## Understanding Diffusion

Diffusion is typically ignored when looking to acoustically treat a room or space – which confuses me. Diffusors not only look amazing, but they are just as important as absorptive surfaces, so what’s not to love? Let’s briefly look into how diffusers work, the math behind them, and how to make one.

Just look at Blackbird Studios, how great does that look? That room would probably sound even better than it looks. That’s because of how important diffusion is in achieving a balanced sound field. Too much absorption can quickly lead to negative consequences in sound – namely ‘liveliness’. All of the great recording studios and rooms have a characteristic sound, a ‘liveliness’ to them. Whether that be from wooden floors and walls, high ceilings, large windows; these surfaces do not absorb sound, they reflect it. But long reverb tails in tracking are not usually desired – if that was the case everyone would simply record in halls and churches.

## What is diffusion?

So, the balance between no reflection and too much reflection? Diffusion. Diffusion can be thought of as the process of scattering an incident waveform into many, random reflections that spread out in all directions, creating a diffuse soundfield. A perfectly diffuse soundfield would have no frequency or level irregularities, decay times would be exponential and these decays would be the same for all frequencies and in all directions, and reverb must be the same at all points in the room. Doesn’t that sound like a dream? This perfect scenario is far from reality, and that is why it is so important to always check your work on multiple systems in different environments (more on that at another time).

The reverb of a room is affected by how diffuse the room is. Room modes cause reverb to become extended at certain room modal frequencies, and low frequency modes cause more pronounced reverb. Reverb time and level will also change with positioning in a room or space. What diffusion panels or diffusers do is provide many reflective surfaces that are needed to scatter incident waves back into a room in a random fashion.

There are a number of ways by which diffusion can be achieved.

- Random surface shape.
- Convex surfaces.
- And mathematically calculated diffusers.

Mathematically calculated diffusers are calculated to their purpose. The most common mathematically calculated diffusers are Reflective Phase Grating diffusors. This type of diffuser can be divided into two types. Quadratic Residue Diffusers, and Primitive Root Diffusers.

These two designs are based off of different mathematical principles. You can calculate what the maximum and minimum wavelengths that are to be affected by a particular panel by measuring the maximum well depth, and approximately half of the width of the well (for maximum wavelength and minimum wavelengths respectively).

The design I ended up focusing on was that of the Primitive Root Diffuser, and because I like my sanity I used a calculator to achieve my design, and adapted it to the available materials. The calculator can be found following this:

## Math (yuck)

For those who actually enjoy mathematics I will briefly entertain your strange brains if you haven’t heard of these concepts and equations already.

Formula for QRD Diffusors.

n2 modulo N

n = sequential numbers i.e 0,1,2,3…..

modulo = remainder

N = any prime number

EG. Prime number 7

02 12 22 32 42 52 62 72 (sequential numbers)

0 1 4 9 16 25 36 49 (squared)

0 1 4 2 2 4 1 0 (remainder)

(the final row numbers are your well depth ratios.)

Here is a forum post discussing the coding for creating a Primitive Root calculator for a diffusion panel:

*“The primitive root diffuser uses a grid of (typically wooden) posts, each with a different height (to obtain a different reflection delay time). The heights of the posts are chosen according to successive powers of a primitive root G, modulo N (a prime number).*

*Suppose we choose N = 41. Our program should select one of the primitive roots of N, which are [6, 7, 11, 12, 13, 15, 17, 19, 22, 24, 26, 28, 29, 30, 34, 35]. Suppose our program selects the smallest primitive root, G = 6.*

*Our program then chooses the squarest dimensions X,Y for the array such that X*Y = N-1. The clear choice is X=8 and Y=5.*

*Then our program populates the array with successive powers of G modulo N (starting with G^0), traversing diagonally. The program then returns/prints the array:*

*1 14 32 38 40 27 9 3*

*18 6 2 28 23 35 39 13*

*37 26 36 12 4 15 5 29*

*10 17 33 11 31 24 8 30*

*16 19 20 34 25 22 21 7*

*Note how it begins with 6^0 mod 41 = 1, then 6^1 mod 41 = 6, then 6^2 mod 41 = 36, then 6^3 mod 41 = 11, etc.*

*To clarify, the sequence of powers of 6 modulo 41 is:*

*[1, 6, 36, 11, 25, 27, 39, 29, 10, 19, 32, 28, 4, 24, 21, 3, 18, 26, 33, 34, 40, 35, 5, 30, 16, 14, 2, 12, 31, 22, 9, 13, 37, 17, 20, 38, 23, 15, 8, 7]”*

## The build

This is the design we used, but with a few alterations. We used wooden pillars with a width of 50mm (5cm), and a ground-plate that measured 600×900 (60cmx90cm).

The changes were due to material accessibility, and wanting a slightly wider and taller diffuser panel. If you end up falling into the situation where you want to change the dimensions of the ground-plate, or if you have to by necessity (wider wooden pillars than used in the calculation), do the following:

Multiply the number of rows and the number of columns by the width of the wooden pillars. This will be the dimensions of your backplate. I suggest keeping the design close to the calculated design (either 12×12, or adding another half to the panel such as 18×12).

Then, to know how much timber you need for this design if you have changed the number of rows or columns, go through either the top of bottom 6 rows and count up each 1 through to 4 and multiple the amounts of each by the nominated length of the cuts as displayed on the calculator (e.g., 15×22.93cm).

You will then add this additional length on to the length the calculator gives you. Keep in mind, ** you will be dealing with many meters of timber. **We ended up using 28 meters of timber, the end product will deceive you in its weight, its bloody heavy!If you are wanting a bigger design, split it up into smaller sections of perhaps 6×6. Make sure that your wall is also capable of taking the weight of your diffuser – screw into the studs for example.

The building process from here is quite simple, but time consuming. It is essentially just cutting various lengths of timber for hours, and then gluing them to the ground-plate. You can opt to secure the larger ‘4’ pillars with screws for extra strength; we didn’t and found that all pillars were fairly sturdy after leaving the glue to set overnight.

## The result

After we managed to carry the diffuser into the studio from the workshop, it was interesting securing it to the wall. The walls of the studio are fairly thick MDF which are screwed into the studs of the building in many areas, and as such the wall is quite sturdy. We ended up raising the diffuser up and resting it on wooden offcuts which enabled us to screw the ground-plate to the wall from the ‘0’ sections. I would recommend leaving the corner pieces off so as you can screw in the ground-plate easily. You can then glue the missing pieces on afterwards.

Here is a video from our Instagram showing the building process, and the final result.

Through placing the diffuser behind my speakers on what was a previously bare wall, I have noticed that my stereo image seems to be more precise, that the mid-range is more defined (which would make sense as the diffuser we made targets between 750-4000hz (likely to actually be a larger range due to wider wooden pillars being used), and more fine detail seems to be present. The diffuser was, however, installed at the same time as some of our up and coming acoustic panels and bass traps, so it can be hard to pinpoint what has caused the perceived increase in monitoring quality. Regardless, an improvement in sound quality in the room was made, and without breaking the bank. Besides, doesn’t the panel just look amazing?

Diffusers are the means to keep your room sounding lively and full whilst controlling level and frequency irregularities. Placing them at first reflection points around your speakers is a great method of ensuring the removal of comb filtering if you opt not to use absorption in your situation. Primitive Root Diffusers can be used anywhere in the room, they are most notably used on the rear and front walls of studios.Hopefully I’ve inspired a bit of DIY action, making this diffuser was great fun and it has been a fine addition to the studio thus far, I’m sure your space would also benefit from such a panel.