Last Updated: October 2023 | Verified for Mathematical Accuracy
Optimize your studio’s acoustics with our Skyline Diffuser Calculator. This tool helps you determine the exact block heights needed for a professional-grade two-dimensional primitive root diffuser, ensuring balanced sound diffusion across your target frequency range.
Skyline Diffuser Calculator
Skyline Diffuser Calculator Formula
The height of each well ($H_{n,m}$) is calculated using the Quadratic Residue sequence:
H(n,m) = [(n² + m²) mod P] * (c / (2 * f_max))
Where:
- n, m: Grid coordinates (0 to P-1).
- P: Chosen Prime Number.
- c: Speed of Sound (~343 m/s).
- f_max: High-frequency cutoff (based on well width).
Formula Source: Acoustic Engineering Reference | Sound on Sound Acoustics
Variables Explained
- Prime Number: A mathematical seed that determines the randomness and dimensions of the diffuser.
- Design Frequency: The target frequency where the diffuser is most effective at breaking up standing waves.
- Well Width: Determines the high-frequency limit ($f_{hf} = c / (2 \times \text{width})$).
What is a Skyline Diffuser?
A Skyline Diffuser is a 2D acoustic treatment device designed to scatter sound waves in both horizontal and vertical planes. Unlike 1D panels, it uses a grid of blocks with varying heights (calculated via prime number sequences) to eliminate flutter echoes and minimize acoustic glare without removing energy from the room.
These are widely used in recording studios, home cinemas, and mastering suites to create a “larger” soundstage while maintaining room “liveliness” that absorption alone cannot provide.
How to Calculate Skyline Diffuser (Example)
- Choose your Prime: Let’s use 13. This creates a 13×13 grid.
- Determine Cutoff: With a 5cm block, the high frequency limit is approx 3,430Hz.
- Apply Modulo: For each cell (x,y), calculate $(x^2 + y^2) \mod 13$.
- Scale to Depth: Multiply the remainder by the unit depth (determined by your design frequency).
Related Calculators
Frequently Asked Questions (FAQ)
What is the best material for a skyline diffuser? Hardwoods like Oak or Maple are best for reflection, but EPS (Styrofoam) is commonly used for its light weight and ease of mounting.
Does a skyline diffuser help with bass? No, skyline diffusers are primarily effective for mid-to-high frequencies. Bass requires deep traps or resonators.
Where should I place it? Ideally on the rear wall of the control room or at first reflection points on the ceiling.
Can I use any number for P? No, it must be a Prime Number to ensure the mathematical diffusion properties are maintained.