Waveguide & Modal Synthesis — User Guide

What this does

The script generates a new mono Sound; no input Sound is required. The six model choices are deliberately explicit rather than attempts to reproduce complete acoustic instruments.

The selected Damping control affects the two families differently: in waveguide models it is the loop-feedback multiplier; in modal models it controls a common decay-rate scale applied to every modal template.

Quick start

1. Choose one of the six synthesis methods.
2. Leave Melody demo off for one note, or enable it for the built-in eight-note phrase.
3. For a single note, set Frequency and Duration.
4. Set Damping and choose one of the ten envelope modes.
5. Use Edit details for Sample rate, Envelope amount, Output peak, and Random seed.
6. Run the script. The output is generated offline and optionally visualized and played.

Waveguide models

Both waveguide modes use the same fractional-delay feedback structure. The target period in samples is:

The -0.5-sample compensation offsets the approximate half-sample phase delay contributed by the two-point loss averaging. Fractional interpolation then avoids restricting the pitch to integer delay lengths.

1 — Waveguide: Plucked String

2 — Waveguide: Breath-driven Loop

Modal models

Modal methods directly sum damped sinusoids. For mode m:

Higher Damping values therefore produce smaller decay exponents and longer modal persistence. Each model uses a fixed ratio/amplitude/decay template:

3 — Modal: Bell-like Inharmonic

4 — Modal: Plucked String

5 — Modal: Struck Bar

6 — Modal: Circular Membrane

Envelope shapers

The selected envelope is applied after the waveguide or modal model. Envelope amount affects the parameterized envelopes but does not change the underlying synthesis model.

Universal note-boundary taper

After the selected envelope, every note receives a short raised-cosine fade-in and fade-out:

This is separate from the user-selectable envelope and is always applied.

Melody demo

Melody demo ignores the Single-note Frequency and Duration controls and renders this fixed eight-note sequence with the currently selected model, Damping, Envelope, Details settings, and seed:

Total duration is 3.8 s. Every note is generated and tapered separately, the eight Sounds are concatenated, and only then is one final peak normalization applied. There is no per-note normalization.

Controls

Main page

Details page

Validation and workload guards

Sample-rate range

Waveguide period guard

For the two waveguide models:

In Single-note mode, highestFundamental is the requested Frequency. In Melody demo it is 523.25 Hz.

Modal Nyquist guard

For modal methods, the highest template mode must remain below 95% of Nyquist:

The maximum ratios are 6.250 (Bell), 8.080 (Modal Plucked String), 13.344 (Struck Bar), and 2.917 (Circular Membrane).

Single-note workload guard — v1.1.2

Version 1.1.2 adds a render-size limit before Single-note generation:

If the requested render exceeds this limit, the script stops and reports the maximum permitted Duration for the selected Sample rate. Melody demo is fixed at 3.8 seconds and is not subject to this additional size check.

Randomness and reproducibility

Randomness is used by:

• the initial delay-line state of both waveguide models;
• the continuous noise drive of Breath-driven Loop;
• the Poisson event times and random event amplitudes of Random Bursts.

The four modal models are deterministic when a deterministic envelope is selected. Random Bursts makes any model stochastic.

With Random seed > 0, the script initializes Praat's random generator predictably before synthesis. Repeating the same model and settings with the same positive seed reproduces the script's random sequence. With seed 0, the current RNG state is used.

Output and normalization

There is no per-note normalization in Melody demo. The single final gain factor therefore preserves the relative levels created by the model, envelope, and note sequence.

Visualization and QC

The visualization compares the model's internal prediction with measurements from the generated Sound. For Melody demo, the first 261.63 Hz / 0.4 s note is used as the representative analysis note; Single-note mode uses the requested note.

Process strip

Waveguide methods show noise excitation → fractional delay → two-sample loss → damping feedback → envelope → output. Modal methods show impulse-like excitation → modal frequency bank → per-mode decay → envelope → summed output.

A — Model structure

• Waveguide: a loop diagram labels target period, integer + fractional delay, the 0.5(1+z^-1) loss stage, and Damping.
• Modal: a time/frequency score draws every template mode; line thickness follows template amplitude and line length follows predicted T60, limited to the representative note duration.

B — Predicted decay

• Waveguide: the plot estimates loop decay from Damping, the two-sample averaging magnitude, and the fractional interpolation magnitude at F0.
• Modal: every template mode is plotted from its explicit exponential decay law.

C — Expected resonances vs measured spectrum

A Spectrum is measured from the representative generated note. Blue circles show the model template; red stems show measured magnitudes at the corresponding frequencies. Waveguides use the first eight harmonic locations; modal models use their exact ratio sets.

D — Measured output

The final normalized waveform is drawn over the complete output duration.

QC strip

The QC rows report model, representative F0, Sample rate, Damping, Envelope, target waveguide period or modal count/max ratio, Nyquist, and measured final Peak/RMS.