GENDYN Synthesis — User Guide

Dynamic stochastic synthesis based on Iannis Xenakis's GENDY3 algorithm: breakpoint evolution with stochastic barriers for organic, unpredictable sonic textures.

Author: Shai Cohen Affiliation: Department of Music, Bar-Ilan University, Israel Version: 1.0 (2025) License: MIT License Repo: https://github.com/ShaiCohen-ops/Praat-plugin_AudioTools

Contents:

What this does Quick start GENDYN Theory Algorithm Details Built-in Presets Applications

What this does

🎻 Tribute to Iannis Xenakis (1922–2001)

GENDY3 (1991): Xenakis's pioneering work in dynamic stochastic synthesis. The name derives from "GENeration DYNAmique" – dynamic generation. Xenakis applied principles of probability theory, statistical mechanics, and game theory to musical composition, creating what he called "stochastic music." This plugin implements a Praat-based interpretation of his GENDY3 algorithm for sound synthesis.

This script implements GENDYN (Dynamic Stochastic) Synthesis — a breakpoint-based synthesis method where waveform parameters evolve stochastically within defined barriers. Core concept: A waveform defined by breakpoints (amplitude/duration pairs) undergoes continuous random mutations, with evolution constrained by barrier conditions. The result: Organic, evolving sonic textures that are neither purely random nor deterministic, occupying the fascinating space between order and chaos.

Key Features:

9 Artistic Presets — From Xenakis tributes to modern textures
Stochastic Evolution — Parameters mutate with 4 probability distributions
Breakpoint Architecture — Configurable number of waveform control points
Barrier Constraints — Keep evolution within musical bounds
Spatial Processing — Mono, stereo dual, or rotating outputs
Visual Feedback — Real-time waveform and spectrogram visualization
Dynamic Generation Counter — Track stochastic evolution cycles

What is stochastic synthesis? Traditional synthesis: Oscillators, filters, envelopes with fixed or LFO-modulated parameters. Stochastic synthesis: Parameters evolve according to probability distributions, creating inherently unpredictable yet constrained evolution. Xenakis's approach: Treat sound particles as molecules in Brownian motion, subject to statistical laws. GENDYN's innovation: Instead of pre-composing sounds, define rules for sound generation and let the system evolve. Advantages: (1) Organic quality: Sounds evolve like natural processes. (2) Unpredictability: Each generation unique yet related. (3) Complexity from simplicity: Simple rules generate complex results. (4) Bridge composition/synthesis: Compositional thinking built into synthesis method. Use cases: Experimental music, sound design for film/games, generative art, academic study of stochastic processes, meditation/ambient music.

Technical Implementation: (1) Breakpoint initialization: Create N breakpoints with random amplitudes and equal durations. (2) Phase accumulation: Traverse breakpoints at current frequency rate. (3) Linear interpolation: Generate samples between breakpoints. (4) Stochastic evolution: After each cycle, mutate amplitudes, durations, and frequency using chosen distribution. (5) Barrier application: Constrain mutations to prevent extreme values. (6) Control rate synthesis: Generate at high control rate, then resample to audio rate. (7) Spatial processing: Apply mono/stereo/rotating spatialization. (8) Visualization: Display waveform detail and spectrogram of result.

Quick start

In Praat, ensure no objects are selected (GENDYN creates from scratch).
Run script… → GENDYN_Synthesis.praat.
Choose Preset or select "Custom" for manual control.
Set Duration (seconds) and Sample rate.
Configure Number of breakpoints (complexity) and Base frequency.
Select Distribution type (Cauchy = Xenakis's choice).
Set Amplitude/Duration steps (mutation sizes).
Define Frequency barriers (min/max Hz to contain evolution).
Choose Spatial mode (mono, stereo, or rotating).
Enable Draw visualization to see waveform and spectrogram.
Click OK — synthesis begins, progress shown in Info window.

Quick tip: Start with presets — "GENDY3 Tribute" for authentic Xenakis sound, "Insect Swarm" for granular textures, "Slow Evolution" for ambient drones. Use Cauchy distribution for Xenakis's characteristic "heavy-tailed" mutations (more extreme jumps). Breakpoints (8-16) balance complexity and evolution speed. Amplitude step (0.1-0.2) controls how much amplitudes change each generation. Duration step (0.1-0.2) controls timing mutations. Barriers prevent evolution into inaudible extremes. Visualization shows both waveform detail and spectral evolution. Longer durations (30+ seconds) reveal gradual transformation. Each run is unique — seed is random.

Important: COMPUTATIONALLY INTENSIVE — longer durations with many breakpoints require significant processing. No undo — save output if valuable. Stochastic nature means results unpredictable — same parameters yield different outputs each run. Barriers essential — without frequency barriers, sound may evolve into ultrasonic or subsonic ranges. Cauchy distribution can produce extreme jumps — use smaller steps or barriers. Control rate auto-adjusted based on frequency and breakpoints. Visualization shows first 300ms of waveform and full spectrogram. Stereo modes create two independent evolutions or rotating panning. Be patient for long durations — progress reported every 2 seconds.

GENDYN Theory

The Xenakis Philosophy

🎼 Stochastic Music Principles

From "Formalized Music" (1963): Xenakis proposed applying probability theory to music composition. Instead of writing specific notes, define stochastic processes that generate music. GENDYN extends this to sound synthesis: instead of defining specific waveforms, define stochastic processes that generate waveforms.

Key concepts:

Brownian motion: Sound particles as molecules in random motion
Markov chains: Next state depends only on current state
Probability distributions: Different statistical models for different musical results
Constraints/barriers: Freedom within limits — artistic control of stochastic processes

Breakpoint Waveform Model

📈 Breakpoint Representation

A waveform defined by N breakpoints, each with:

Amplitude: Value at breakpoint (-1 to 1)
Duration: Time to next breakpoint (relative proportion)

Waveform generation: Linear interpolation between consecutive breakpoints. When last breakpoint reached, wrap to first (cyclic waveform).

Breakpoint structure for N = 4: BP1: amplitude = a1, duration = d1 (fraction of cycle) BP2: amplitude = a2, duration = d2 BP3: amplitude = a3, duration = d3 BP4: amplitude = a4, duration = d4 Total duration = d1 + d2 + d3 + d4 = 1.0 (one cycle) Waveform generation (phase φ from 0 to 1): if φ < d1: output = a1 + (a2 - a1) × (φ / d1) else if φ < d1 + d2: output = a2 + (a3 - a2) × ((φ - d1) / d2) else if φ < d1 + d2 + d3: output = a3 + (a4 - a3) × ((φ - d1 - d2) / d3) else: output = a4 + (a1 - a4) × ((φ - d1 - d2 - d3) / d4) Frequency control: phase_increment = frequency / samplerate Actual time between breakpoints = duration × (1 / frequency)

Stochastic Evolution

🎲 Mutation Process

After each complete cycle (all breakpoints traversed), three types of mutation occur:

Amplitude mutations: Each breakpoint amplitude changes randomly
Duration mutations: Each breakpoint duration changes randomly, then normalized
Frequency mutation: Fundamental frequency changes randomly

Evolution rate: Controlled by step size parameters. Larger steps = more dramatic changes per generation.

Mutation formulas (one generation): FOR each breakpoint i (1 to N): AMPLITUDE MUTATION: delta_amp = random_step(amplitude_step, distribution) new_amp[i] = amp[i] + delta_amp Apply barrier: -barrier ≤ new_amp[i] ≤ barrier DURATION MUTATION: delta_dur = random_step(duration_step, distribution) new_dur[i] = dur[i] × (1 + delta_dur) Constrain: new_dur[i] ≥ 0.01 (minimum) END FOR DURATION NORMALIZATION: total_dur = sum(new_dur[1..N]) FOR i = 1 to N: dur[i] = new_dur[i] / total_dur FREQUENCY MUTATION: delta_freq = random_step(duration_step, distribution) × 0.5 new_freq = current_freq × (1 + delta_freq) Apply barrier: min_freq ≤ new_freq ≤ max_freq current_freq = new_freq Where random_step(step_size, distribution) returns value in range approximately [-step_size, step_size] according to chosen distribution.

Barrier System

🚧 Constrained Freedom

Barriers prevent evolution from escaping musically useful ranges. When a value hits a barrier, it "bounces" back into allowed range.

Types of barriers:

Amplitude barriers: Keep waveform within [-barrier, barrier] (typically 0.9-0.95)
Frequency barriers: Keep fundamental within [min_freq, max_freq] (audible range)

Bounce behavior: If value exceeds barrier by amount X, it's set to barrier - X (reflection). If still outside, set to barrier.

Barrier application algorithm: procedure applyBarrier(value, min, max): result = value if result < min: # Bounce from lower barrier result = min + (min - result) if result > max: result = min # Double bounce to min elsif result > max: # Bounce from upper barrier result = max - (result - max) if result < min: result = max # Double bounce to max return result Example (amplitude barrier = 0.9): Current amp = 0.8 Mutation adds +0.2 → new amp = 1.0 1.0 > 0.9 → bounce: 0.9 - (1.0 - 0.9) = 0.8 Result: 0.8 (back where started) Example with extreme mutation: Current amp = 0.85 Mutation adds +0.3 → new amp = 1.15 1.15 > 0.9 → bounce: 0.9 - (1.15 - 0.9) = 0.65 0.65 within range → result: 0.65

Probability Distributions

📊 Statistical Models for Mutation

1. Uniform Distribution

Equal probability across range [-step, step]

Character: Predictable, bounded mutations

Use: Gentle, controlled evolution

2. Cauchy Distribution (Xenakis's Choice)

Heavy-tailed distribution: f(x) = 1 / [πγ(1 + ((x-x₀)/γ)²)]

Character: Mostly small changes with occasional extreme jumps

Use: Dramatic evolution, surprising changes

3. Gaussian (Normal) Distribution

Bell curve: f(x) = (1/σ√2π) exp[-½((x-μ)/σ)²]

Character: Small changes common, large changes rare

Use: Natural, organic evolution

4. Logistic Distribution

Similar to Cauchy but with less extreme tails

Character: Smooth, moderate evolution

Use: Balanced stochastic process

Implementation details: UNIFORM: result = randomUniform(-step, step) CAUCHY (heavy tails): u = randomUniform(0.01, 0.99) # avoid extremes cauchy = tan(π × (u - 0.5)) result = step × cauchy / 5 Clamp to [-2×step, 2×step] # practical limits GAUSSIAN: result = randomGauss(0, step × 0.5) LOGISTIC: u = randomUniform(0.01, 0.99) logistic = ln(u / (1 - u)) result = step × logistic / 5 Clamp to [-2×step, 2×step] Note: Cauchy/Logistic divided by 5 and clamped to keep mutations comparable across distributions.

Spatial Processing Modes

Three spatialization options: 1. MONO: Single voice, single evolution process 2. STEREO DUAL: Two independent voices, each with own evolution Voice 2 initialized with slight frequency variation (±5%) Each evolves independently with same parameters Combined to stereo (left = voice1, right = voice2) 3. ROTATING: Two voices with rotating amplitude panning Voice1: amplitude × (0.5 + 0.5 × cos(2π × 0.08 × time)) Voice2: amplitude × (0.5 + 0.5 × sin(2π × 0.08 × time)) 0.08 Hz = completes pan cycle every 12.5 seconds Creates slowly moving stereo image Control rate note: Synthesis first occurs at high control rate (8-22 kHz) Then resampled to audio rate (e.g., 44.1 kHz) Control rate auto-adjusted: max(8000, base_freq × breakpoints × 2)

Complete Processing Pipeline

SETUP: Parse parameters (preset or custom) Generate unique ID for objects Calculate control rate based on frequency/breakpoints Initialize breakpoint arrays (amplitudes, durations) INITIALIZATION: Amplitudes: randomUniform(-0.5, 0.5) Durations: equal (1.0 / number_of_breakpoints) Frequency: base_frequency_Hz Phase: 0 Generation counter: 0 MAIN SYNTHESIS LOOP (control rate): FOR each control sample: # Find current segment cum_dur = 0 FOR bp = 1 to N: next_cum_dur = cum_dur + dur[bp] IF phase ≥ cum_dur AND phase < next_cum_dur: next_bp = (bp mod N) + 1 local_phase = (phase - cum_dur) / dur[bp] value = amp[bp] + (amp[next_bp] - amp[bp]) × local_phase BREAK cum_dur = next_cum_dur # Store sample Set control sample to value # Advance phase phase = phase + (current_freq / control_rate) # Wrap and evolve IF phase ≥ 1: phase = phase - 1 generation = generation + 1 # Evolve amplitudes, durations, frequency # Apply barriers # Normalize durations Report progress every 2 seconds POST-PROCESSING: Resample control sound to audio rate Apply 50ms fade in/out Apply spatial processing (mono/stereo/rotating) Normalize peak to 0.9 (if enabled) VISUALIZATION (if enabled): Draw title and parameters Draw waveform (first 300ms) Draw spectrogram (full duration) Display generation count OUTPUT: Sound object named "gendyn_[preset]_[UID]" Select object for playback/further processing

Algorithm Details

Control Rate Optimization

Control rate calculation: base_rate = 8000 Hz (minimum) needed_rate = base_frequency_Hz × number_of_breakpoints × 2 control_rate = max(base_rate, needed_rate) control_rate = min(control_rate, 22050) # maximum Rationale: Each breakpoint segment should have multiple samples Factor 2 ensures at least 2 samples per segment Minimum 8000 Hz for reasonable waveform definition Maximum 22050 Hz (half typical audio rate) for efficiency Example: base_freq = 180 Hz, breakpoints = 12 needed_rate = 180 × 12 × 2 = 4320 Hz control_rate = max(8000, 4320) = 8000 Hz Example (high): base_freq = 1000 Hz, breakpoints = 20 needed_rate = 1000 × 20 × 2 = 40000 Hz control_rate = min(40000, 22050) = 22050 Hz Number of control samples: n_control_samples = round(duration_s × control_rate) Resampling: Control sound resampled to audio rate using Praat's Resample command with 50-point interpolation

Generation Counter Significance

🔢 Measuring Evolution

One generation = one complete traversal of all breakpoints (one cycle of the waveform).

Generation rate = frequency (Hz) = cycles per second.

Total generations in output = frequency × duration (approximately).

Musical interpretation: Each generation is like a "note" in traditional music, but here notes evolve. Higher frequency = faster evolution. More breakpoints = more complex evolution per generation.

Generations calculation: Approximate generations = base_frequency_Hz × duration_s Example: 180 Hz × 12 seconds = 2160 generations Example: 20 Hz × 30 seconds = 600 generations Actual generations may differ because: 1. Frequency evolves (changes during synthesis) 2. Phase wrapping occurs at phase ≥ 1 (not exactly at 1.0) 3. Initial phase not zero Display in Info window: "Total generations: X" shows actual count Progress reports show current generation during synthesis Evolution per generation: Amplitudes: N mutations (one per breakpoint) Durations: N mutations + normalization Frequency: 1 mutation Total: 2N + 1 mutations per generation For N=12: 25 mutations per generation For 2160 generations: 54,000 total mutations

Visualization System

Three-part visualization: 1. TITLE AREA (top): Main title: "GENDYN Synthesis — [Preset Name]" Subtitle: "Tribute to Iannis Xenakis (1922–2001)" Drawn in separate viewport for clean layout 2. WAVEFORM DETAIL: Shows first 300ms (or less if shorter than total) Demonstrates waveform character and complexity Color: Dark green (0.2, 0.5, 0.3) for visual clarity Y-axis: -1 to 1 (amplitude range) X-axis: time in milliseconds 3. SPECTROGRAM: Full duration spectrogram Frequency range: up to min(8000, max_frequency_Hz × 1.5) Uses Praat's Spectrogram object Window: 0.02s, maximum frequency, 0.005s time step Dynamic range: 50 dB, window shape: Gaussian 4. FOOTER: Parameter summary: "BP: N | Amp: X | Dur: Y | Dist | Gen: Z" Centered at bottom Viewport layout: Title: viewport(0,7, 0.5,1.2) Waveform: viewport(0,7, 1.2,2.8) with inner margins Spectro: viewport(0,7, 3.0,5.6) with inner margins Footer: viewport(0,7, 5.7,6.2) Inner margins: left=0.6, right=6.5 for waveform/spectro

Built-in Presets

🎨 Curated Sound Worlds

Each preset embodies a different sonic character while maintaining the GENDYN stochastic philosophy. Presets are starting points — adjust parameters to explore variations.

Xenakis Tributes

Preset	Parameters	Character	Duration
GENDY3 Tribute	12 BP, 180 Hz, Cauchy, 2.5 range	Authentic Xenakis: metallic, complex, evolving	12s
Deep Mutations	16 BP, 60 Hz, Gaussian, 1.8 range	Slow, profound evolution, subharmonic richness	20s
Whispered Stochasm	14 BP, 150 Hz, Logistic, 1.5 range	Delicate, breathy, subtle transformations	15s

Textural Explorations

Preset	Parameters	Character	Duration
Insect Swarm	8 BP, 400 Hz, Cauchy, 1.5 range	Granular, buzzing, dense high-frequency activity	8s
Crystalline Fractures	10 BP, 800 Hz, Cauchy, 2.0 range	Glass-like, brittle, sharp transients	10s
Electronic Organisms	12 BP, 120 Hz, Logistic, 2.2 range	Synth-like, synthetic life forms, artificial biology	12s

Evolutionary Processes

Preset	Parameters	Character	Duration
Slow Evolution	20 BP, 100 Hz, Gaussian, 1.2 range	Gradual transformation, ambient, meditative	30s
Chaotic Bursts	8 BP, 200 Hz, Cauchy, 4.0 range	Eruptive, unpredictable, dramatic mutations	8s

Parameter Reference

Parameter	Type	Range	Description
Preset	option	1-9	Built-in configurations or Custom
Duration_s	positive	0.1-300	Output duration in seconds
Sample_rate_Hz	integer	8000-192000	Audio sample rate (typically 44100)
Number_of_breakpoints	integer	2-100	Complexity of waveform (typically 8-20)
Base_frequency_Hz	positive	1-5000	Starting fundamental frequency
Frequency_range	real	1.0-10.0	Multiplier for frequency variation
Amplitude_step	real	0.01-1.0	Size of amplitude mutations (typically 0.05-0.3)
Duration_step	real	0.01-1.0	Size of duration mutations (typically 0.05-0.3)
Distribution_type	option	1-4	Uniform, Cauchy, Gaussian, Logistic
Amplitude_barrier	real	0.1-1.0	Maximum amplitude (typically 0.8-0.95)
Min_frequency_Hz	real	1-1000	Lower frequency limit (typically 20-100)
Max_frequency_Hz	real	100-20000	Upper frequency limit (typically 1000-5000)
Spatial_mode	option	1-3	Mono, Stereo Dual, Rotating
Normalize_output	boolean	0/1	Scale peak to 0.9 (prevents clipping)
Draw_visualization	boolean	0/1	Create visual display of waveform/spectrum
Play_result	boolean	0/1	Auto-play after synthesis

Applications

Experimental Music Composition

Use case: Generate unique sonic materials for electroacoustic composition

Techniques:

Stochastic counterpoint: Layer multiple GENDYN outputs with different parameters
Evolutionary forms: Use long durations (60+ seconds) to create developmental structures
Parameter automation: Script gradual changes to parameters over time
Hybrid synthesis: Combine GENDYN with traditional synthesis methods

Sound Design for Media

Use case: Create evolving textures for film, games, installations

Techniques:

Sci-fi atmospheres: "Electronic Organisms" preset for alien environments
Horror tension: "Deep Mutations" with low frequencies for unsettling drones
Nature abstraction: "Insect Swarm" for abstracted insect/water sounds
UI sounds: Short "Crystalline Fractures" for futuristic interface feedback

Generative Art & Installation

Use case: Sound for generative visual art or interactive installations

Techniques:

Parameter mapping: Link GENDYN parameters to visual parameters
Live evolution: Use in real-time systems with gradual parameter shifts
Spatial audio: Use rotating stereo mode with multichannel systems
Interactive control: Allow audience to influence mutation parameters

Academic Research & Teaching

Use case: Study stochastic processes and Xenakis's theories

Techniques:

Distribution comparison: Compare results from different probability models
Barrier studies: Experiment with/without barriers to understand constraints
Complexity analysis: Relate breakpoint count to perceptual complexity
Historical context: Connect to Xenakis's GENDY3 and other stochastic works

Practical Workflow Examples

🎬 Sci-Fi Film Atmosphere

Goal: Create evolving background for space scene

Settings:

Preset: Electronic Organisms
Duration: 60 seconds
Spatial: Rotating stereo
Adjust: Lower amplitude_step to 0.08 for slower evolution
Adjust: Set frequency barriers to 80-1200 Hz

Result: Slowly evolving synthetic ecosystem sound

Post-process: Add reverb, layer with other sounds

🎵 Experimental Music Segment

Goal: Create 2-minute stochastic composition section

Settings:

Preset: GENDY3 Tribute
Duration: 120 seconds
Spatial: Stereo Dual
Adjust: Increase breakpoints to 16 for more complexity
Adjust: Set Cauchy distribution for dramatic changes

Result: Authentic Xenakis-style stochastic music

Composition: Extract interesting sections, layer, process further

🔬 Academic Study: Distribution Effects

Goal: Compare different probability distributions

Method:

Create 4 versions with same parameters except distribution
Duration: 10 seconds each
Record generation count and spectral centroid over time
Listen for perceptual differences

Findings: Cauchy produces most dramatic changes, Uniform most predictable, Gaussian most "natural"

Advanced Techniques

Parameter automation via scripting:

Gradual evolution: Script that slowly changes amplitude_step over time
Sectional form: Different presets for different sections of a piece
Responsive synthesis: Modify parameters based on analysis of other sounds
Multi-voice counterpoint: Generate multiple independent voices and combine

Creative parameter combinations:

Low frequency + many breakpoints: Complex subharmonic structures
High frequency + few breakpoints: Buzzy, insect-like textures
Large steps + tight barriers: Chaotic but constrained evolution
Small steps + no barriers: Slow drift into new territories
Extreme frequency range (20-5000 Hz): Full-spectrum exploration

Troubleshooting Common Issues

Problem: Synthesis very slow
Causes: Long duration + many breakpoints + high sample rate
Solutions: Reduce duration, reduce breakpoints, use lower sample rate, be patient

Problem: Output too static/boring
Causes: Step sizes too small, barriers too tight, uniform distribution
Solutions: Increase amplitude_step/duration_step, use Cauchy distribution, loosen barriers

Problem: Output too chaotic/noisy
Causes: Step sizes too large, too many breakpoints, frequency too high
Solutions: Decrease step sizes, reduce breakpoints, lower base frequency

Problem: Frequency drifts out of audible range
Causes: Insufficient barriers, large duration_step
Solutions: Set appropriate min/max frequency barriers, reduce duration_step

Problem: Visualization errors or missing
Causes: Praat drawing issues, very short durations
Solutions: Ensure Praat Picture window is open, use longer durations for better visualization

Performance Optimization

FOR SPEED: • Reduce number_of_breakpoints (most significant factor) • Reduce duration • Lower sample_rate_Hz • Use fewer breakpoints (8-12 is optimal) FOR COMPLEXITY: • Increase number_of_breakpoints (12-20) • Use Cauchy distribution • Increase step sizes (0.2-0.3) • Use stereo dual mode for two independent evolutions FOR MUSICAL RESULTS: • Set frequency barriers to musical range (e.g., 80-800 Hz) • Use moderate step sizes (0.1-0.2) • Gaussian or Logistic distribution for natural evolution • 30+ second durations to hear evolution CONTROL RATE NOTES: • Auto-adjusted based on frequency × breakpoints • Minimum 8000 Hz ensures waveform definition • Maximum 22050 Hz prevents excessive computation • Actual audio rate comes from resampling step

Historical & Theoretical Context

Iannis Xenakis: Architect of Stochastic Music

🏛️ From Architecture to Music

Background: Greek-French composer, architect, engineer (1922-2001). Worked with Le Corbusier, survived WWII, studied mathematics and music.

Key works: Metastasis (1955), Pithoprakta (1956), ST/48 (1962), GENDY3 (1991).

Theoretical contributions: Formalized Music (1963) — first comprehensive theory of stochastic music.

GENDY3 significance: One of first computer implementations of his stochastic theories for sound synthesis (1991, at CEMAMu).

Stochastic Music Theory

KEY CONCEPTS: 1. PROBABILITY DISTRIBUTIONS: Xenakis used: Uniform, Exponential, Cauchy, Gaussian Each creates different musical character Cauchy favored for "dynamic stochastic" (GENDY) 2. MARKOV CHAINS: Next state depends only on current state Implemented in GENDYN as: next amplitude depends on current amplitude + random step 3. BROWNIAN MOTION: Random walk of sound particles In GENDYN: amplitudes/durations undergo random walks with barriers 4. GAME THEORY: Xenakis applied min-max strategies to composition In GENDYN: barriers implement "rules of the game" MATHEMATICAL FOUNDATIONS: Xenakis's formula for sound mass density: N(t) = ∫₀ᵗ n(u) du where n(u) = number of sounds at time u GENDYN extends this to waveform level: Each breakpoint represents a "sound particle" Evolution follows stochastic differential equations

GENDY3 vs This Implementation

Aspect	Original GENDY3 (Xenakis)	This Praat Implementation
Platform	Custom software at CEMAMu	Praat scripting language
Parameters	More extensive stochastic controls	Simplified for usability
Distributions	Cauchy primarily	4 distributions including Cauchy
Output	Monophonic	Mono, stereo, rotating options
Visualization	Separate graphical output	Integrated in Praat Picture
Accessibility	Research institution only	Freely available Praat plugin
Philosophy	Pure stochastic exploration	Balanced: stochastic + musical usability

Related Xenakis Techniques

OTHER XENAKIS METHODS IMPLEMENTABLE IN PRAAT: 1. SCREENING (Dynamic Stochastic Synthesis): Similar to GENDYN but with more parameters Could be implemented as extension 2. GRANULAR SYNTHESIS: Xenakis pioneered with Analogique B (1959) Praat has built-in granular capabilities 3. MARKOV CHAIN COMPOSITION: Implementable via Praat scripting Transition probabilities between sounds/notes 4. SIEVE THEORY: Mathematical filtering of pitch sets Implementable for scale/mode generation 5. ARBOrescences: Tree-like formal structures Could guide parameter evolution in GENDYN THIS IMPLEMENTATION AS GATEWAY: GENDYN introduces Xenakis's concepts accessibly Foundation for exploring more advanced stochastic methods Bridge between mathematical theory and musical practice

What this does

🎻 Tribute to Iannis Xenakis (1922–2001)

Quick start

GENDYN Theory

The Xenakis Philosophy

🎼 Stochastic Music Principles

Breakpoint Waveform Model

📈 Breakpoint Representation

Stochastic Evolution

🎲 Mutation Process

Barrier System

🚧 Constrained Freedom

Probability Distributions

📊 Statistical Models for Mutation

Spatial Processing Modes

Complete Processing Pipeline

Algorithm Details

Control Rate Optimization

Generation Counter Significance

🔢 Measuring Evolution

Visualization System

Built-in Presets

🎨 Curated Sound Worlds

Xenakis Tributes

Textural Explorations

Evolutionary Processes

Parameter Reference

Applications

Experimental Music Composition

Sound Design for Media

Generative Art & Installation

Academic Research & Teaching

Practical Workflow Examples

🎬 Sci-Fi Film Atmosphere

🎵 Experimental Music Segment

🔬 Academic Study: Distribution Effects

Advanced Techniques

Troubleshooting Common Issues

Performance Optimization

Historical & Theoretical Context

Iannis Xenakis: Architect of Stochastic Music

🏛️ From Architecture to Music

Stochastic Music Theory

GENDY3 vs This Implementation

Related Xenakis Techniques

Further Reading & Resources