"Weird Reverbs in Max" Prompt

Mark Renker

— 2 min read

My prompt to ChatGPT 5:

"Outline esoteric reverb algorithms found in work from Julius Smith."

ChatGPT 5's response:

"Here’s a compact outline of the more “esoteric” reverb architectures you’ll find in Julius O. Smith’s notes and papers (with pointers to the relevant sections):

  • Closed Waveguide Networks → Allpass Digital Waveguide Networks (DWN)
    Energy-conserving networks of bidirectional delay lines (digital waveguides) arranged in closed loops yield multi-input/multi-output allpass filters. You can tap and cross-feed broadly while staying lossless; classic FDNs fall out as a special case. (dsprelated.com)
  • Gerzon’s Nested MIMO Allpass (vector allpass)
    A Schroeder allpass “vectorized”: replace the single delay with a paraunitary matrix U(z)\mathbf{U}(z) and allow frequency-dependent gains ±G(z)\pm G(z). Great for high-density, decorrelated tails; used in IRCAM’s Spatialisateur. (dsprelated.com)
  • FDNs as generalized state-space / vector combs
    Smith formulates FDNs with A=ΓQ\mathbf{A}=\Gamma \mathbf{Q} (low-pass diagonal Γ\Gamma and orthogonal Q\mathbf{Q}) for guaranteed losslessness before damping; also notes special choices like circulant Q\mathbf{Q}. (dsprelated.com)
  • Lossless feedback-matrix design (mixing choices that matter)
    Hadamard matrices (multiply-free for certain sizes) and Householder reflections (efficient, dense mixing; 2N−12N-1 adds) are highlighted for fast, well-diffusing FDNs. Smith also surveys triangular and “most general” unitary cases and why they’re stable. (dsprelated.com)
  • Digital Waveguide Networks & Mesh reverbs
    View an FDN as a single scattering junction in a more general DWN; embed multiple FDNs in a DWN for richer, energy-controlled cross-coupling. For room-like behavior, 2D/3D waveguide meshes produce true diffuse fields with naturally increasing echo/mode density; dispersion is controlled with coarse-mesh tricks. (dsprelated.com)
  • Time-varying reverberators (physically motivated modulation)
    Smith argues path delays should vary slowly (thermal convection analog) to break periodicities and “flutter” while staying plausible. (dsprelated.com)
  • Prime-power delay schemes, mean-free-path & mode-density design
    Practical, nerdy design rules: choose mutually prime delays; use prime-power lengths when you need to retune interactively (keeps coprimeness); tie average delay to mean free path; ensure order MM meets mode-density target M≥0.15 t60fsM \ge 0.15\, t_{60} f_s. (dsprelated.com)
  • FDN damping & coloration control
    Per-delay multiband damping filters to impose a specified t60(f)t_{60}(f), plus inserting allpass-comb sections in each loop (e.g., zita-rev1) for extra diffusion without extra coloration. (dsprelated.com)
  • “Small-box” reverberators via waveguide meshes / banded approaches
    For instrument bodies (not just rooms), Smith co-authors mesh-based reverbs that match high-frequency modal statistics and Bark-band decay (e.g., violin body). These are effectively structured reverbs tuned to resonator spectra. (Quodilibet)

If you want, I can turn any of these into implementation notes or a minimal reference design (e.g., a 4×4 Householder FDN with prime-power delays and three-band damping) you can drop into a plugin."

I'm working on implementing these in Max. More to come!

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