John Sayers' Recording Studio Design Forum

Below I've attached a generic design for a 10 slat primitive root sequence (prime root = 11). The depth D of each slat in the sequence is simply calculated by multiplying the unit width W by the sequence multiplier m then adding in a minimum depth d. The slot width s should be relatively small compared to the unit width. A slot width of a 10th to an 8th of W is probably a good choice. No need to vary s since the varying slot depths already make this a broadband absorber!

Thomas

Neat

You are right I did use a quadratic residue sequence - residue of n squared divided by the prime root. Then normalized the series so the max = 5 5/8" (to use 2x6 lumber).

Your diagram is fantastic. Using 2x6 lumber - the high point would be 40 inches - would the design still function by normalizing the series so 10 = 5-5/8" but keep the width at 2" ?

You & John should write a book - you'd make a fortune with both of your skills combined.

Andrew,

Notice I updated my post. Actually, I was the one who was mistaken. I thought primitive root diffusors were the only ones that didn't require partitions. However, I did some further reading and found that ideally primitive root diffusors should also use partitions. Removing the partitions is just a compromise and can be done with either quadratic residue or primitive root diffusors. The diffusive characteristics are slightly degraded, but they are much easier to build without the partitions.

Still, I guess I'll stay with primitive root sequences for the time being. I find it's better to stick with as many known quantities a possible when developing a new design. PRDs are the only ones I actually know I've seen without partitions. Maybe they handle it better...?

Anyhow, my bad.

Thanks!
Thomas

Hey people,
those quadratic residue Helmholz resonators look way cool. This was of course the effect I had in mind, only much better achieved than my idea.

Love this forum. Thanks guys.

Cheers
/Henrik

And, um, I'm not REALLY a math dummy - I understand math, but I've never really been taught anything that you'd call the least bit advanced. So can anyone explain a little more at length what operations you actually do to get that quadratic residue secuence out of a figure?

Cheers
/Henrik

Henrick,

I think this is the easiest way to describe it.

First of all we pick a prime number. The bigger the prime number the longer the sequence, the greater the aspect ratio of D/W, and the wider the bandwidth of the diffusor. I think 11 is a good compromise.

p = 11

For a quadratic residue:

n = 0 to p-1 = 0,1,2,3,4,5,6,7,8,9,10

and the sequence is given by:

QR = n^2 OR the remainder of (n^2)/p if n^2 > p

so

n^2 = 0,1,4,9,16,25,36....

We can only use the first four values of n^2 because they are the only ones less than 11. The following values, however, are greater than 11. So we have to divide them by 11 and find the remainder.

16/11 = 1 remainder 5, 25/11 = 2 remainder 3, 36/11 = 3 remainder 3, .....

Therefore:

QR = 0,1,4,9,5,3,3,5,9,4,1,0

Similarly for a primitive root:

n = 1 to p-1 = 1,2,3,4,5,6,7,8,9,10

and the sequence is given by:

PR = 2^n OR the remainder of (n^2)/p if 2^n > p

PR = 2,4,8,5,10,9,7,3,6,1

Now remember, QR and PR are the multipliers to determine the well depths of a partitioned diffusor. With this non-partitioned DSR design we're interested in the slat depth not the well depth in front of it.

So our multiplier sequence is given by

m = QR(max) - QR

or

m = PR(max) - PR

Make sense?

Thomas

Thomas

one question on the calc in the diagram. Is it important to tie W to m in calculating D? If the aim is to use say 2x6 lumber. W =approx 2, so the largest D would be 2x9 = 18 - which would be impractical.

With the W*m +d I don't follow the minimum value being d - isn't that d=0?

How about

D = (m/9) * d

where d = the max length of D allowed (limited by lumber size selected)

It could well be that I am missing something.

Hello Thomas. Wow, this is the first time I've visited your forum. Cool. I'm sorry about not getting back to you about Stylmark. I've been offline for three months while looking for a new home. I'm now in Oregon. Just wanted to say this thread is toooooooo good.
I will try to use this to solve the extrusion problem. I'll post my plan section soon and see if it is any way near what your saying here. First I have to unpack the Stylmark stuff and detail the extrusions. That will take a while. In the meanwhile, I will check the whole site out. Gotta go say hi to
John and Steve.

First though, I want to reply to this:

Hey Fitz, good to see you here!:)

I'll check to make sure I have the design methodology correct. However, tying the depth to the unit width just makes intuitive sense to me, considering the diffusion is two-dimensional. How can a two-dimensional effect be independent of one of the dimensions?

Thomas

Hello Thomas, me again. Ok, I only had a minute to look at the diagram, and then look at the equasions. HOLY COW!
YOU explained some missing pieces of puzzle that I have been asking about for 2 decades.
This concept is similar to some I saw on the web at an acoustics lab in England 2 yrs ago. They had some of the slots covered with a piece of 703(thats what it looked like. They also had hollow slats, with the rear open to a reflection panel, which was the bottom of the well on one side. Damn thats hard to explain. Inside the slats were 703 or some kind of absorber. Interesting configuration but totally experimental and not proven they worked yet.
This was the basis for the Stylmark extrusion concept. So you can seperate the slats with a slot, and some of the slats were open to a reflection panel. Ha! Totally guessing at the quadratic sequence, but the shape of some extrusions lend themself to the concept. Even flanges for 703 in the wells!
Whether or not it would work is exactly why I contacted you in the first place. I'll see if I can look the site up again and post the what do you call it, URL? If thats allowed here?
Anyway, I know I'm in the wrong league here, and hate to show my ignorance in this field, so if things I'm referring to here are totally stupid, please say so, so I don't make a fool out of myself any more than necessary to find it out.
fitZ

Yeah, let us see what you're talking about. Posting URLs is most definitely allowed here.

Turns out the design methodology I described was both wrong and right. The depth is indeed tied to the width.... but it's more complicated then what I outlined. I'll post another detailed design method - only a completely CORRECT only one this time.:D

Thomas

Ok Thomas, thats cool. I'm still moving in and just got this connection up and running. Lot's to do but I'll get it up as soon as I get my other computer hooked up.
I'll definetly be following your forum Thomas. From a total laymens viewpoint though I'm finally in a place to build my studio, but over time. I would love to throw some CAD stuff on here to illustrate my questions regarding the acoustics, but I have to get the software you, John and Steve were talking about first. Doggone, you know what they say about "teaching old dogs new tricks". I'm used to Autocad but I'll use the others for conversion. Although, I dig the way Johns drawings come out in Smartdraw, so I guess I'll have to woodshed this winter!.
First hour, autocad(drawing), second, my guitar practice, third, Nuendo, fourth, Smartdraw, ffth, building the studio, ah, breaktime. Doggone I'm tired already! Let's see, we still have ......work on the shop, work on the house, work on the polebarn and oh yea.....bla bla bla here!! Oh , record a track of the tune I was writing before I moved Hmmmm, is it bedtime yet?
fitZ

Yeah, I'm certainly up for "warm milk and cookies" - only, make it a cold beer, and those cookies better be shaped like a pretzel, and don't EVEN forget those little lumps of salt on 'em, and...

wouldnt W + about 1.5" with a piece of 2 x material? that would make the deepest bit around 16" if you made "d" around 2-3" deep, right?