Self-Oscillating FDN Synthesizer — Nonlinear Feedback Network Synthesis

What this does

Self-Oscillating FDN Synthesizer is a pure-Praat nonlinear feedback delay network designed as a synthesizer rather than a conventional reverberator. Eight delay lines are coupled through an energy-preserving feedback matrix, filtered, DC-blocked, passed through a bounded nonlinearity, and written back into the network. A short excitation starts the system; after that, the sound is generated by the feedback dynamics themselves.

Key Features:

• Pure Praat implementation — no Python, external executable, plugin, cloud service, or DSP library.
• Eight-line nonlinear FDN — normalised Hadamard feedback by default, with Householder and decoupled reference modes.
• Physically meaningful instability control — the user control is mapped to a growth rate in dB per second, with per-delay feedback radii derived from each delay length.
• Bounded nonlinear feedback — tanh, softsign, cubic soft clip, or harder saturation, with optional asymmetry.
• Evolving dynamics — separate start/end values for instability, drive, and damping, plus optional sinusoidal growth-rate drift.
• Prime delay design — delay lengths are distributed geometrically, perturbed by irregularity, then snapped to distinct prime sample lengths.
• Five excitation modes — impulse, noise burst, sparse impulses, initial random state, or bipolar pulse.
• Three spatial modes — Orthogonal Field, state-driven Distributed Network, and Orbiting Network.
• Stereo, quad, or 8-channel output — including a full 8-channel ring layout.
• 20 supplied presets + Custom — five reference regimes and fifteen experimental synthesis designs.
• Explanatory Praat Picture visualisation — spectrogram, network energy, measured spatial map, growth curve, early/late state-space plots, and a technical summary.

Quick start

1. Run Self_Oscillating_FDN_Synthesizer.praat. No input Sound is required.
2. For a first run, choose Self-Oscillating, the default preset.
3. Keep Duration = 8 s, Sample rate = 44100 Hz, Output layout = Stereo, and Normalization = Peak.
4. Enable Draw visualisation to see how the network evolves after the excitation ends.
5. Try Damped Resonator, Critical Network, and Strong Nonlinear to hear the main dynamical regimes.
6. Then explore the experimental presets, especially Metallic Organism, Slow Attractor, Breathing Metal, Ignition, and Chaotic Edge.
7. Enable Show parameters to expose the network, excitation, nonlinear, spatial, and drift controls behind the chosen preset.

Core concept

The synthesis loop combines delayed state, damping, DC blocking, matrix coupling, and bounded nonlinear feedback. Each delay line has its own delay length and its own damping/DC state, but all eight lines interact through the feedback matrix.

The default feedback matrix is a normalised 8 × 8 Sylvester-Hadamard matrix. In the ideal linear case it preserves energy while redistributing it among the lines. The nonlinearity then bounds growth when the network is operated above the critical region.

20 Presets + Custom

Reference regimes

Experimental presets

Controls

Main dialog

Network parameters

Excitation & advanced parameters

Instability & growth rate

The user-facing Instability parameter is not used as a single raw feedback multiplier. It is mapped cubically to a growth rate in dB per second:

The cubic mapping gives much finer control around zero, where very small changes can move the network between decay, sustained resonance, and self-oscillation.

Each delay line receives its own per-pass feedback radius according to its delay length:

This keeps the growth or decay rate consistent per second across delay lines of different lengths. A single shared per-pass gain would make short and long delays grow at radically different rates.

Nonlinearity & damping

The nonlinear stage is designed so its small-signal gain remains approximately unity. This separates the primary growth/decay control from the character of the saturation:

Asymmetry shifts the nonlinear operating point. At zero asymmetry the sustained behavior is close to scale-invariant with respect to Drive; non-zero asymmetry breaks that invariance, introduces even harmonics, and can substantially change the long-term spectral state.

Damping is a separate one-pole low-pass state for every delay line. The 0–1 control maps logarithmically from a high cutoff near 20 kHz toward 150 Hz, capped appropriately by the current Nyquist frequency.

Excitation

Excitation only starts the network. It is not a continuous synthesis source.

Spatial output

The spatial layer is generated from the eight FDN states themselves. No reverb or post-hoc spatial effect is required.

Output layouts

Normalisation & ending

Version 1.1 applies fades before final normalisation. The processing order is:

The supplied Damped Resonator and Critical Network use a short noise burst rather than a single impulse. This avoids a needle-like initial transient dominating peak normalisation while leaving the resonant body perceptually weak.

Ending can be Hard stop, a 20 ms Short fade, or a Longer fade covering 10% of the rendered duration.

Visualisation

When Draw visualisation is enabled, the tool creates a Praat Picture figure intended to explain what the network actually did rather than merely decorate the result.

Technical behavior

• Creates eight delay-line state channels internally and never requires an input Sound.
• Delay lengths are generated from Base delay, geometric Spread, and a deterministic golden-ratio-derived irregularity offset, then snapped to distinct prime sample lengths.
• The default feedback matrix is a normalised 8 × 8 Sylvester-Hadamard matrix. Householder and identity reference modes are also available.
• Each line has an independent one-pole damping state and DC blocker before matrix mixing.
• Instability is converted to a growth rate with ρ = 60u³ dB/s; each line then receives a delay-dependent per-pass radius.
• Start/end Instability, Drive, and Damping values use raised-cosine interpolation across the rendered duration.
• Optional Drift adds sinusoidal modulation directly to the growth rate in dB/s.
• The nonlinear stage is explicitly bounded and contains an emergency internal safety clamp; the report states if that clamp was reached.
• Asymmetry is internally capped when Drive × Asymmetry would move the chosen saturator too far into a near-flat region.
• The synthesis loop is evaluated in exact blocks of up to the shortest delay length. Because no newly written value can be read before that delay has elapsed, block processing remains equivalent to the required sample recursion while avoiding a slow command-per-sample script.
• The script reports the last-quarter vs first-quarter RMS change as a practical level-evolution diagnostic.
• Output is generated directly as a multichannel Praat Sound and remains inside Praat.

Signal path

Requirements & installation

Limitations

• Offline only: the network is rendered as a Sound object rather than performed in real time.
• Eight-line architecture: the synthesis core is fixed at eight feedback delay lines.
• Very short delays cost more: the exact block method uses more processing blocks when the shortest delay is extremely small.
• Preset names are artistic descriptions: a name such as Chaotic Edge does not constitute a mathematical proof of chaos.
• High feedback is intentionally nonlinear: results can change strongly with excitation, asymmetry, drive, and damping, especially near regime boundaries.
• 8-channel monitoring depends on the playback environment: Praat creates the multichannel Sound, but audible routing depends on the user's audio system.

Outputs

The script creates one new multichannel Sound named from the preset:

FDN_<PresetName>

Examples:

FDN_SelfOscillating
FDN_MetallicOrganism
FDN_SlowAttractor

The result contains 2, 4, or 8 channels according to Output layout. The Info window reports the actual prime delay lengths, growth regime, per-pass feedback radii, nonlinear settings, excitation, spatial mode, normalisation result, numerical safety state, and render statistics.

Applications

Critical resonance

Use case: create resonant textures that sit between obvious decay and autonomous oscillation.

Starting point: Critical Network or Frozen Resonance.

Autonomous nonlinear synthesis

Use case: generate sustained sound whose waveform and spectrum arise from coupled feedback rather than predefined oscillators.

Starting point: Self-Oscillating or Strong Nonlinear.

State-driven spatial composition

Use case: let the network's changing internal energy distribution generate spatial movement without a panning LFO.

Starting point: Metallic Organism with Distributed Network.

Slow dynamical transitions

Use case: compose a trajectory through stability regimes rather than holding one fixed feedback condition.

Starting point: Ignition or Collapse and Recover.

Orbiting nonlinear fields

Use case: combine internal state-driven movement with a slow global spatial swing.

Starting point: Slow Attractor, Breathing Metal, Unstable Choir, or Chaotic Edge.

Dense high-frequency structures

Use case: use sub-millisecond and very short delays as the basis for metallic, insect-like, or microstructural spectra.

Starting point: Glass Swarm, Digital Insects, or Microstructure.