I have a question about which QRD prime sequences would be best in my live room -- I'm just about to build several arrays ...

I read the Everest book, sorted through the math, read various threads, papers, saw videos, read specs.

The Room:
My live room is 5m (16'5")L x 3.45m (11'ish)W x 2.4m (7.8')H. It has a 'nook' for a drummer. Generally speaking the room is somewhat similar to that presented in "The Ultimate Home Studio" video at RealTraps (an impressive aid to me).

I plan to do bass trapping in all corners, and from the floor to 60cm (2') around the walls, and put a cloud esp. at the center of the ceiling and above the drummer.

My first step is building a diffusor along the 5m wall. I designed 94cm (3') x 94cm (3') frames. Four frames in a row, is about 3.8m (12'5"). Wells are mounted vertically. (Later, 94cm (3') x 45cm (1.5') horizontal QRDs will be above these).

QRD well dimensions:
My max. well depth is 13.5cm (5.32"), and well width is 3cm (1.18"). Well dividers are 25mm plywood.

Due to my mic positions, between 1.2m-2m (4'-6'6") from the wall, I fear building a deeper QRD.

Here is my main question:
I can build all 7-prime QRDs (16 periods), 4-per-frame (oriented in the sequence 1112212111, '2' being flipped). Or, I can build per-frame: "11-prime(well0=Left) + 7-prime + 11Prime(well0=Right)" -- making a total of eight 11-prime periods and four 7-prime periods, and the alternation: 11/7/11/11/7/11/11, etc.

Bandwidth of the 7-prime (LF/HF):
728 - 5746 Hz (= 5021Hz)


Bandwidth of the 11-prime (LF/HF):
1043 - 5746 Hz (= 4703Hz)


The RealTraps QRD seems a 13-prime (well depth @ 6"), so according to the math it is effective from about 1100Hz or higher. One period fits nicely into a 2' frame (is that why it was selected), or because 1100Hz+ is a reasonable LF? It seems rather high to me. (Gusstimate well width around 1.4"~1.5"?) So HF is less than my build I believe. Several periods are placed together in that room build. I follow the math, but "effective" concerning LF is something I read; mysterious...

I want the QRD to be as effective as possible, so bandwidth seems an issue.

On paper, the 7-prime looks best (bandwidth). The higher the prime the less the bandwidth-per-depth, and my QRD depth is not great. But, is there a problem with many repeating 7-primes? And with the 7-prime itself? If so, what? Should I scrap my frames and build 13, 17, 32, and sacrifice some LF?

Given the size of my room, and the repeating QRD periods, are there any suggestions or recommendations for a best or better approach? Thanks in advance for your thoughts.

Diffusers in practice are usually effective one octave above and one octave below the frequencies given by the standard equations.

It is not really a matter of fewer wells being effective to lower frequencies, but rather the percentage that the deepest well is compared to the total number of wells. i.e. the deepest section of a 7 qrd is 4/7 for an 11 qrd the deepest section is 9/11. Though, you can use a modulation technique to the 11 sequence to make it shallower...8/11 or 7/11...I don't remember which it works out to off the top of my head.

Repetition is going to be your biggest real practical problem here. using a combination of 11 and 7's is a great way to combat this. Also, the 7's have greater issues with the "flat plate" frequency issue (the design frequency * the number of wells...in your example 728hz *7 = ~ 5Khz) which will limit the high frequency effectiveness of the unit. The flat plate frequency is the frequency range around which your diffuser behaves like....well....a flat plate. For an 11 diffuser the flat plate frequency is 1Khz*11 = ~ 11Khz.

So, I would definitely go with the combination of 11's and 7's. I would also recommend making your well widths a little wider 1.5" at least or 2" being better. You just end up with so much more absorption when you make the wells that narrow. You could end up with some weird absorption peak ...for example an absorption coefficient of .75 at 500 hz.

Jason

well dividers 25mm plywood, that was meant to be 2.5mm??

remember..pics!

Some numbers might help....

The standard N11 equation..
well depth = (well number squared + 2) mod 11

gives well ratios of:
0 1 4 9 5 3 3 5 9 4 1
(maximum depth 9/11)

The N11 panel can achieve a more economical depth by using
well depth = (well number squared + 2) mod 11

giving well ratios of:
2 3 6 0 7 5 5 7 0 6 3
(maximum depth 7/11)

For your maximum depth of 135mm, these translate to:
38mm 57mm 115mm 0mm 134mm 96mm 96mm 134mm 0mm 115mm 57mm

Giving a design frequency of 811hz

Switching to your N7 panel...

Design frequency of 811hz gives a maximum well depth of 121mm
Depths: 0mm 30mm 121mm 60mm 60mm 121mm 30mm

Since the diffuser acts optimally at multiples of the design frequency, a nice target for the HF cutoff is 4 times the design frequency. Lower than this and you are short changing yourself, higher and you run into frictional losses in the deeper wells.

This gives you a well width of 53mm. (half-wavelength of HF cutoff)

You want the panel width to be no smaller than the wavelength of the design frequency, which is 424mm.

25mm fins give you an N7 panel width of 546mm
8mm fins give you an N7 panel width of 427mm

For fins any smaller than 8mm, you would need to increase the well width to maintain the panel width>design wavelength relationship.
This then starts eating into your bandwidth.

Going back to your N11 panel...

For a well width of 53mm
25mm fins give you an N11 panel width of 858mm
8mm fins give you an N11 panel width of 671mm


And I agree with Terry - we will require pictures....heh

Thanks everyone, this is really helpful!

Sorry to make a mistake, my dividers are 2.5mm (not 25mm!) plywood (I read that 2.5mm would be acoustically transparent or near-to).

These two equations are the same, below?

"The N11 panel can achieve a more economical depth by using
well depth = (well number squared + 2) mod 11" (is the same as the first equation)?

how did you arrive at:
2 3 6 0 7 5 5 7 0 6 3
(maximum depth 7/11)
?

I am surprised to learn that the well width might need to be wider than 3cm, in relation to the 13.5cm depth?

I think you're suggesting that both N7 + N11 have the same LF cutoff. And to build the N7 shallower (max. well depth = 121mm) to match the LF of the N11 (max well depth = 135mm), yes?

Sorry, no pictures yet as nothing is built, though I can diagram the room... When I do construction I'll be taking pictures, for sure.

Jason you wrote:
With N7, it seems that my HF cut of 5.7kHz is 'close' to the flat plate Hz (5096Hz). If I raise my N-7 LF to 811Hz, my HF cutoff becomes 5677Hz, matching my well width of 3cm. I would prefer not to alter the 3cm well width, if possible. My plan is to cut 3cmW 1pcf construction foam (polystyrene? - the blue stuff, very hard to cut with a knife, very light, flexible) to the well depths, and face them with 2.5mm plywood. (I am not building much LF absorption into the unit, but the foam will eliminate well resonances.) It makes the build MUCH easier.

I'm excited to go with the N-11/7/11/11/7 idea, and it looks like I should raise my 7-prime LF to 811Hz.

According to your ideas about the relationship of LF to HF cutoff, how could the RPG QRD-4311 possibly work, with a well width of 1.1" and max well depth of 16". I think then that LF=404 - HF=6164 Hz. (404 x 4 = 1616Hz, but the unit cuts off at 6164Hz). Please explain why the depth is so great to the very narrow well?

Alton Everest says (pp. 311-12, 2001 ed.):
"The number of wells and [narrowness of] well widths affect the performance of the units. The QRD 4311 having the deepest well depths and the narrowest well widths (feasible from a manufacturing standpoint) gives the highest diffusion coefficient over the greatest frequency range. For comparison, two other units ... the QRD-1925 and QRD-734 are built with primes of 19 and 7 and well widths of 2.5 and 3.4 inches. The performance of these, while good, is somewhat inferior to the QRD model 4311.

So I'm a bit confused here, concerning the LF relationship to well width. My choices are either 3cm (1.18") or 5cm (2") well width, in terms of available materials/construction methods.

I'm making headway, thanks to your suggestions, but would like to clarify the well width/HF/flat plate issue...

Comments? I'm probably missing something.

Sorry - that's a cut and paste and then forget to edit typo
Should be:
Standard N11 panel ........well depth = (well number squared) mod 11
Optional N11 panel ........well depth = (well number squared + 2) mod 11


Using well depth = (well number squared + 2) mod 11
Well 0.....depth=(0^2 + 2) mod 11 = 2 mod 11 = 2
Well 1.....depth=(1^2 + 2) mod 11 = 3 mod 11 = 3
Well 2.....depth=(2^2 + 2) mod 11 = 6 mod 11 = 6
Well 3.....depth=(3^2 + 2) mod 11 = 11 mod 11 = 0
Well 4.....depth=(4^2 + 2) mod 11 = 18 mod 11 = 7
Well 5.....depth=(5^2 + 2) mod 11 = 27 mod 11 = 5
Well 6.....depth=(6^2 + 2) mod 11 = 38 mod 11 = 5
Well 7.....depth=(7^2 + 2) mod 11 = 51 mod 11 = 7
Well 8.....depth=(8^2 + 2) mod 11 = 66 mod 11 = 0
Well 9.....depth=(9^2 + 2) mod 11 = 83 mod 11 = 6
Well 10...depth=(10^2 + 2) mod 11 = 102 mod 11 = 3


That's correct. Pack the N7's out from the wall with 14mm spacers and they will be flush with the N11's



From your constraints of Fins=2.5mm, Well width=30mm, maximum depth 135mm, you get:
N7 panel width = 228mm
N11 panel width = 358mm
both of which are less than the 424mm panel width needed to diffuse 811 hz.

The N7 panel would need wells 59mm wide to fix this. Since the N11 has more wells, they would only need to be 53mm, but then the HF cutoff would be different. Better to make them the same. Why not glue two pieces of your foam together for 60mm wide wells?

There are plenty of ways to mix up the panels. Some would argue that you can have a different frequency for the 2nd panel. Jason would know more than me on this.....

Thanks, your information above makes the situation much more clear. This option:

"Optional N11 panel ........well depth = (well number squared + 2) mod 11"
is very cool! Thanks.

(By the way, can the above formula be successfully applied for higher N values as well? Does the '+2' constant change?)


Taking your comments into account, please consider these new options, below. I found out I can get 4cm depth EPS board, so:

1x N17 with 5cm wells + 2.5mm fins, fits almost perfectly (89.25cm) into 91cm (3') frame (1199LF - 3442HF Hz).

2x N11's (squared + 2 option) + 2.5mm fins with 4cm wells (811LF - 4318HF Hz). The 93.5cm length can incorporate the frame (1.75cm at each end) by beginning and ending with a zero well (same derivatives as you posted, just starting from a different point):

0 7 5 5 7 0 6 3 2 3 6 | 6 3 2 3 6 0 7 5 5 7 0

Well depth = 0mm 134mm 96mm 96mm 134mm 0mm 115mm 57mm 38mm 57mm 115mm "Giving a design frequency of 811hz." I think 811Hz - 4318Hz looks quite good on paper for this depth diffusor. To continue, looking at 2x N11's with 4cm well width + .25cm fins = 467.5mm, which is over your 424mm Length to diffuse 811Hz. Did I miss a HF problem though, with the 4cm well width (you were recommending 6cm wells)? (If so, would there be a problem with the 2' x 4' x (5.75") N13 made by RealTraps, which likely has an approx. 4~4.5cm well width?)

Easier to build too. However, there's the unavoidable issue of repetition. Will this symmetry (through 4 periods) create problematic acoustic issues? What are these issues? (Andre, in another thread, cautions against over-repetition of QRD periods.)


Extra notes.
Here is more DIY information on my proposed build. The costs are very low.

I looked at building absorption into the tall wells, but am leaning towards EPS foam (almost no absorption), because it is so much easier and cheaper to build. I think I will get enough bass reduction through the many traps placed above, below and in the corners of my room. If I am mistaken about this, please let me know ...

The problem I have is that the rigid rock wool I can get (in Japan) is costly, and does not provide a solid base for a well face, thus complicating the build. If I go this route, I can get and rip two 4cm faces from cheap 9mm D x 9cm W x 100cm L fir stripping boards -- ($0.55 each = $0.28 per face). But then, it's necessary to nailgun to height suports, nailgun face to fins, then glue/seal the wells - it's complicated.

Today I further investigated EPS "Blueboard" options. Can get 1cm, 2cm, 3cm, 4cm, 5cm depths (each comes as a 91cm x 183cm panel). I can go over 5cm to 6cm as you recommend (yes, doubling a 3cm piece). EPS is very light and stiff (not flexible as I said before tutt), easy to work with and lengths can be cut on a table saw, with the right blade.

I have two construction options for the well faces:
1) My first thought, for beauty as well as density, is to face the EPS with 2.5mm plywood (as I wrote before).

I am also considering though to,
2) use the EPS alone for facing, prime it with a water-based latex color, then shoot it with polyurethane lacquer, creating a harder, reflective surface. What do you think of this foam-face + latex + polyurethane idea? (I was thinking that EPS "blueboard" alone does not make a good reflective surface, due to its low density.)

FYI, even with wood faces, I've priced out a 93.5cm c 93.5cm (3' x 3') diffusor, including plywood faces of 2.5mm plywood, fins, EPS foam, plywood backing, 12mm x 13.75cm wood outer frame (ripped from a plywood panel), silicone sealer, glue, corner braces = $35. USD or less, total cost. If I go with foam-only faces + polyurethane, the price drops and labor drops a lot!

Notes.
I was thinking that my HF (therefore well widths) should remain the same for all N-primes (all diffusors on the wall). It makes the build much easier, too, with one standard. I could adjust width to 4cm or 5cm, but don't you think that if you raise the LF (less depth) and/or build wider wells you are reducing bandwidth to the point that the diffusor doesn't function so well?

And what about that RPG QRD-4311, which seems to go against the HF recommendations? This QRD seems rather awesome...

That will work for sure, and another option, if you choose to keep all backings flat against the wall, is to build up from in front of the backing: place a 10mm EPS sheet panel faced with a 4mm piece of plywood in front of the backing, the same size as the N7, then build the N7 on top of it. thumbsup

I hugely appreciate your input, suggestions, and help with the mathematics. It's an exciting project, I don't want to waste the time and effort due to my inadequate understanding and experience.

Some poor digital camera shots of the live room. Nothing has happened yet! & please forgive, the room harbors audio/instrument storage -- it will be beautiful ...

1) Live room diffusor wall in question
first step in the process (500cm x 240cm)

2) Live room - drum nook
it's too small, must live with it

3) Vocal/iso booth & mix room side
everywhere is insulated, double-wall construction

4) Windows look out on cypress and bamboo, on a mountainside

5) Mixing desk, looking in (A & H ZED-R16)
I and a friend built this custom desk.
Underneath: 8r rack, 1500W APC Smart-UPS, PC. Powered monitors are off-camera (not in position).

The main recording work is shakuhachi, koto, acoustic/electric guitar, and voiceover. I do multimedia educational production and cultural preservation as part of my research work ...

Hi Jason,

As you see, due to certain unknowns and wanting a standard well width, I am presently thinking of going with all N11 arrays, which would be 8 periods on the wall. Your discussion of proportions and "flat plate frequency" is really helpful. And Collo filled in the missing math for the mod option.

I have upped my well width to 4cm (1.57")... Doing this means that I must either change my frame size, or find different N-primes. Easiest is to use all N11, as 2 N11's fit my existing dimensions.

But for more $$, if I make frames that are 104cm long, I can get:

N7 (12.1cm deep) + N11 (13.5cm deep) + N7 (12.1cm) = 106.25cm (use of framing material for the 0 well adds up to the needed total).

-------N7--------------N11---------------N7-----
0 1 4 2 2 4 1 | 2 3 6 0 7 5 5 7 0 6 3 | 1 4 2 2 4 1 0

But it seems that 4cm wells in the N7 are 'iffy.' ? Also, that's a lot of 'backing' issues, with the shorter N7 versus the N11.

So, is it better to use only N11 (2 per frame, in mirror symmetry):

---------N11------------------N11--------
0 7 5 5 7 0 6 3 2 3 6 | 6 3 2 3 6 0 7 5 5 7 0

Hmm, I'm a bit stumped ...

The amount to add inside the modulus varies with the panel order.
I can't give you a formula, but here are the optimums for a few

N7 already at best depth saving
N11 use +2
N13 use +4
N17 use +4
N19 use +3
N23 already at best depth saving


If you're looking at an N17 / N11 combo, you might be best to go for different frequencies for the panels. This will break up the periodicity and let you utilise the full 135mm depth in each case

Your N17 stats are right, but you can do better...

Adding +4 inside the modulus gives you a design frequency of 972hz for your 135mm depth.

Here's the breakdown: (since you were side-shifting the N11's you may as well do the N17 so it will mate up)

Data for One Dimensional QRD (Quadratic Residue) Diffuser
Custom N17 panel: Shifted down 4 depth units and left 8 wells
Design frequency 972 hz
Number of wells: 17
Deepest well in mm 135
Fin width in mm: 2.5
Width of wells in mm: 50
Ratios 0 0 2 6 12 3 13 8 5 4 5 8 13 3 12 6 2
Well depths in mm 0 0 20 62 124 31 135 83 52 41 52 83 135 31 124 62 20
Phase shift in degrees 0 0 42 127 254 63 275 169 105 84 105 169 275 63 254 127 42
LF cutoff frequency 486 hz HF cutoff 3440 hz
Panel width 892.5 mm
Minimum distance to seating position 2124mm (3 times wavelength of LF cutoff frequency)

Your side-shifted N11's come in at:
Data for One Dimensional QRD (Quadratic Residue) Diffuser
Custom N11 panel: Shifted down 2 depth units and left 3 wells
Design frequency 811 hz
Number of wells: 11
Deepest well in mm 135
Fin width in mm: 2.5
Width of wells in mm: 40
Ratios 0 7 5 5 7 0 6 3 2 3 6
Well depths in mm 0 134 96 96 134 0 115 57 38 57 115
Phase shift in degrees 0 229 163 163 229 0 196 98 65 98 196
LF cutoff frequency 405 hz HF cutoff 4300 hz
Panel width 467.5 mm
Minimum distance to seating position 2544mm (3 times wavelength of LF cutoff frequency)

Since these are both shallower panels than normal, either the 40mm well width or the 50mm will be fine. (HF cutoff 4300hz vs 3440 ... I would go for the 40mm for the better bandwidth, but it depends on your needs as far as overall panel sizes goes)

The 424mm panel width referred to earlier is the minimum you need for a design frequency 811hz (one wavelength). The panels can be larger than this though.

The Realtraps dimensions you gave model fine. For the RPG QRD-4311 you would need to know the overall width and depth to model it.

As for adding absorption into the wells, I think that's a whole other area of expertise. The above figures are for the standard maths, assuming solid well bottoms.

phew!!!

Hi collo,

Wow, thanks for your detailed reply. You've communicated a treasure trove of specifics I've not seen elsewhere, and thanks too for thinking of my room, frame size and searching out some possibilities, especially with the higher N-prime QRDs. I was stumped earlier, feeling that the best dimensional fit was using only 8 periods of N11 --- a bad thing with the repetition.

Looking everything over, Let me throw this idea out, see what you think -- working with approx. 93.5cm (3') frame size:

Assuming these dimensions (all just as before):
well width = 4cm
well depth (max) = 13.5cm
fins = 2.5mm
frame = 91cm H x 91cm i.d., 93.5cm (o.d.)
(o.d. = if left+right wood-framing members, 12.5mm each, are added).

4 frames = 375cm (12'4") length coverage.

Ok, so a well-segment is defined as: 4cm + 2.5mm fin = 4.25cm.

Then, 22 well-segments = 93.5cm -- a perfect fit. This is why 2 periods of 11N works nicely.

As the 4 frames will mate up against each other, the two adjoining frame pieces = 2.5cm potentially of 'zero well dimension'. Let's say I now add a solid wood spacer of 1.75cm between the frames, making a total zero-well dimension of 4.25cm = one well-segment. Bear with me, I will try fitting an N23:

The N23 will have 11 wells in one frame, 11 wells in the next, and the zero well across the adjoining frame members (plus small spacer) at its midpoint.

Using four frames, put 1.75cm spacers wherever an N23 spans two frames (or in other options, put the zero well hard left or right, and add spacer; see further below):

Frames:
1 [spacer] 2 3 [spacer] 4

This creates the extra zero well, so just adjust your N23 zero well by shifting the N23 pattern over by 11 places.

Now this can be built:
[----1---]|[---2--][----3----]|[--4---]
A. N11+N2\3 + N11|+ N11 + N2\3 + N11|

Arrange the N23 to span frames 1+2, with the zero well right on the frame(+spacer) itself. So the first 11 wells of N23 are in frame 1 and the last 11 wells of N23 are in the first half of frame 2. Fill the last half of frame 2 with an N11. Follow the pattern again for the last two frames. Note that the repeating symmetry is broken up, though I'm not sure about the symmetrical N11 at the center. (See other options below.)

I mention the N23 because on my calculator it seems to have a surprisingly low LF for its period: "Approximate frequency range: 997 - 4318 Hz" (effective to 500Hz or so).

What do you think?

Using the same logic, and putting N23 zero wells across two frames (with a spacer) It's also possible to build:

3x N23 + 2x N11 (3 spacers):
B. | N23 | N11+\N23\|/N23/+N11 | N23 |

2x N23 + 4x N11 (2 spacers):
C. | N11+N11 | N23 | N23 | N11+N11 |

2x N23 + 4x N11 (2 spacers):
D. | N23 | N11+\N23\|/N23/+N11 | N11+N11 |

2x N23 + 4x N11 (2 spacers):
E. | N23 | N11+N11 | N23 | N11+N11 |

('\ /' indicates half of the N23)
In C. N23 zero-wells are shifted left/right; in E. shifted right/right.)

If this idea is acceptable, then 22 well-segments of 4.25cm each in the 93.5 (3') length frame looks pretty good. Though I'm not sure which of the patterns (A~E) is best ... though B. or A. seems most appealing.

If this isn't crazy... I think it's also possible to add 'zero-well' material to each end of the full array, if necessary, which will make a kind of, er, meta-frame decor.
stike

You can build an N23 as two panels with a packer between....


Data for One Dimensional QRD (Quadratic Residue) Diffuser
Standard N23 panel: Shifted left 12 wells
Design frequency 994 hz
Number of wells: 23
Deepest well in mm 135
Fin width in mm: 2.5
Width of wells in mm: 40
Ratios 6 8 12 18 3 13 2 16 9 4 1 0 1 4 9 16 2 13 3 18 12 8 6
Well depths in mm 45 60 90 135 22 97 15 120 67 30 7 0 7 30 67 120 15 97 22 135 90 60 45
Phase shift in degrees 93 125 187 281 46 203 31 250 140 62 15 0 15 62 140 250 31 203 46 281 187 125 93
LF cutoff frequency 497 hz HF cutoff 4300 hz
Panel width 977.5 mm
Minimum distance to seating position 2076mm (3 times wavelength of LF cutoff frequency)





Here are the N23 and the N11 - re-arrange to get what you are looking for...



Since you have used up the zero-depth well of the N23 to split the panel, there's no need to left-shift the N11's.

The N11 is thus:

Data for One Dimensional QRD (Quadratic Residue) Diffuser
Custom N11 panel: Shifted down 2 depth units
Design frequency 811 hz
Number of wells: 11
Deepest well in mm 135
Fin width in mm: 2.5
Width of wells in mm: 40
Ratios 2 3 6 0 7 5 5 7 0 6 3
Well depths in mm 38 57 115 0 134 96 96 134 0 115 57
Phase shift in degrees 65 98 196 0 229 163 163 229 0 196 98
LF cutoff frequency 405 hz HF cutoff 4300 hz
Panel width 467.5 mm
Minimum distance to seating position 2544mm (3 times wavelength of LF cutoff frequency)


Arrange the panels with the Barker Code:


I guess two lots of the pattern for 3 panels gives you

N11 N11 N23 N11 N11 N23

This would build up like:



Dressing up each end of the completed array of panels with an extra zero-depth well shouldn't hurt anything

Now that you are in 'explaining for dummies' mode...and I DON'T mean xenon...I just can't see the need for (or how you used it) the barker code in this instance.

It is just this sort of manipulation of the data that makes qrdude the 'dudest' calc on the planet!

Well done dude.

( a link to this thread as 'an example of how you can now manipulate for your build' might be useful, saves a wordy explanation in the calc)

Man, that's beautiful!

I have a question, is QRDUDE available to download? The eye-candy factor alone is stunning. I'll be making more QRDs for other walls! (Actually, this brings up a question about using different depth/size QRDs on an opposing wall in a small-room, like if I build a 8cm (3.1") depth QRD opposite, with 2cm wells for HF/flutter?)
. . . . . . . .

I think I'll re-arrange the design pattern slightly, as my frames (4 panels) each hold 22 well-segments. (This goes against the Barker code though.)

Re-orienting from your diagram below, each of your panel pairs (1+2) (3+4) (5+5) (7+8) being one unit, the pattern will change to the "B" option, in my post above. In this pattern: | | = F (Frame of 22 wells = 93.5 cm (3') long).

Note that there is left-right mirror symmetry here (F1+F2 mirror F3+F4), but is it really an issue? It will make the acoustics of my small room more similar, between front and back, I feel, where having a 2N11 left-side and N23 right side will create 'difference'? Or should I not think this way? Anyhow, here is my thought:

For F1 ~ F4 frames:

| N23 | N11+\N2|3/+N11 | N23 |

1. F1: has an N23. I put the zero well on the left, and attach a 'dress up' zero well to the left-side frame member.

2. F2: I shift the N11 so that the zero well is on the left side, and use part of the left-frame as the zero well for it. I shift the N23 so the zero well is at the center of the period (and exact center of the wall and room), and this well spans F2+F3.

3. F3: Last half of the N23 and N11 with its zero well shifted right, and I use part of the right-side frame for that N11 zero-well.

4. F4: Shift the N23 zero well all the way right, and attach a 'dress up' zero well to the right-side frame member.

I note in the above pattern, 3 N23's and 2N11's. Probably it's better to have more N23 periods and fewer N11, given the option... (closer micing, greater 'resolution'). But the symmetry could be a problem.

This is very cool

Very pretty! My friend who's helping with the build is a visual person, so the graphic image is really valuable. Zooming, printing, and posting near our work area will be really helpful.

QRDude is still a couple of weeks from release.

Moving to your B option is OK

N23 N11 N23 N23 is still a valid Barker sequence (you can run the sequence backwards)

To get the benefits of multiple panels of the same order adding together to give more effective diffusion, you would want them all to be the same.
This means all the N23's should have the same amount of left shift as each other, and none of them reversed.

The main reason emphasis is put on having a zero-depth well at the left end is so that you can move one half well to the other end.

If all your panels are built this way, they sit together nicely.
To achieve this, you would need to build the centre N23 as a full unit, and the N11's as separates.

This would look like:



The N23's:
Data for One Dimensional QRD (Quadratic Residue) Diffuser
Standard N23 Panel
Design frequency 994 hz
Number of wells: 23
Deepest well in mm 135
Fin width in mm: 2.5
Width of wells in mm: 40
Ratios 0 1 4 9 16 2 13 3 18 12 8 6 6 8 12 18 3 13 2 16 9 4 1
Well depths in mm 0 7 30 67 120 15 97 22 135 90 60 45 45 60 90 135 22 97 15 120 67 30 7
Phase shift in degrees 0 15 62 140 250 31 203 46 281 187 125 93 93 125 187 281 46 203 31 250 140 62 15
LF cutoff frequency 497 hz HF cutoff 4300 hz
Panel width 977.5 mm
Minimum distance to seating position 2076mm (3 times wavelength of LF cutoff frequency)

The N11's
Data for One Dimensional QRD (Quadratic Residue) Diffuser
Custom N11 panel: Shifted down 2 depth units and left 3 wells
Design frequency 811 hz
Number of wells: 11
Deepest well in mm 135
Fin width in mm: 2.5
Width of wells in mm: 40
Ratios 0 7 5 5 7 0 6 3 2 3 6
Well depths in mm 0 134 96 96 134 0 115 57 38 57 115
Phase shift in degrees 0 229 163 163 229 0 196 98 65 98 196
LF cutoff frequency 405 hz HF cutoff 4300 hz
Panel width 467.5 mm
Minimum distance to seating position 2544mm (3 times wavelength of LF cutoff frequency)

Hi Collo,

I follow you here:
but I can't build a half-panel N11 so easily. I noticed in the ripple tank image that a pair of N11s had a nice spectral spread. Anyway, I need to add an N11 into the picture:

#1 N23 N11 N23 N23 N11? but not:

#2 N23 N11 N11 N23 N23?

Because #2 is an easy build, where #1 has issues. Any thoughts on this?

In that case, go old school and have a look at 3 N23's and one inverse (I23)
The depths are different, but if you go for the +2 design, you get the best mix. For your 135mm depth, your design frequency will be 1162hz

Whilst this gets the lowest design frequency, you give up any zero-depth wells, meaning there is no point in side-shifting.

The N23:
Data for One Dimensional QRD (Quadratic Residue) Diffuser
Custom N23 panel: Shifted down 2 depth units
Design frequency 1162 hz
Number of wells: 23
Deepest well in mm 129
Fin width in mm: 2.5
Width of wells in mm: 40
Ratios 2 3 6 11 18 4 15 5 20 14 10 8 8 10 14 20 5 15 4 18 11 6 3
Well depths in mm 12 19 38 70 115 25 96 32 128 90 64 51 51 64 90 128 32 96 25 115 70 38 19
Phase shift in degrees 31 46 93 172 281 62 234 78 313 219 156 125 125 156 219 313 78 234 62 281 172 93 46
LF cutoff frequency 581 hz HF cutoff 4300 hz
Panel width 977.5 mm
Minimum distance to seating position 1776mm (3 times wavelength of LF cutoff frequency)

The I23:
Data for One Dimensional QRD (Quadratic Residue) Diffuser
Custom Inverse N23 panel: Shifted up 2 depth units
Design frequency 1162 hz
Number of wells: 23
Deepest well in mm 135
Fin width in mm: 2.5
Width of wells in mm: 40
Ratios 21 20 17 12 5 19 8 18 3 9 13 15 15 13 9 3 18 8 19 5 12 17 20
Well depths in mm 135 128 109 77 32 122 51 115 19 57 83 96 96 83 57 19 115 51 122 32 77 109 128
Phase shift in degrees 328 313 266 187 78 297 125 281 46 140 203 234 234 203 140 46 281 125 297 78 187 266 313
LF cutoff frequency 581 hz HF cutoff 4300 hz
Panel width 977.5 mm
Minimum distance to seating position 1776mm (3 times wavelength of LF cutoff frequency)

Barker coding:
N23 N23 I23 N23

Once again, thanks -- every post, new information revealed -- how did you come by all this (forgive my ignorance).

I'll comment on your 'old school' formulation:
Can I ask, why 'old' and 'school'? Just curious...

On the way to work today I realized something. I'd like to return to your post #15 where you have an N11 in a half-frame (46.75cm (1.5') long x 93.5cm H). It's true, building half-frames takes more time and materials, but I'm planning to build half-frames of N11 laid horizontally over the 4 vertical panels, in any case. It can't hurt to build two more.

In Post #15 you write:
"N23 N11 N23 N23 is still a valid Barker sequence (you can run the sequence backwards) ... To get the benefits of multiple panels of the same order adding together to give more effective diffusion, you would want them all to be the same. This means all the N23's should have the same amount of left shift as each other, and none of them reversed."

Thus the need for half-frames of 11N, as all N23 must have a zero-well (choose one) hard left or hard right -- they cannot span frames as suggested (by me) before. I follow the Barker code for 4 arrays of two types as:

+1 +1 −1 +1
+1 −1 +1 +1 (reversed)
or
+1 +1 +1 −1
−1 +1 +1 +1 (reversed)

Which looks like:
(N23 +, N11 = -)

N23 N23 N11 N23
N23 N11 N23 N23 (reversed, as suggested)
or
N23 N23 N23 N11
N11 N23 N23 N23 (reversed)

But I am short one N11 panel I need a minimum of @380cm length coverage -- where can it go? A Barker Code for 5 is needed:

+1 +1 +1 −1 +1
+1 −1 +1 +1 +1 (reversed)

And the problem is that the code calls for 4 N23 and 1 N11 (or the opposite). A possible solution, keeping in mind my wall is 500cm and I want corner traps,

I can build:
N23 N23 N23 N11 N23 - 437.75cm

This means 4 pcs. 93.5cm frames (plus left-side spacer) for the N23, and an additional half-frame for the N11, which will have its zero-well on the left side.

This would be the perfect arrangement, but it's too long. For the corner trap I need at least 45cm (1.5') on each side of the diffusor -- and my plan calls for 60cm on each side, nominal. So I can't go beyond 410cm in length and would prefer 380cm of diffusion.

This problem encourages me to void the Barker code. In terms of dimension, the wall works perfectly with 3 N23 + 2 N11, so to void the Barker code, by taking the code for 5 and altering the last digit:
from
+1 −1 +1 +1 +1
to
+1 −1 +1 +1 −1

= N23 N11 N23 N23 N11

I'm not sure how badly the Barker code alteration will affect dispersion; the pattern is non-symmetrical -- it seems a compromise I have to make, as I don't want to alter my well depths or widths (and the relatively low LF of this-type N23 doesn't hurt. Also, the 4 horizontal half-frames will fit perfectly overhead the vertical frames.) In this design, all zero wells will be on the left side of each panel (and each N).

Not perfect ... heh

Quick revision....
To get the best out of diffusers, you need a few repeats - some say four at least if you can fit 'em in. Whilst this increases the diffusion, it increases the output at certain angles, known as lobing

To fix the lobing, you insert a different panel into the sequence using the Barker code to pick it's location.

The absolute best panel to use for this job is a matching inverse panel. This why I used the term "old school" when referring to this solution.

There are other solutions, such as different order panels and different design frequency panels, that also cut the lobing, but perhaps slightly at the expense of the even energy distribution that you get with using an inverse panel.
---End revision--


It's always best to start with the space available.

You have:

Total width 3800mm absolute maximum 4100mm
Max depth 135mm
Preferred Fin + Well width 42.5mm

That gives you:
Total wells = 3800 / 42.5 = 89.4 ... let's aim for 89.

If you're happy to depart from the panel width we've been discussing, you may find a good fit using:

5 * N17's gets you 85 wells
This would give you an overall width of 3613 - fairly close to what you are looking for.

You would build this as 4 * N17's plus one inverse I17

Using standard panels, you would have a design frequency of 1274hz.
The inverse panel would be 135mm deep and the normal panel would be 127mm.

We can do better...
Using the trick of adding inside the modulus, we find that +6 for the N17 and -6 for it's inverse, brings the panels to the same depth. (Most orders don't get to the same depth - N17 is just lucky!). This gives a design frequency of 1124hz.

Since neither of these panels have zero-depth wells, there is no point in side shifting them.

Barker 'em up as....

N17 N17 N17 I17 N17


The N17:
Data for One Dimensional QRD (Quadratic Residue) Diffuser
Custom N17 panel: Shifted down 6 depth units
Design frequency 1124 hz
Number of wells: 17
Deepest well in mm 135
Fin width in mm: 2.5
Width of wells in mm: 40
Ratios 6 7 10 15 5 14 8 4 2 2 4 8 14 5 15 10 7
Well depths in mm 54 63 90 135 45 126 72 36 18 18 36 72 126 45 135 90 63
Phase shift in degrees 127 148 211 317 105 296 169 84 42 42 84 169 296 105 317 211 148
LF cutoff frequency 562 hz HF cutoff 4300 hz
Panel width 722.5 mm
Minimum distance to seating position 1836mm (3 times wavelength of LF cutoff frequency)

The I17
Data for One Dimensional QRD (Quadratic Residue) Diffuser
Custom Inverse N17 panel: Shifted up 6 depth units
Design frequency 1124 hz
Number of wells: 17
Deepest well in mm 135
Fin width in mm: 2.5
Width of wells in mm: 40
Ratios 11 10 7 2 12 3 9 13 15 15 13 9 3 12 2 7 10
Well depths in mm 99 90 63 18 108 27 81 116 135 135 116 81 27 108 18 63 90
Phase shift in degrees 232 211 148 42 254 63 190 275 317 317 275 190 63 254 42 148 211
LF cutoff frequency 562 hz HF cutoff 4300 hz
Panel width 722.5 mm
Minimum distance to seating position 1836mm (3 times wavelength of LF cutoff frequency)

ps: How did I come by this info?.... Lot's of reading and discussion. Thanks to users TerryJ and Lupo for spurring me on!

Have we sorted this yet???? AFAIR we were 'still' looking for a reputable reference for this (atm) factoid.

I did quote the dutch guy saying this in my thread, but for all we know this could simply be internet lore? That he mainly sells 7 primes may or may not have something to do with it.

7 primes are convenient to manufacture and ship (and the depth gain of course) so to me that is a reasonable first approximation of their prevalence.

It also leads to these lobing and barker code questions.

So why do we not just go to a straight 89 prime then? If the 'problem' is the frame sizes, a little bit of ingenuity will get around that?

A quick look at THE qrd calc on the net (qrdude for those not yet in the 'club'hehheh) gives us a design frequency of 1265 (Flow 632) which has gotta be in the ballpark.

Hah, utilising the amazing inbuilt capabilities of the calculator, +25 gives us an flow of 593, and the recommended width is about 36mm, just shy of the 40 here.

Gee, all that swiss army knife of a calculator needs is a flat plate frequency.

Anyway, atm I am not convinced that repetition will necessarily give the best results, why not take advantage of the better diffusion a higher prime will give?

No, I am not the one volunteering to draw an 89 prime qrd in the ripple tank!!

EDIT..hmm, an option for those who may need it (eg for some fool who will remain nameless who tries to draw an 89 prime in a ripple tank) would be a 'remain on top' button, save flicking back and forth. Dunno if that is doable or needed, just a thought.

The best article I've found is the google books partial reproduction of the RPG document.

It suggests five periods as being a good target.
It also covers the concept of adding a constant inside that modulus that is at the heart of QRDude running in advanced mode.
Also mentioned is the Plate frequency.

As good as the article is, it doesn't answer the question of whether a single large order panel is better or worse than a Barker sequence of lower order panels comprising a similar number of wells. Perhaps that is covered on the missing pages. Lupo is the only person we know that could actually afford the book!

Interesting discussion!

Yes, it would be clever to locate a source on the repeating 'N'x periods. The inverse 'iN' following the Barker code is likewise clever.

In terms of an 89 prime, I would like to pipe up on behalf of, the builder --especially a builder who may not have tried this before. My first attempt was with a 5.1cm well (2") and height of 135cm (53"). Working with 2.5mm plywood strips (which are bendy) is really tough, as is cutting them straight, even with a table saw.

I have gone to the 93.5cm (3') square frame as a general ok not too big and not too small size. It's also nice that with 4.25cm well-segments, 2 11N's fit, and with a spacer a 23N fits, and you can also do 3 N7s (with a 1cm filler on each side).

I feel the frame size is non-trivial in realworld build it in your backroom life. Once you have an approximate size (and I am happy to expand or shrink a couple of wells, or even go half-size), then it must be remembered that zero well placement comes into play when moving across the frames. Which is why an 89 prime is likely quite difficult, unless you can make various odd frame sizes.

The next point -- I'm not so willing to sacrifice the LF Hz -- which is where I started: I was really impressed with the LF performance of the N7 (read my first post). It's been quite a journey from (2 days?) ago, but I remain concerned to build as wide a bandwidth QRD as reasonable for the room.

I feel the 23N + 11N is very workable. I'm considering the 17N suggestion, but in terms of frame size and overall length it's not ideal (too short on both counts).

Another perhaps small point is that if one is able to arrange zero wells across the frames you are actually getting 100% QRD across the entire array. Surely this must is a good thing, rather than having your array periods broken up by framing which can be 3-5cm (of nothing).

A last point for me concerns the room itself. The array I'm planning passes opposite a 45 deg. wall which is narrowing the room and then into a drum nook, which is about 1meter shallower than the rest of the room. This must skew all the theory to some not very accountable (by me) extent.

Again, for the builder, a modular technique has many advantages. My 93.5cm frames sit on top of 93.5cm absorbers, and on top of the vertical diffusor will be 93.5cm horizontal diffusion. (Also half-frames remain modular, you just need 2.) And if I want to move these frames, mix and match, it's all easy -- to stack, to get through the door, even to store. I doubt this will happen -- (but I always say that) ...

So I think a reasonable size frame and modular construction, with the rest of the treatment considered, is just as worthwhile a pre-production step as overall dimension. (is this a rant?)

I come back to the original goal -- to build the best possible diffusion into the room, given certain dimensional and construction constraints. Collo's last suggestion is the 17N, which I'm still considering... though the N23 has some real advantages of its own. Also just to mention, I am thinking of Heimholtz corners with absorption (John Sayers style, claimed 150Hz-500Hz spec.) -- this works well with an effective diffusion LF of 581Hz:N21 and 405Hz:N11).

In terms of the same repeating N-periods, how about all N11s, (there would be 8). You gain quite a bit of LF over the N17, right? With inverse N11s following the Barker code (or)?

Collo, what do you think of this idea, especially in comparison to all N17?

8 * N11's sounds OK.

Your would need to make a couple of them inverses to keep Mr Barker happy.

If you use +4 for the N11's and -4 for the I11's you get them the same depth.

You don't get any zero-depth wells, but I would suggest leaving the right hand wall off all but the last panel. With the foam material you are going to use in the wells, they will seal up when you mount them firmly against each other. Visually, this would look like a single panel.

"Another perhaps small point is that if one is able to arrange zero wells across the frames you are actually getting 100% QRD across the entire array"
I'm not sure what you meant by that!

It's good to get some hands-on info about build techniques. I'm looking to build some in the near future too, so am interested in how the build goes.

This thread goes to show that there are many ways to organise these. It's something that I suspect intimidates a lot of people.

And understand it....my brain just fogged over, but was that the beer?? (I suspect you two would follow it pretty well tho)

Argh, can't copy and paste from it. This caught my eye tho, "If a perfect binary sequence could be found then the single diffusor response would be recovered, but there are no such 1D sequences."

That suggests to me that (theoretically at least) a single large prime would be preferable over multiple smaller ones. On a practical level (as pointed out by xenon) other factors come into play.

Does it? I could have missed it but have seen nothing that suggests that.

Hmm, I must stump for the book soonish. Anyway, unless it is answered more definitively elsewhere, I go away with the interpretation above.

In any case, the point of ease of manufacture is not to be sneezed at. That is the reason why *I* prefer applying the barker code by rotation of the same qrd by 180 degrees. Saves making two different types (normal and inverse). If you are going to do a Mr Ford, do it completely.

This is just theoretical now (not trying to impose any thoughts on anyone) but just how much bottom end is being sacrificed? There is so much 'fluff room' in these theoretical calcs that 30 hz or so on paper is nothing in the real world, surely. (EDIT just looked back and see what you mean)

Yeah, this is not so 'simple' as throwing a few batts on the wall or in the corners! Still, fun stuff.

The "five repeats" comes from page 238:



Unfortunately, the last 3 paragraphs referred to would be on page 237, which is not present in the Google book preview. This is like one of those "treasure hunt" movies...

Flipping a normal panel over 180 degrees and presenting the back face to use as an inverse, only works if the panel is made to the full design depth. This of course negates the 4/7 gain you get with an N7.

Hi Terry,

Well, yes I have the same question as yourself, if I go with all N11, can't you just flip some upside down, following the Barker code?

Another question: what is gained (beyond a bit of closer mic-ing, and loss of LF), between 2x N11 and 1x N23?

To your thoughts:
My question is related -- why not just flip some of the N11s (using the +2 constant) as Collo described above, and here:
--------
The N11 panel can achieve a more economical depth by using
well depth = (well number squared + 2) mod 11

giving well ratios of:
2 3 6 0 7 5 5 7 0 6 3
(maximum depth 7/11)

For your maximum depth of 135mm, these translate to:
38mm 57mm 115mm 0mm 134mm 96mm 96mm 134mm 0mm 115mm 57mm

Giving a design [LF] frequency of 811hz
---------

But since Barker fails for 8, 9, 10, 12 periods of the same type, one must have either 5, 7 or 11 periods (etc.) of the same type, it seems. What does 'flipping really do, for an N11? Can you in fact use 8 periods of the same N-prime effectively?

Barker Code Chart
1[-1]
2[-1 1]
3[-1 -1 1]
4[-1 -1 1 -1]
5[-1 -1 -1 1 -1]
7[-1 -1 -1 1 1 -1 1]
11[-1 -1 -1 1 1 1 -1 1 1 -1 1]
13[-1 -1 -1 -1 -1 1 1 -1 -1 1 -1 1 -1]

If 'flipping' worked, then why not substitute 4 N23 for the 8 N11, as this fits in Barker, and just do this: -1 -1 1 -1? If only it were this easy ... 'Flipping' has been mentioned before in other threads

So there is another way to get close to my 380cm length with 4 arrays (qudude to the rescue):

N23 N23 N19[+3] N23 = 377cm

N19 with a constant of +3 yields: 940LF - 4300HF
(effective: 470Hz - 8600HF)

- - - - - -

Collo, what I meant by "if one is able to arrange zero wells across the frames you are actually getting 100% QRD across the entire array"

Just that in multiple arrays which each have a frame put around all the wells of a particular N-period, the two adjoining QRD arrays are then split apart by the doubled frame width. Wouldn't this part -- the 'flat zero space' between, act like a flat wall between the periods? But if you span the two frame members with a zero well that's part of a QRD array itself (like I had suggested with the N23), acoustically there is no frame -- that is, no extra space between the wells of adjoining arrays -- I think.

Hey xenon, ask collo! (or lupo when he comes back)

I'm just here as the sidekick! The Baldrick to Blackadder I spose.heh

I just make the assumption that you will have better dispersion with the higher primes. That leaves out ease of manufacture of course, but I have a 'theory' that says there are always compromises, swings and roundabouts in engineering. What you gain in one area you lose in another.

So at the cost of extra difficulty and complexity, you should gain better diffusion with a higher prime. Alternatively, at the cost of better diffusion you gain ease of building with a lower prime.

You takes your chances.

In my case (tho the available space for me is not as big as yours) I'd prob take ease and quickness of building, tho I could be tempted IF I had the space of yours!





Ah, so you are suggesting I should have gone backwards as well as forwards from the page you linked to?

Hmm, that might stand me in good stead later in life. Must remember that one!!


Funny, page 237 appeared for me!

I think we are (again???!!) mixing terms? I mean by rotating 180 the wells go 1234567 to 7654321, rather than 'turn it over' or upside down.

Think pinwheel.

At least, that is how I understand it.

You just answered my question:

So if you can't flip the N23 (due to issues with the inverse N23 build), how about, to get close to my 380cm length with 4 arrays:

N23 N23 N19[+3] N23 = 377cm

N19 with a constant of +3 yields: 940LF - 4300HF
(effective: 470Hz - 8600HF)
Follows the Barker code.

Any thoughts on this?

PS From above, in the text, "the best design is one with a small number of periods..." just taking this partial statement, "small number" isn't specific. Then the sentence continues, "say, five" perhaps implying that 5 periods is recommended -- but in all situations, large and small rooms, opposite walls close or distant, mic position, etc. Unexplained?

Thanks too for your comments, Terry.

Ah, there lies the confusion.

Because the panels are basically symetrical, your "flipped" panel would give the same diffusion pattern - no use as the alternate panel in a Barker sequence.


I think the more general usage of the term "flipped" is as I referred to above.

Whatever term is used to describe using the back of the panel, it's worth presenting the following drawing. It shows why the panel needs to be the full design depth to be used in this fashion. "Design depth" is the full half-wavelength of the design frequency. It's the depth of a standard inverse panel.

The first row shows that the back of a normal panel will have fins that are too short to allow it's use as an inverse.

In reality, the well bottoms have thickness that would require the panel to be deeper than the design depth by this amount.

That sounds OK.
If you left-shift the N19[+3] by 4 wells, you get a zero-depth well on the left end of all panels.

As you alluded to earlier, this lets you use the trick of moving a half well to the right hand end of each panel. The frames of adjoining panels, plus any packing if required, form the zero-depth wells. (QRDude has this as a menu option)