QRD Sound Diffuser Set – 4 Tuned Bands

🎛️ Real Acoustic Diffusion — Engineered, Not Eyeballed

This is a set of four genuinely engineered quadratic-residue diffusers (QRD) — the same number-theory math used in professional recording studios and concert halls since the 1970s — each tuned to a different frequency band so you can treat a whole room, not just one slice of the spectrum.

Foam absorbs. A diffuser scatters. Foam soaks up energy (mostly the highs) and can leave a room dull and lifeless. A diffuser scatters reflections evenly in every direction — killing flutter echo and harsh first reflections without deadening the room. That is exactly why mix rooms put diffusion behind the listening position: the room stays alive and the stereo image snaps into focus.

📐 Why Four Tiles?

A diffuser only works between two frequencies set by its geometry: well depth sets the lowest scattered frequency; well width sets the highest. One tile physically cannot cover speech, guitars and cymbals at once — so this set splits the spectrum across four tuned tiles:

• 🟤 LOW-MID “Voice” — 252 mm, 100 mm deep — ~1.5–5 kHz. The vocal-presence band. Behind the mic in a vocal booth, or the rear wall of a mix room. The workhorse for voice. Full-bed print — needs an A1 or a bed ≥260 mm (see Print Settings).
• 🟠 MID “All-Rounder” — 150 mm, 70 mm deep — ~2.1–8.8 kHz. The widest single-tile bandwidth in the set (over two octaves). If you print only one, print this.
• 🟡 UPPER-MID “Slim” — 150 mm, 35 mm deep — ~4.2–8.8 kHz. Low-profile for doors, narrow walls and reflection points where 70 mm is too chunky.
• ⚪ HIGH “Air & Detail” — 150 mm, 11×11 grid — ~5.2–14.7 kHz. Fine grid for cymbal sizzle, sibilance and “air” — desk reflections and near-field treatment.

🏙 Two Constructions — Both Included for Every Band

Same quadratic-residue math, same scatter — pick by taste, or print both:

• Skyline blocks — solid varying-height columns, the iconic “city skyline” studio look. No grid lines, chunky and robust. The construction of the most famous 2D diffuser ever made.
• Finned wells — the textbook Schroeder construction: every cell is an isolated quarter-wave well, exactly what the design equations model. The purist’s pick, strongest at steep off-axis angles.

They tile seamlessly. Skyline tiles continue the pattern automatically; well tiles carry half-width border walls that fuse into one continuous grid. Mix bands, cover a wall, make it look like sculpture — because it is.

🔬 The Science (with receipts)

• Well depths follow the quadratic-residue sequence s = (x² + y²) mod N (N prime), from Schroeder’s 1979 JASA paper — number theory guarantees the reflected energy spreads evenly into all diffraction orders.
• The tuning equations (f₀ = c·s_max / (2·N·d_max) and f_max ≈ c / 2w) come from D’Antonio & Konnert and the Cox & D’Antonio textbook — every band number here was computed, not invented.
• This is a 2D (“skyline-style”) grid that scatters hemispherically — in every direction — unlike the half-cylinder scatter of 1D groove diffusers.
• Diffusion behind the listening position is textbook control-room design (the LEDE concept).
• 3D-printed QRDs are not a gimmick: peer-reviewed studies have printed and measured this exact geometry class and matched theory.

All four tiles stay near a ~3:1 depth-to-width ratio — clear of the deep-narrow-well regime where diffusers start absorbing instead of scattering.

🖨️ Print Settings

• Orientation: flat on the bed, wells / blocks facing up.
• Supports: none — every cavity opens upward.
• Layer height: 0.2 mm (0.28 mm is fine on the big 252 tile to save time).
• Walls: 3  ·  Infill: ~10% gyroid.
• Material: PLA is perfect — it is a wall panel, not a bumper. Matte filament looks incredible.
• Bed: the three 150 mm tiles fit any 256 mm bed (P1S / X1C / A1). The 252 mm LOW-MID uses the full bed: print it on an A1 (its whole 256 mm plate is usable) or any printer with a bed ≥260 mm (H2D…). P1S/X1C reserve an 18×28 mm wipe cut-out in the front-left corner, so they cannot take a full-width 252 mm part in one piece.

🧱 Mounting & Placement

• Mount with double-sided foam tape, Command strips, or screws through the base.
• Wall-mount “-mount” versions included (all 8 tiles): a +6 mm back slab with 4 blind holes for M3 heat-set inserts (Ø4.0 × 6.5 mm — fits the common M3×5.7 brass insert). Holes sit on a 100×100 mm grid (150 mm tiles) or 200×200 mm grid (252 mm tile) — drill the same grid in your panel and screw the tiles on from behind (M3 screws). Acoustics are unchanged: the wells/columns are identical, only the solid backing is thicker.
• Mixing: rear wall at ear height, behind the listening position.
• Recording: the wall facing the mic, or a vocal booth.
• Listening & hi-fi: first-reflection points and the wall behind the speakers.
• Arrays: tile 2×2 or 3×3 — more area means more diffusion, and arrays extend low-frequency performance.

❓ FAQ

Does printed plastic really diffuse sound? Yes. The scattering is set by the geometry (depths and widths), not the material — measured studies confirm printed QRDs perform as the math predicts.

Diffuser or absorber — which do I need? Usually both. Absorb harsh first reflections; diffuse the rear wall to keep the room lively. This set is the diffusion half.

Which one should I print first? The MID “All-Rounder” — widest bandwidth, 150 mm, prints fast.

Skyline or Wells? Most people hang the Skyline (the look); engineers print the Wells (theory fidelity). Identical scatter math.

Why does the LOW-MID say A1? The 252 mm tile needs the full plate. On the A1 all 256 mm are usable, so it fits with room to spare; P1S/X1C keep a wipe zone in the front-left corner that a full-width part cannot clear. Any bed ≥260 mm works too. Want a two-piece split for P1S/X1C? Ask in the comments.

Custom size or band? It is a fully parametric original design — just ask in the comments.

📦 What’s Included

16 print-ready Bambu-native 3MF files — 4 frequency bands × 2 constructions (Skyline + Wells), each in a flat-back version (tape/strip mounting) and a “-mount” wall-mount version (M3 heat-set insert bosses for panel mounting). 100% original clean-room geometry. License: Standard Digital File License. Designed and tuned by THE WORKSHOP. If you print one, post a Make — I’d love to see it. 🎚️