF and 3015 are parallel about 20 degrees apart, while the 3015LF phase line criss-crosses the 2x3012LF. 3015LF plots are the bold ones.

 

[fast_frank_d]

@agedhorse just attempting to put together what you are saying with what @ThisBass is saying, and my last batch of modeling, I am wondering if parallel phase plots might lead to "coherency" to use your term, and thus cab compatability. If they criss cross, converge, or diverge, then each harmonic of cabinet B will have a different phase offset from cabinet A. If I understand correctly, parrallel phase plots 20 degrees apart would be a straight up echo, albeit small, for all frequencies/harmonics. But if the phase plots criss cross, then each harmonic will have a different offset, possibly causing a smearing effect on the sound, even if everything is +/- 15 degrees for example. Speculating here. Thoughts anyone?

 

[AlexanderB]

@agedhorse just attempting to put together what you are saying with what @ThisBass is saying, and my last batch of modeling, I am wondering if parallel phase plots might lead to "coherency" to use your term, and thus cab compatability. If they criss cross, converge, or diverge, then each harmonic of cabinet B will have a different phase offset from cabinet A. If I understand correctly, parrallel phase plots 20 degrees apart would be a straight up echo, albeit small, for all frequencies/harmonics. But if the phase plots criss cross, then each harmonic will have a different offset, possibly causing a smearing effect on the sound, even if everything is +/- 15 degrees for example. Speculating here. Thoughts anyone?

Great to see you diving deep into finding the root cause and relations between parameters! I will just add a couple of generic comments, as I have no time for longer replies:

Most commercial cabs are not mainly designed with audio as only target. Weight, size, cost, labor time, work environment, tooling overhead cost, minimizing raw material waste, robustness, keeping to a brand typical design etc will be at least as important! Because of this, bass cabs will radiate lots of sound in all direction. They will also "store" and "release" audio energy out of phase with the input.
This will contribute to inaccurate and muddy sound compared to the calculations.

Secondly, the Q value (transducer as well as complete system) will affect the matching of cabs of similar size and tuning. Curves will be closed match in general, but close to the Fbox, they will separate, with diminished output and articulation. Personally, I think most Eminence drivers have too high of an fs and too high of Qes/Qts ("weak motors", or sensitivity prioritized over bass performance) They will not go very deep, and the already excessive q will rise further once the driver heats up.

Good luck!

 

[agedhorse]

The phase offset will not be perceived as a delay (way too short of a delta T) but will serve to smear the sound at those frequencies as well as to be related to the other artifacts that I mentioned.

The challenge is that we are trying to describe a complicated multi-variable mechanism with a single variable. Not going to be very accurate.

 

[xk49w]

There is definitely something I am not understanding. I would not have expected the maximum difference in group delay between the 2 cabs (4ms at 50Hz) to be at a frequency when the transfer function phases are nearly identical. Clearly I have more reading to do.

They are different because group delay indicates only the slope of the phase shift at a frequency. The two networks can have exactly the same phase shift at a frequency but because their slopes differ they can have a very different group delay.

It is often misunderstood here, but in the general case, group delay does not indicate the time delay of a frequency through a network, though it can under a specific condition. If however you want the actual delay time vs frequency then you need something called "phase delay", defined as the phase_shift(w)/w (whereas group delay is the derivative of the phase shift). Given your previous example where two networks had the same phase at a frequency but different group delays, they have the same phase delay and consequently the same time delay at that frequency.

Regardless of my lack of understanding here, maybe the 2-4ms group delay difference in the bass region is the real culprit in the muddiness of these 2 cabs operated together? 4ms seems like a lot to this ignorant fool. Not sure if it's relevant, but just thinking about my 5.1 home theater speaker calibrations as a reference, and the audible effect of a 4ms delay to the rear channels.

Per the previous, the group delay number does not give the time delay of audio through the system - the phase delay does. I don't think I have ever seen it specified.

BTW, this is all from the Bell System Technical Journal. Those are the folks that invented group delay as a way to measure phase distortion through a long network without needing a phase reference on the receiving end of the measurement.

There is wiki for the curious.

 

[fdeck]

One thing to consider is that you can't just look at the phase plots, because the effect of a phase error at a particular frequency will be greatly diminished if the two speakers have substantially different sensitivities at that frequency. The "louder" speaker will dominate if the difference is more than a few dB. For mainstream sealed and ported speakers at low frequencies (below about 250 Hz), differences in phase response are always accompanied by differences in amplitude response.

 

[fast_frank_d]

Thanks for all the great input everyone, I feel like I'm learning a lot. So putting more of the pieces of the puzzle together of what people are saying, the next thing I'm thinking about is the Q or damping of the system. So if I understand correctly, all of these plots define when the start of the signal occurs, but not stops. So in other words, if Q of 1 system is substantially different from another, and you move from note A to note B, one box could still be ringing out on Note A while the other box has already moved to note B, and that would create a muddy sound. So let's assume I could get the transfer function curves to look similar, and the group delay curves to look alike, and the phase charts look parallel, Is there a value or values I can look at to numerically compare system damping of the 2 boxes?