64 Cell (8x8) PRD (Skyline Diffuser) question

[Nordenstam]

That's false, QRD's do not need to be symmetrical.

2D panels modulated - nine asymmetrical N5 2D QRD panels with three rotated. You can shift the position of the pattern, test it out with any 2D QRD generator.

Any 2D QRD calculator? As far as I know, there's only cool QRD calculator around and especially only one that goes to 2D. The one you linked to above made by Bill Collison. For those interested, it can be found here: http://www.subwoofer-builder.com/qrdude.htm and there's loads of text here: http://www.subwoofer-builder.com/qrd.htm

I don't know if he started writing on the calculator independently, or if it was Terry J's thread at gearslutz that set the ball rolling. (the same Terry as in this thread - hello mate! ). In any case, I think it's pretty safe for me to claim that thread to be essential in the making of the calculator and the accompanying text page. And I don't think it's too much bragging to claim that my input on the subject have been quintessential. The thread is here and my nick at gearslutz is Lupo: http://www.gearslutz.com/board/bass...2-ch-listening-room-aiming-best-possible.html - the first contribution by Bill is at post number 71, which shows the rudementary start of the calculator.


The picture you linked to above is a combination of different QRD's. It doesn't mean they're not symmetrical on their own. All QRD's are symmetrical around their middle point, except for the starting well. A QRD sequence is:
n^2 modulo N, where the n is the sequence step and the N is the prime number.

For the prime 5 N, the sequence is:
0^2 mod 5 = 0
1^2 mod 5 = 1
2^2 mod 5 = 4
3^2 mod 5 = 4
4^2 mod 5 = 1

The first line in the 2D QRD you posted above is the result of inserting a constant in the sequence:
(0^2 + 1) mod 5 = 1
(1^2 + 1) mod 5 = 2
(2^2 + 1) mod 5 = 0
(3^2 + 1) mod 5 = 0
(4^2 + 1) mod 5 = 2

And this 1-2-0-0-2 pattern is shifted one step to the left, giving the 2-0-0-2-1 depth sequence seen in the first row. All the rows in the 2D sequence can be decomposed in a similar pattern. The "1" is 0 depth starting well pluss 1, and the rest of the sequence is symmetrical. Ditto for any QRD sequence you can manage to procure forth. They're all symmetrical.


--- back on track:
the smaller 3x3 parts of the golden horn diffuser does not match the prime 3 QRD pattern. Neither does the overall larger pattern look like a QRD as they are strikingly symmetrical:

The picture above is from this thread at gearslutz: http://www.gearslutz.com/board/so-m.../431360-diffusor-baffles-skywalker-sound.html - which, as you can see, is where the 2D portion of the QRD calculator started.

 

[terryj]

I don't know if he started writing on the calculator independently, or if it was Terry J's thread at gearslutz that set the ball rolling. (the same Terry as in this thread - hello mate!

hi mate! picking up the aussie lingo I see haha. well done.

Still love those skywalker baffles, beautiful.

take care.

 

[kareface]

Any 2D QRD calculator? As far as I know, there's only cool QRD calculator around and especially only one that goes to 2D. The one you linked to above made by Bill Collison. For those interested, it can be found here: http://www.subwoofer-builder.com/qrdude.htm and there's loads of text here: http://www.subwoofer-builder.com/qrd.htm

I actually didn't use QRD dude, I just have an excel file.

The picture you linked to above is a combination of different QRD's. It doesn't mean they're not symmetrical on their own. All QRD's are symmetrical around their middle point, except for the starting well. A QRD sequence is:
n^2 modulo N, where the n is the sequence step and the N is the prime number.

For the prime 5 N, the sequence is:
0^2 mod 5 = 0
1^2 mod 5 = 1
2^2 mod 5 = 4
3^2 mod 5 = 4
4^2 mod 5 = 1

The first line in the 2D QRD you posted above is the result of inserting a constant in the sequence:
(0^2 + 1) mod 5 = 1
(1^2 + 1) mod 5 = 2
(2^2 + 1) mod 5 = 0
(3^2 + 1) mod 5 = 0
(4^2 + 1) mod 5 = 2

And this 1-2-0-0-2 pattern is shifted one step to the left, giving the 2-0-0-2-1 depth sequence seen in the first row. All the rows in the 2D sequence can be decomposed in a similar pattern. The "1" is 0 depth starting well pluss 1, and the rest of the sequence is symmetrical. Ditto for any QRD sequence you can manage to procure forth. They're all symmetrical.

They are all symmetrical, except when shifted, then they are no longer symmetrical. They are literally called asymmetrical N5 2D QRD panels. Only 2 of the possible constant values will produce symmetrical results. Your statement is still wrong, QRD's aren't always symmetrical.

And this 1-2-0-0-2 pattern is shifted one step to the left, giving the 2-0-0-2-1 depth sequence seen in the first row. All the rows in the 2D sequence can be decomposed in a similar pattern. The "1" is 0 depth starting well pluss 1, and the rest of the sequence is symmetrical. Ditto for any QRD sequence you can manage to procure forth. They're all symmetrical.

I'll agree that it isn't a normal N3 sequence.

 

[Nordenstam]

I actually didn't use QRD dude, I just have an excel file.

There was a lot of assumptions in my last post, apologies for drawing conclusion out of thin air. On the other hand, QRDude is so cool, why not use it?

They are all symmetrical, except when shifted, then they are no longer symmetrical. They are literally called asymmetrical N5 2D QRD panels. Only 2 of the possible constant values will produce symmetrical results. Your statement is still wrong, QRD's aren't always symmetrical.

Sure. Though it's still a pattern that can be recognized as sporting a symmetrical feature, even if the symmetrical mid point is displaced from exact middle or endpoints. Have a hard time finding that symmetry in the linked diffuser.

Linguistically speaking, how would you differentiate between the displaced symmetry of these "asymmetrical QRD"'s vs the absolute lack of symmetry found in PRD's? Not trying to bang facts into your head or anything, just being curious.

 

[Nordenstam]

Still love those skywalker baffles, beautiful.

Indeed! Though I'm a fan of PRD math over the simpler QRD's, there's something very beautiful about the 2D QRD's. Been tempted to build some just for the cool looks..

 

[kareface]

Sure. Though it's still a pattern that can be recognized as sporting a symmetrical feature, even if the symmetrical mid point is displaced from exact middle or endpoints. Have a hard time finding that symmetry in the linked diffuser.

As am I, but it seemed more akin to a QRD seeing how most PRD's don't use cell walls, can't be 3x3, and usually have more variation in the cell heights. The pattern doesn't match the traditional design, but my thought was If there is a way of generating alternate permutations for PRD's there might be a way of playing with the QRD formula. That's why I said I'd have to think about it.

Linguistically speaking, how would you differentiate between the displaced symmetry of these "asymmetrical QRD"'s vs the absolute lack of symmetry found in PRD's? Not trying to bang facts into your head or anything, just being curious.

I would suggest instead of saying QRD's have to be symmetrical, which would be a false statement, instead saying the starting pattern for 2D QRD's has to be symmetrical. It may sound like semantics, but it's a big difference.

 

[terryj]

As am I, but it seemed more akin to a QRD seeing how most PRD's don't use cell walls.

Ah yes, the simple crude ones you mean!

Ok kareface, he's a theoretical for you. Actually, not so theoretical as more asking you to mine your memory banks.

*We* have tried for a while to answer this question..is there a reference somewhere that 'says' that even a PRD should have cell walls?? (we never did find that after all did we andreas?? was a while ago now so a bit hazy there)

It seemed to us that they should, that it would be better if they did, but no definitive statement that I can recall.

If you cannot find anything explicit, then here is the theoretical question bit, do you feel they would aid it's performance if there were well dividers?

I agree, lupo, I too nearly made a 2dqrd based on the look of those skywalker baffles, there is that 'something' about them.

Well, I guess it is more human, we tend to like and find pattern, symmetry etc in things we look at, which OTOH makes the PRD look alien to us??

What's good for the eyes ain't so good for the ears. (which is why we need to do dbt's eh haha)

 

[kareface]

It would be a hypothetical

I'm not sure about that. QRD's tend to shift the wave front, and their patterns represent the shift in phase necessary to bend it. PRD's don't bend the wave front in the same manor, the pattern is too erratic for small and varying shifts in phase to manipulate. With out the cell walls a QRD won't as effectively bend the wave front, but I don't know if that matters to a PRD. I can't think of anything off hand that mentions requiring cell walls. If I were to make a guess it would be for the reasons stated above, but I can't say with any certainty. I'll read up to see if I can find anything to bring light on the question.

 

[terryj]

It would be a hypothetical .

theoretically speaking of course!

.

I'm not sure about that. QRD's tend to shift the wave front, and their patterns represent the shift in phase necessary to bend it. PRD's don't bend the wave front in the same manor, the pattern is too erratic for small and varying shifts in phase to manipulate. With out the cell walls a QRD won't as effectively bend the wave front, but I don't know if that matters to a PRD. I can't think of anything off hand that mentions requiring cell walls. If I were to make a guess it would be for the reasons stated above, but I can't say with any certainty. I'll read up to see if I can find anything to bring light on the question.

see what you come up with..not too important, just a curiosity thing ya know.

 

[kareface]

theoretically speaking of course!

The word theory and theoretical mean very different things inside and outside the scientific domain. People outside of the scientific community use the term theory as if they mean hypothesis. In reality a theory is the highest level of understanding allowed in science. We would be discussing a hypothetical, or formulating a hypothesis on the issue. I'm normally not the type of person who corrects others grammar online, but I think it's important that people understand the difference.

 

[terryj]

I was joking. When you corrected me my reaction was 'of course!', but then replied that way to have a bit of fun.

So yeah, was not upset or denying it, just playing a bit.

 

[kareface]

Good to know. Sarcasm doesn't translate well online, lol.

 

[Nordenstam]

As am I, but it seemed more akin to a QRD seeing how most PRD's don't use cell walls, can't be 3x3, and usually have more variation in the cell heights. The pattern doesn't match the traditional design, but my thought was If there is a way of generating alternate permutations for PRD's there might be a way of playing with the QRD formula. That's why I said I'd have to think about it.

A way to manipulate the QRD's is outlined previously. The 2D QRD's sorta automatically run through every possible permutation of the modulation described.

I would suggest instead of saying QRD's have to be symmetrical, which would be a false statement, instead saying the starting pattern for 2D QRD's has to be symmetrical. It may sound like semantics, but it's a big difference.

I see your point. Though, in this practical situation, we're looking for a pattern that have to be symmetrical, with the caveat that it can start and stop at any time. The symmetry does not have to be centered on zero.

It may make a big difference to the performance of a single panel. Or it may not. In any case, these sort of sequences are generally regarded to be able to start and stop at any point). This is due to the assumption that they are periodic devices. A single diffuser does not give the expected results. The start/stop fringes of the periodic array will be the exception zones, with the repetitive parts giving the expected outcome. The periodic array will show off the symmetrical feature of QRD's no matter where the sequence starts.

Well, I guess it is more human, we tend to like and find pattern, symmetry etc in things we look at, which OTOH makes the PRD look alien to us??

Possibly. The lack of pattern is also a feature! I like alien. Think that's part of the coolness. The mind is straining to find something that's not there.

QRD's tend to shift the wave front, and their patterns represent the shift in phase necessary to bend it. PRD's don't bend the wave front in the same manor, the pattern is too erratic for small and varying shifts in phase to manipulate.

It makes more sense if you mean small prime number 1D sequence by the term "QRD" and large prime number 2D sequence by the term "PRD", but still doesn't compute. Sound waves doesn't know if it's a QRD or PRD sequence. Both diffusers work on the same principle. It's the sum of the various phase shifts that results in a certain energy level at a certain direction.


Well dividers are needed to have plane wave propagation within the wells. The expected behaviour of these devices are based on the assumption that all wells radiate different phases at the same "points" in space - the openings of the well mouths. Removing the well dividers means this assumption no longer holds true. It doesn't mean that the structures don't work though, it only means that the math is not directly applicable to the simplified behavioural theorems.

 

[kareface]

It makes more sense if you mean small prime number 1D sequence by the term "QRD" and large prime number 2D sequence by the term "PRD", but still doesn't compute. Sound waves doesn't know if it's a QRD or PRD sequence. Both diffusers work on the same principle. It's the sum of the various phase shifts that results in a certain energy level at a certain direction.

The differences in how they deal with phase it how the wave knows. If you alternate dramatic shifts in phase and small shifts in phase frequently it has a summing effect on the front which doesn't impact it the same way. There's a huge difference between how a PRD and QRD work, it's dramatic enough to be audible.

Well dividers are needed to have plane wave propagation within the wells. The expected behaviour of these devices are based on the assumption that all wells radiate different phases at the same "points" in space - the openings of the well mouths. Removing the well dividers means this assumption no longer holds true. It doesn't mean that the structures don't work though, it only means that the math is not directly applicable to the simplified behavioural theorems.

Normally I would completely agree with you. I have to question it tho, as I can't find any citation that suggests using cell walls to increase PRD performance. Even most production PRD's from reputable companies don't use cell walls. I almost wonder if the space is taken into account and phase corrected. Is there any auto correlation data between ones with and without cell walls?

 

[terryj]

wasn't worth a seperate post, but no, I wasn't being sarcsatic at all, (I assumed the acknowledgement was inherent in the reply too) but truly, twas just mucking about.

Normally I would completely agree with you. I have to question it tho, as I can't find any citation that suggests using cell walls to increase PRD performance. Even most production PRD's from reputable companies don't use cell walls. I almost wonder if the space is taken into account and phase corrected. Is there any auto correlation data between ones with and without cell walls?

Surely that would be due more to ease of manufacture and keeping costs down? From vague memory, the only oblique mention to having well dividers in a PRD came from the BBC document describing their ceiling tiles....(???) Gee, been a while since we were trying to answer this question, but I think I'm correct there.

And, in the very same document they also explained that their very coarse depth levels..four I think...also came down to ease of manufacture and lower cost, and IIRC that lower cost was also the rationale for 'removing the dividers'.

Regarding the RPG PRD, from looking at the 'pics' I can only make out fourteen, or was it seventeen, different dpeths in a 156 cell PRD. Optimumly, we know it should have 156 different depths.

Again, back to costs and ease of manufacture.

But others who own the bible cannot seem to find an answer in there on this question, and I would put that at a higher level of authority on the subject than the BBC document!

I guess it is really just curiosity right now, a bit like yours I spose, 'how much audible impact would departure X from the theoretical ideal make?'. In most cases, like having seventeen discrete depths or removal of well dividers (if required by absolute theory) still give enough to make them worthwhile.

Haha, if I have to be honest it's all about bragging rights!! How many other PRDs are out there with 156 discrete depths AND have well dividers??

 

[Nordenstam]

The differences in how they deal with phase it how the wave knows. If you alternate dramatic shifts in phase and small shifts in phase frequently it has a summing effect on the front which doesn't impact it the same way. There's a huge difference between how a PRD and QRD work, it's dramatic enough to be audible.

So, you're saying that these diffusers, prime 7 QRD(left) and PRD(right), behave way different when a sound wave strikes the structures:

I say: meh..

..


Haven't found much on dividers vs divider-less 2D's. Will give a word if I find more!

Haha, if I have to be honest it's all about bragging rights!! How many other PRDs are out there with 156 discrete depths AND have well dividers??

Hehe.. They do look awesome! And probably works as good as anyone can beg for.

 

[kareface]

So, you're saying that these diffusers, prime 7 QRD(left) and PRD(right), behave way different when a sound wave strikes the structures:

The 2D PRD's are audibily different from the 2D QRDs, so yes, in the context of my statement they'll sound different.