Acoustic Horn Design – The Easy Way (Ath4)

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Really? With passive EQ, my best guess is a low-Q notch around 3.8 kHz and a shelf between (low end of passband) and 2.0-2.2 kHz with pelanj's example, and I'm not sure that would be good enough to give a "flat" on-axis or averaged response.
Absolutely, that frequency response doesn't scare me at all :)
Even if a small dip remained such would not be audible...
 
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so a horn's shape doesn't cause response irregularities??
It can but typically not in this way - of course there can be a resonance caused by the horn itself but typically along with a strong diffraction as well. Which is not what we see here - there's almost none diffraction noticeable (i.e. no angle-dependent irregularities), the horn itself is as clean as it can be. The rest is driver's behaviour, easily correctable via a global minimum-phase EQ (electrically - one dimension only), at least up to the breakup/HOM region.
 
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And this is exactly what I would try to do. I already did, actually, with the newest designs presented here. We have now all the machinery to optimize a waveguide for virtually any DI slope we desire.



The point is that if the power DI curve is smooth (e.g. a tilted line) you can be almost sure the other curves are smooth as well, the PIR included, so I still see it as a natural optimization target but it could easily be some different (integral) curve. To get a flat ON/LW is then a no-brainer. I only don't see a reason why would be the SM_PIR disregarded - it would be still there (and smooth as well), IMO.

- I'm pretty sure that the new waveguides optimized for the following DI targets would behave as desired in all other aspects as well:

The point I was trying to make is the following:
- According to the Harman research, there exists a preferred PIR response, see the PIR graph hereafter, the different version of the target are labelled Toole 3rd edit. p373 xx

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- A model predicting the preference rating of a speaker should test against this PIR target and rate a speaker higher when closer to the PIR target, that’s my assumption but this is basically how the current model works albeit with the “target” being described by a line with a slope.
- The current model when applied to a speaker that exhibits a PIR very close to the target returns a lower value for SM_PIR than that of a speaker that exhibits a pure slope PIR (the former PIR target, as used in the current model) in the example Kef 0.986 vs Revel 0.830.
This is true for ALL cases except when the model is extrapolated to its limits i.e. when everything is flat, in which case the flat DI yields the maximum value SM_PIR = 1.
- It seems that in the general case the model has a built-in bias towards a PIR that is not the current preferred PIR response.

Therefore I am wondering if we could somewhat disregard the SM_PIR as currently calculated by the model.
The smoothness being still, at least partially, described by the NBD_PIR.
The NBD_PIR parameter working towards a flatter PIR over the 100 - 12000Hz range with seems to bode well with the observation made on the Revel speaker PIR and DI.

One more point, it seems that the DI should be designed higher, closer to 10dB rather than 5dB and down to about 200Hz or slightly lower, and close to omnidirectional below.
This should yield a closer LF output to the PIR target while keeping the rest of the spectrum untouched.
A very gentle slope will help as you showed with your hand drawn regressions compared with the KEF much steeper DI.
On the other hand, just boosting the LF by the 5dB below 100Hz would do a very similar job but the ON/LW is no longer flat.
 

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The current model is simply kind of chasing its own tail (going as deep as into the full circle of confusion, in fact), that's the crux of the debate - is there really an optimal DI, all other variables as good as they can be? Nobody really knows because of the limited range of loudspekers tested, which were all still quite common. The "optimal" assumed PIR may still be simply a result of that.

As the paper states:
"A speaker with constant, flat directivity could theoretically satisfy the flat sound power criterion and still achieve high preference ratings, so long as it had a smooth on-axis response well-maintained offaxis. However, such speakers are not widely available."

(Certainly not widely available but definitely available, as some of the examples in this thread showed.)
 
The current model is simply kind of chasing its own tail (going as deep as into the full circle of confusion, in fact), that's the crux of the debate - is there really an optimal DI, all other variables as good as they can be? Nobody really knows because of the limited range of loudspekers tested, which were all still quite common. The "optimal" assumed PIR may still be simply a result of that.

As the paper states:
"A speaker with constant, flat directivity could theoretically satisfy the flat sound power criterion and still achieve high preference ratings, so long as it had a smooth on-axis response well-maintained offaxis. However, such speakers are not widely available."

(Certainly not widely available but definitely available, as some of the examples in this thread showed.)

I think the answer is in the preferred PIR curve...
The preferred DIs are those providing the flat ON/LW and a PIR close to target.

The DI should be flat and smooth perhaps with a very gentle upward slope.
Tellingly this is what Revel and JBL (and some others as well) have set as a target for their own speakers.

I have attached a mock up of that.
It more of a sketch to illustrate my point than a real design though.
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I think the answer is in the preferred PIR curve...
The preferred DIs are those providing the flat ON/LW and a PIR close to target.
Perhaps, perhaps not. To this one can object (again): The "preferred" DIs are those that the smoothest loudspeakers in the test had. (From those loudspeakers that you can actually make and sell. Very few people will buy large waveguides, for example, no matter how good they can be. *)

* Yet, we see now that they don't have to be that big after all...
 
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Perhaps, perhaps not. To this one can object (again): The "preferred" DIs are those that the smoothest loudspeakers in the test had

Except that this target, or very close to it, was also derived via a completely different path using headphones, as I mentioned in my first post.

See some highlights here:
http://www.juloaudio.sk/Umiestnenie_reprosustav/History%20of%20Harman%20Target%20Curve.pdf

It seems that loudspeakers preferred PIR and headphones preferred response (DI, and directivity in general is probably not a significant factor there) are converging towards the same target.
Both are starting with a flat response, the loudspeaker being engineered with a certain directivity that yields the preferred PIR, and the headphone being equalized to the preferred response, the "ON" and the "PIR" are the same in the headphone case.
The added bonus is that in the headphone case, the room, that is often cited as an uncontrolled variable between users, is not a factor here, the Headphone type (open close etc.) maybe though.

I would think that it is an argument against the objection you made regarding the "circular" PIR preference that it was caused by the loudspeakers population used during the study.

What we think a speaker should be like:
- Flat and smooth (no resonances) ON/LW response
- Both on and off axis responses should be similar (i.e. flat DI) so that the early and late reflections are similar in tonal balance to the direct sound.
- PIR close to the preferred target

Hence my description
I think the answer is in the preferred PIR curve...
The preferred DIs are those providing the flat ON/LW and a PIR close to target.

For my money, it should be fairly flat, smooth, as high in level and as low in frequency as practicable, with a slightly fally listening axis response. There are lots of reasons to support this[...]

You are one of the persons that have been working on he matter the longest, can you elaborate on it? One more time.

Matbat work provides a stepping stone towards improving loudspeakers design.
The price of DSP and amps are now fairly low and controlling LF directivity is no longer outside of the possibilities of the real world.
If we are on this forum discussing these matters, let's face it, it's because we not afraid of thinking out-of the shinny boxes, understand as much as possible and make speakers that we would not be able find anywhere else.
 
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Except that this target, or very close to it, was also derived via a completely different path using headphones, as I mentioned in my first post.
There's really no escaping from the circle of confusion, as they even admit in the conclusion.

It seems that loudspeakers preferred PIR and headphones preferred response (DI, and directivity in general is probably not a significant factor there) are converging towards the same target.
Both are starting with a flat response, the loudspeaker being engineered with a certain directivity that yields the preferred PIR, and the headphone being equalized to the preferred response, the "ON" and the "PIR" are the same in the headphone case.
There's only one case where the two would "converge" to the same target - if the loudspeakers had a flat DI, otherwise it wouldn't be possible - I don't understand how one could compare the two different target curves for loudspeakers (LW flat/PIR tilted) with only one curve for headphones. The situation is so different IMHO that I doubt that this comparison can actually shed more light into this.

- To me, there's one unanswered question that underlines the whole issue: If we now make a loudspeaker with a flat DI, most of us will then tilt the response(s) downward a bit to sound more neutral in the end. Why? Is this really only the circle of confusion issue or is there a deeper reason? In other words, if there were everywhere only loudspeakers with flat DI, would there still be a need for this downward tilt?
 
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TNT

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Exciting indeed! About downwards tilting FR - it's for me still a mystery and I cant say that I have heard a really good story to accept that it is how it should be. I have a feeling that as: distorsion (also IM!!) go down, dispersion is even and wide + no diffraction; less tilt of FR is preferred.

//