Waveguide & Modal Synthesis — User Guide

What this does

This script synthesizes realistic acoustic instrument sounds using physical modeling — simulating the actual physics of vibrating strings, resonating air columns, struck bars, and other mechanical sound sources. Rather than playing back recordings or using abstract oscillators, it models the propagation of waves through physical structures in real-time.

Key Features:

• 15 Instrument Models — Strings, winds, percussion, membranes, vocal tract, and experimental sounds
• Waveguide Synthesis — Delay-line feedback simulates wave propagation through materials
• Modal Synthesis — Bank of resonant modes creates complex timbres (bells, bars, membranes)
• Excitation Control — Adjustable striking force, bowing pressure, breath pressure, etc.
• 10 Envelope Options — From natural percussive decay to experimental gating and stuttering
• Chaos Integration — Optional parameter randomization for organic variation

Technical Implementation: The script uses two primary techniques. Waveguide synthesis implements digital delay lines with feedback, where delay_samples = sampling_rate / frequency creates the fundamental pitch. Each model type uses specific feedback equations: simple subtraction for strings (Karplus-Strong), nonlinear functions for winds (jet-resonator coupling), multiple delays for bars/bells (inharmonic partials). Modal synthesis (model 15) sums exponentially decaying sinusoids at specific frequency ratios. The chaos parameter introduces controlled randomness into physical parameters (bow pressure variation, reed stiffness fluctuation) rather than adding noise to the output signal.

Quick start

1. In Praat, Run script… → Waveguide & Modal Synthesis.praat.
2. Select a Model_type (try "Bowed String" or "Struck Bar" first).
3. Set Duration (3 seconds default is good for most models).
4. Choose Frequency (220 Hz = A3, common starting point).
5. Adjust Excitation_strength (0.7 default works well, higher = louder/more aggressive).
6. Select Envelope (use "No Envelope" first to hear raw model, then try "Percussive").
7. Click OK — sound generates and plays immediately.

Physical Modeling Basics

Fundamental Physics Concepts

1. Delay Lines (Pitch Generation)

The core of waveguide synthesis. For frequency F Hz at sample rate 44100 Hz:

delay_samples = 44100 / F

Example: 220 Hz (A3) → 44100/220 = 200.45 samples delay ≈ 4.5 ms round-trip time

This delay makes the output "remember" itself from one period ago, creating the fundamental frequency.

2. Feedback & Damping (Sustain)

Damping parameter (0.9-0.999) controls how much energy remains after each cycle:

• 0.99: Fast decay (~1 second sustain) — percussion-like
• 0.995: Medium decay (~3-5 seconds) — plucked strings
• 0.999: Long decay (~10+ seconds) — bowed strings, bells

Each cycle, signal multiplies by damping value. After N cycles: amplitude = initial × damping^N

3. Excitation (Initial Energy)

Different instruments are excited differently:

• Impulsive: Struck/plucked — noise burst at start only (guitar, xylophone)
• Sustained: Bowed/blown — continuous energy injection (violin, flute)
• Intermittent: Friction/scraping — irregular energy pulses (friction drum)

4. Nonlinearity (Realism)

Real instruments aren't perfectly linear. Nonlinear elements create:

• Harmonics: Bow pressure dependence → rich overtones
• Attack transients: Brass lip buzz → characteristic "pop"
• Chaos: Reed flutter → organic variation

Modal Synthesis Approach

An alternative to waveguides. Instead of simulating wave propagation, modal synthesis directly generates resonant frequencies (modes):

Sum of modes: output = Σ (amplitude[i] × sin(2πf[i]t) × exp(-decay[i]t))

Each mode = one resonant frequency of the object. Works well for inharmonic sounds (bells, gongs, bars) where partials aren't integer multiples of fundamental.

Model Types (15 Instruments)

String Instruments

Wind Instruments

Percussion & Bars

Membranes & Surfaces

Vocal & Resonator Models

Envelope Shapers (10 Options)

Envelopes shape the amplitude evolution over time. Applied after synthesis, they don't affect the physical model itself but control how the sound is presented.