Posts Tagged similar yet different
For this installment of “Similar, yet Different”, we will be going retro – The Barrel Vs. The Pyramid! These two shapes are the historic foundations for modern acoustic treatments. How did they come about? Why do they work? How are they different?
These two shapes have origins before written history. The pyramids of Egypt may not have been renowned for their acoustic properties, but they certainly show the historical age of this shape. The barrel is also an ancient shape, born from the pillars of historic temples and gathering places. Both of these shapes have been used in architecture for the expanse of human history, and their acoustic properties have been studied in numerous environments, in many different applications.
These shapes are often referred to as “primitive.” The barrel, in its basic form, is a truncated cylinder – basically a segment of the cylinder. The pyramidal is, in this case, a modified/offset pyramid… a pyramid without equal sides. Their differences begin with this fundamental variable – the pyramid has angled planes and the Double Duty™ is a large curved surface.
Symmetry vs. Asymmetry
Another simple difference is the fact that the Double Duty™ is symmetric and the offset pyramid is asymmetric. The barrel primarily scatters sound across the curve of the face – sending acoustic energy in a wide arc. However, the pyramid’s facets are all angled slightly differently – reflecting in different directions. This allows the pyramid to be installed in complex arrays which create more “random” reflections due to their different facet angles. The Barrel is primarily a one-dimensional diffuser, and installs either horizontally or vertically.
There is another phenomenon that helps to contribute to diffusion – and that is diffraction. Diffraction is what happens to sound when it hits a corner or edge. Unlike light, acoustic energy is the physical fluctuation of pressure changes – which gives sound the ability to travel around corners. This bending varies by the wavelength of the sound and the size of the object in encounters. Both barrels and pyramids have facets which introduce diffraction, and while both can be made in different sizes, the offset pyramid has different sized facets on each device – contributing to more randomized diffraction at different frequencies.
Inverse Square Law
Without getting too heavy into math, as sound travels it decreases in intensity. This is due to the fact that sound “spreads out” as it travels. It is produced with a finite amount of energy, so intensity drops as it covers more space. Both the barrel and pyramid increase the rate that sound “spreads out,” which diminishes the intensity of the sound – however, they both do it slightly differently, however..
The Double Duty’s™ curvature leaves the wave primarily intact, but it increases the rate of expansion across the curve. This redirection is very smooth and predictable, where the random facets of the offset pyramid break up the sound into sections which travel in different directions. At the intersection of those facets, diffraction takes the reigns and scatters sound even further.
By increasing the rate of expansion of the wave, you decrease its intensity while also breaking up the wavefront which helps to reduce echoes and flutter. Both the barrel and the pyramid are perfect for larger spaces, as those massive surfaces do a great job of controlling reflections from large wave fronts. Also, due to their simple shapes, they can be made really big, which helps!
There is one more feature which is sometimes overlooked. Because of the material of their construction, and the large volume of air behind them, these diffusers exhibit a certain amount of “bass trapping.” The Double Duty™ diffuser got it’s name due to this characteristic. It’s not just a diffuser, but also a bass trap. The Pyramidal diffuser also exhibits bass absorption, though it is slightly less.
So there it is… the battle of the classics! Sometimes, keeping it simple is the way to go!
Today on, “Similar, yet different…” we are going to analyze two more of our acoustic diffusers and compare/contrast their designs and functionality… and this one is a doozy; The Model D vs. The Aeolian®. These two diffusers have some very interesting similarities and some surprising differences – so lets get started!
We have discussed the Aeolian® construction before, so we will start here with a quick recap as a reference point. The Aeolian® started life as a blocky-looking diffuser – just like the Model C, but the implementation is different. While the Model C retains its “blocky” appearance, the Aeolian® has run through a mathematical process called “bicubic interpolation.” This smooths the transition from one block to the next, creating the wavy appearance of the Aeolian® diffuser.
So, keep that in mind: The diffuser was tuned with different height blocks and then the transitions were smoothed.
The Art Diffusor® Model D has multiple layers of math below its curved surface. While the Aeolian® started life as “Blocks” of different heights… the Model D started life as “Rings” of different sizes and heights. The calculation for the heights is identical to the mathematics used in tuning the Aeolian®, but why different sized rings?
There is an older diffuser design known as a Maximum Length Sequence (MLS) diffuser. These were tuned to different frequencies using a specific depth, and different spacings of “lands and valleys.”
The Model D started with the concept of twisting the MLS spacings into rings, and changing the size of the rings. Then to break the “MLS mold” of having the same depth, this MLS ring structure is raised to different heights using Quadratic Residue calculations… effectively combining the rings of MLS spacings with different QRD heights. While this could have been where this stopped, we wanted to interject more randomness into the equation.
Wherever the rings of different heights intersected, we decided to change the heights by values relative to the difference between the two rings. This height variation is what is responsible for the “random” waviness. This was accomplished with different Boolean Functions, to either add or subtract height where the rings intersected.
This method of using Boolean Functions inserts a known-height randomization into a hybrid MLS/Quadratic system. (That’s a mouthful.) The final step, after refining the ring size, height, position and intersection parameters… was to smooth the whole geometry with “Bicubic Interpolation.” That’s right. This final step smooths all the transitions from the heights, just like the blocks of the Aeolian®.
So onto the Simple Similarities!
Both diffusers use a quadratic residue calculations to get the main heights of the diffusive elements. Both diffusers are finished off with a helping of “Bicubic Interpolation” to smooth it all out. This gives them both a very organic look… The Aeolian® looks a bit like rolling waves, and the Model D resembles droplets of rain in a puddle…
They do perform quite a bit differently though.
The Aeolian® has great lower mid-band performance… while the Model D is a beast in the upper mid-bands starting about 2.5K. The difference is in the severity of the geometry. The Aeolian® is a gently rolling surface which redirects the waveforms uniformly through a wide range of frequencies. The Model D has a very irregular surface. With the different ring sizes, heights, locations and boolean functions… it’s meant to target and shred mid to high frequencies. Both diffusers are asymmetric – and affect different frequencies in different ways.
The Aeolian® is also deeper than the Model D – and this depth is a single resonant cavity… allowing it to be a great bass absorber as well. The Model D is useful in environments where you have bass control in place, but really need to diffuse the upper mid range and bring those frequencies to life… or maybe shred some flutter echos or comb filtering. There are scenarios where both are used in the same environment – but for different reasons.
While both the ArtDiffusor® Model D and the Aeolian® both look like liquids frozen in time, they have some other similarities in the math behind them… Yet they are still as different as rolling waves versus droplets of rain in a puddle.