Hexaphonic Serial Audio Processor — User Guide
Advanced serial composition techniques applied to audio processing: six independent 12-tone rows control amplitude modulation, timing, and spatialization parameters.
What this does
This script implements hexaphonic serial audio processing — an advanced application of twelve-tone serial composition techniques to digital audio effects. Six independent serial rows control different audio processing parameters, creating complex, algorithmically determined transformations that evolve over time according to strict serialist principles.
Key Features:
- Six Independent Serial Rows — Control modulation, timing, and spatialization
- Classical Serial Presets — Rows based on Webern, Berg, and Schoenberg
- Mathematical Transformations — Prime, inversion, retrograde, retrograde-inversion
- Cross-Coupled Sections — Different transformation combinations per section
- Multiple Waveform Types — Sine, triangle, square, sawtooth modulation
- Perceptual Parameter Scaling — Logarithmic mapping for natural perception
- Real-time Pitch Shifting — ±6 semitone range with serial control
What is serial audio processing? Traditional audio effects: manual parameter control, predictable patterns. Serial audio processing: Applies twelve-tone serial composition principles to audio effect parameters. Advantages: (1) Algorithmic complexity: Creates intricate, evolving patterns impossible to design manually. (2) Historical connection: Links digital audio processing to 20th-century avant-garde composition. (3) Parameter integration: Multiple effects parameters controlled by unified mathematical system. (4) Reproducibility: Same serial rows produce identical results. (5) Creative exploration: Discovers unexpected audio transformations through systematic processes. Use cases: Experimental music composition, sound design for media, academic research in algorithmic composition, audio art installations, music theory pedagogy.
Technical Implementation: (1) Row Definition: Six 12-value rows define parameter sequences. (2) Transformations: Generate prime, inversion, retrograde, and retrograde-inversion forms. (3) Section Structure: Four sections with different transformation combinations. (4) Parameter Mapping: Convert row values (0-11) to audio parameters. (5) Segment Processing: Apply amplitude modulation with different waveforms. (6) Spatialization: Stereo panning controlled by serial values. (7) Time Stretching: Pitch shifting via resampling with serial control. (8) Quality Control: Perceptual scaling and parameter validation.
Quick start
- In Praat, select exactly one Sound object.
- Run script… →
hexaphonic_serial_processor.praat. - Choose Preset or select "Custom" for manual row definition.
- If using custom, define six 12-tone rows (values 0-11 separated by spaces).
- Set parameter ranges for modulation rate, depth, and duration.
- Enable perceptual_rate_scaling for natural frequency perception.
- Click OK — processing begins with detailed progress reporting.
- Result appears as "originalname_AM" and plays automatically.
Quick tip: Start with Classic Webern preset for balanced, symmetrical processing. Use perceptual_rate_scaling = yes for more musical modulation rates. The six rows control: (1) Modulation rate, (2) Modulation depth, (3) Waveform shape, (4) Segment duration, (5) Stereo panning, (6) Playback speed. Values 0-11 map to parameter ranges — for example, modulation rate from 0.5 Hz to 50 Hz. The processing divides your audio into 48 segments (4 sections × 12 steps) with serial-controlled transformations. Listen for the systematic evolution of textures across sections.
Important: PROCESSING TIME — Creates 48 individual audio segments + transformations. Long audio files will take significant time. EXTREME PARAMETERS — Very high modulation rates or depths can create harsh, noisy results. SERIAL CONSTRAINTS — Each value 0-11 appears exactly once per row (true 12-tone rows). SECTIONAL STRUCTURE — Audio is processed in fixed sequential sections, not real-time. MEMORY USAGE — High segment count may require substantial RAM for long files. QUALITY CONSIDERATIONS — Resampling for pitch shifting may slightly reduce audio quality. Original sound is preserved unchanged.
Serial Composition Theory
Twelve-Tone Serialism Basics
🎵 The Twelve-Tone System
Concept: Equal treatment of all twelve pitch classes through ordered sequences
Historical context: Arnold Schoenberg's method from 1920s
Audio adaptation: Apply same principles to effect parameters
Core serial principles:
PRIME ROW (P): Original ordered sequence of 12 values
Example: [0, 3, 7, 11, 2, 6, 9, 1, 5, 8, 4, 10]
Properties: Each value 0-11 appears exactly once
INVERSION (I): Subtract each value from 11
Formula: I[n] = 11 - P[n]
Example: [11, 8, 4, 0, 9, 5, 2, 10, 6, 3, 7, 1]
RETROGRADE (R): Reverse the order
Formula: R[n] = P[12-n]
Example: [10, 4, 8, 5, 1, 9, 6, 2, 11, 7, 3, 0]
RETROGRADE-INVERSION (RI): Reverse then invert
Formula: RI[n] = 11 - P[12-n]
Example: [1, 7, 3, 6, 10, 2, 5, 9, 0, 4, 8, 11]
Musical significance:
Creates systematic variation while maintaining structure
All transformations preserve the "all-interval" property
Provides mathematical foundation for creative work
Hexaphonic Extension
Six Independent Parameter Rows
Multi-parameter serial control:
This script uses SIX simultaneous serial rows:
1. MODULATION RATE: Controls LFO frequency for AM
Range: min_rate to max_rate (typically 0.5-50 Hz)
2. MODULATION DEPTH: Controls AM intensity
Range: min_depth to max_depth (typically 0.05-0.95)
3. WAVEFORM SHAPE: Determines modulator waveform
Mapping: 0-2=sine, 3-5=triangle, 6-8=square, 9-11=sawtooth
4. SEGMENT DURATION: Controls time segment length
Range: min_duration to max_duration (typically 0.1-3.0s)
5. STEREO PANNING: Controls left-right position
Mapping: 0=left, 6=center, 11=right
6. PLAYBACK SPEED: Controls pitch shifting
Mapping: 0=-6 semitones, 6=original, 11=+5 semitones
Each row operates independently but follows same transformation rules
Classical Serial Presets
Preset 1: Classic Webern
⚪ Anton Webern Style
Characteristics: Symmetrical structures, economical material
Audio effect: Balanced, subtle transformations
Best for: Delicate textures, academic demonstrations
Webern row properties:
Modulation Rate: "0 11 3 8 4 7 9 2 10 1 5 6"
Features: Symmetrical intervals, palindromic tendencies
Duration: "5 6 4 7 3 8 2 9 1 10 0 11"
Creates varied but balanced time structure
Speed: "6 6 6 5 7 5 7 6 6 6 6 6"
Mostly centered with slight variations
Maintains pitch coherence
Overall effect: Mathematical precision with subtle variations
Preset 2: Berg Symmetrical
🔵 Alban Berg Influence
Characteristics: Lyrical, with hidden symmetries
Audio effect: Expressive, evolving transformations
Best for: Emotional content, dramatic development
Preset 3: Schoenberg Op.25
🟡 Original Serial Master
Characteristics: Historic first completely serial piece
Audio effect: Classic serial sound, academic reference
Best for: Historical studies, fundamental demonstrations
Other Specialized Presets
| Preset | Style | Characteristics | Best For |
|---|---|---|---|
| Chromatic Ascent | Linear | Sequential values 0-11 | Clear progression |
| All-Interval | Complex | Contains all 11 intervals | Maximum variety |
| Pentatonic Serial | Modal | Emphasizes pentatonic intervals | Musical accessibility |
| Whole-Tone Serial | Symmetrical | Whole-tone scale emphasis | Dreamlike quality |
| Random Chaos | Stochastic | Random permutations | Experimental textures |
Parameter Mapping System
Modulation Parameters
Amplitude Modulation (Ring Modulation)
Mathematical foundation:
AMPLITUDE MODULATION formula:
output(t) = input(t) × [1 + depth × modulator(t)]
Where modulator(t) is:
Sine: sin(2π × rate × t)
Triangle: 1 - 4 × |round(rate×t) - rate×t|
Square: sign(sin(2π × rate × t))
Sawtooth: 2 × ((rate×t) - floor(rate×t)) - 1
Parameter mapping:
Rate: row value → frequency (0.5-50 Hz)
Depth: row value → modulation intensity (5%-95%)
Shape: row value → waveform type
Effect characteristics:
Sine: Smooth, musical tremolo
Triangle: Gentle, evolving sweeps
Square: Rhythmic, pulsed effect
Sawtooth: Sweeping, siren-like
Perceptual Rate Scaling
Logarithmic frequency mapping:
LINEAR mapping (perceptual_rate_scaling = no):
frequency = min_rate + (value/11) × (max_rate - min_rate)
LOGARITHMIC mapping (perceptual_rate_scaling = yes):
frequency = min_rate × (max_rate/min_rate) ^ (value/11)
Comparison example (min_rate=0.5, max_rate=50):
Value 0: Linear=0.5 Hz, Log=0.5 Hz
Value 3: Linear=14.0 Hz, Log=1.7 Hz
Value 6: Linear=27.5 Hz, Log=5.9 Hz
Value 9: Linear=41.0 Hz, Log=20.2 Hz
Value 11: Linear=50.0 Hz, Log=50.0 Hz
Perceptual advantage:
Logarithmic matches human frequency perception
Better distribution of musically useful rates
Avoids clustering most values at high end
Spatial and Temporal Parameters
Stereo Panning System
Linear panning control:
Panning mapping:
pan_position = row_value / 11
left_gain = 1 - pan_position
right_gain = pan_position
Examples:
Value 0: pan_position=0.0 → left_gain=1.0, right_gain=0.0 (full left)
Value 6: pan_position=0.545 → left_gain=0.455, right_gain=0.545 (slight right)
Value 11: pan_position=1.0 → left_gain=0.0, right_gain=1.0 (full right)
Implementation:
Extract left and right channels
Apply gain factors separately
Recombine into stereo
Alternative approach (not used):
Equal-power panning: left=√(1-pan), right=√(pan)
More natural but computationally expensive
Time and Pitch Control
Segment duration and speed:
DURATION mapping:
duration = min_duration + (value/11) × (max_duration - min_duration)
Example: min=0.1s, max=3.0s, value=6 → duration = 1.55s
SPEED mapping (pitch shifting):
semitones = value - 6 (range: -6 to +5 semitones)
speed_factor = 2 ^ (semitones / 12)
target_hz = original_hz × speed_factor
Examples:
Value 0: -6 semitones, factor=0.5, target_hz=11025 (half speed)
Value 6: 0 semitones, factor=1.0, target_hz=22050 (original)
Value 11: +5 semitones, factor=1.334, target_hz=29433 (higher pitch)
Resampling process:
Resample to target_hz, then back to original_hz
Preserves duration while changing pitch
Waveform Shape Mapping
Four Modulator Waveforms
Shape value interpretation:
Value ranges determine waveform:
0-2: SINE WAVE
Formula: sin(2π × rate × t)
Character: Smooth, musical, classic tremolo
3-5: TRIANGLE WAVE
Formula: 1 - 4 × |round(rate×t) - rate×t|
Character: Gentle sweeps, evolving texture
6-8: SQUARE WAVE
Formula: sign(sin(2π × rate × t))
Character: Rhythmic, pulsed, aggressive
9-11: SAWTOOTH WAVE
Formula: 2 × ((rate×t) - floor(rate×t)) - 1
Character: Sweeping, siren-like, intense
Distribution:
Each waveform gets 3 of 12 possible values
Equal probability in random rows
Systematic variation in composed rows
Serial Transformations
Four Standard Transformations
🔄 Mathematical Variations
Concept: Systematic generation of related row forms
Purpose: Create variation while maintaining structural integrity
Audio effect: Coherent yet evolving parameter sequences
Transformation algorithms:
PRIME (P): Original row
P[n] = original_row[n]
INVERSION (I): Subtract from 11
I[n] = 11 - P[n]
Effect: Creates complementary parameter values
RETROGRADE (R): Reverse order
R[n] = P[13 - n]
Effect: Time-reversed parameter sequence
RETROGRADE-INVERSION (RI): Reverse then invert
RI[n] = 11 - P[13 - n]
Effect: Maximum transformation while preserving structure
Example with row [0, 3, 7, 11, 2, 6, 9, 1, 5, 8, 4, 10]:
P: [0, 3, 7, 11, 2, 6, 9, 1, 5, 8, 4, 10]
I: [11, 8, 4, 0, 9, 5, 2, 10, 6, 3, 7, 1]
R: [10, 4, 8, 5, 1, 9, 6, 2, 11, 7, 3, 0]
RI: [1, 7, 3, 6, 10, 2, 5, 9, 0, 4, 8, 11]
Cross-Coupled Section Structure
Four-Part Formal Design
Section transformation assignments:
SECTION A: PRIME COMBINATION
Rate: P, Depth: P, Shape: P, Duration: P, Panning: P, Speed: P
Character: Direct presentation of original rows
SECTION B: CROSS-COUPLED
Rate: I, Depth: R, Shape: P, Duration: I, Panning: R, Speed: I
Character: Inverted rates with retrograde depth/panning
SECTION C: CROSS-COUPLED
Rate: R, Depth: P, Shape: I, Duration: R, Panning: I, Speed: R
Character: Retrograde rates with inverted shape/panning
SECTION D: CROSS-COUPLED
Rate: RI, Depth: I, Shape: R, Duration: RI, Panning: P, Speed: RI
Character: Maximum transformation with prime panning
Design philosophy:
Each section has unique transformation combination
Creates systematic evolution across piece
Maintains relationships between parameters
Provides large-scale formal structure
Mathematical Properties
Transformation relationships:
Identity relationships:
I(I(row)) = P(row) (Double inversion returns prime)
R(R(row)) = P(row) (Double retrograde returns prime)
RI(RI(row)) = P(row) (Double RI returns prime)
Combination properties:
R(I(row)) = RI(row)
I(R(row)) = RI(row)
These are equivalent definitions
Group theory perspective:
The four transformations form a mathematical group
Closure: Any combination of transformations yields another transformation
Identity: P serves as identity element
Inverses: Each transformation has an inverse
Audio significance:
Guarantees coherent parameter evolution
Creates perceptible structural relationships
Provides mathematical foundation for artistic results
Processing Architecture
Segment-by-Segment Processing
Step-wise audio transformation:
FOR each of 4 sections:
FOR each of 12 steps in section:
EXTRACT segment using duration row value
APPLY speed transformation (pitch shift)
APPLY amplitude modulation with rate/depth/shape
APPLY panning transformation
STORE processed segment
END FOR
END FOR
CONCATENATE all 48 segments
OUTPUT final combined sound
Segment properties:
Each segment has unique parameter combination
Duration varies according to duration row
Processing order follows serial sequence
Total processing: 4×12 = 48 individual segments
Quality Control Measures
Parameter validation and safety:
Duration validation:
IF current_time + step_duration > total_duration
step_duration = total_duration - current_time
END IF
IF step_duration ≤ 0.01: skip segment
Resampling safety:
IF |speed_factor - 1.0| > 0.01: apply resampling
ELSE: skip resampling to preserve quality
Memory management:
Remove temporary objects after each segment
Final cleanup of all intermediate segments
Preserve only original and final result
Progress reporting:
Detailed info window output
Step-by-step parameter display
Final summary statistics
Applications
Experimental Music Composition
Use case: Creating complex, evolving textures for avant-garde music
Technique: Apply to instrumental recordings or electronic sounds
Settings: Use composed rows like Webern or Berg for structural integrity
Sound Design for Media
Use case: Generating unique sound transformations for film/games
Technique: Process Foley sounds or synth patches with serial transformations
Settings: Random Chaos preset for unexpected results
Music Theory Pedagogy
Use case: Demonstrating serial composition principles audibly
Technique: Use simple audio examples to hear serial transformations
Settings: Chromatic Ascent for clear parameter progression
Algorithmic Composition Research
Use case: Studying systematic parameter control in audio processing
Technique: Analyze relationships between serial structures and audio results
Settings: Custom rows with specific interval properties
Audio Art Installation
Use case: Creating evolving soundscapes for gallery settings
Technique: Process environmental sounds with serial methods
Settings: Long durations with subtle parameter ranges
Practical Workflow Examples
🎼 Academic Demonstration
Goal: Teach serial composition through audio examples
Settings:
- Preset: Classic Webern
- Sound: Simple sine wave or piano note
- Parameters: Moderate ranges for clarity
- Duration: Short audio for quick demonstration
Result: Clear audible demonstration of serial transformations
🎬 Sci-Fi Sound Design
Goal: Create alien or futuristic sound effects
Settings:
- Preset: Random Chaos
- Sound: Synthetic textures or processed vocals
- Parameters: Extreme ranges for dramatic effect
- Waveforms: Square and sawtooth for edgy character
Result: Unpredictable, evolving sci-fi textures
🔬 Research Experiment
Goal: Study parameter perception in serial structures
Settings:
- Preset: Custom designed rows
- Sound: Controlled test signals
- Parameters: Specific ranges for experimental control
- Analysis: Detailed parameter logging
Result: Systematic data on serial audio perception
Creative Techniques
Row design strategies:
- Symmetrical rows: Create balanced, palindromic effects
- Extreme intervals: Use large jumps for dramatic changes
- Clustered values: Group similar values for cohesive sections
- Complementary rows: Design rows that work well together
- Cultural references: Base rows on existing serial compositions
Parameter combination ideas:
- Slow rates + deep modulation: Creates evolving swells
- Fast rates + square waves: Creates rhythmic textures
- Extreme panning + pitch shifts: Creates spatial disorientation
- Varied durations + consistent rates: Creates formal structure
- Complementary transformations: Highlights serial relationships
Troubleshooting Common Issues
Problem: Processing takes extremely long time
Cause: Very long audio file, complex parameter combinations
Solution: Use shorter audio segments, simplify parameter ranges
Cause: Very long audio file, complex parameter combinations
Solution: Use shorter audio segments, simplify parameter ranges
Problem: Output sounds noisy or distorted
Cause: Extreme modulation depths or rates, square/sawtooth waves
Solution: Reduce depth range, use sine/triangle waves, lower amplitudes
Cause: Extreme modulation depths or rates, square/sawtooth waves
Solution: Reduce depth range, use sine/triangle waves, lower amplitudes
Problem: Cannot hear serial structure
Cause: Too complex source material, subtle parameter changes
Solution: Use simpler sounds, increase parameter contrast, listen multiple times
Cause: Too complex source material, subtle parameter changes
Solution: Use simpler sounds, increase parameter contrast, listen multiple times
Problem: Memory errors during processing
Cause: Too many segments, insufficient RAM
Solution: Process shorter files, increase system memory, close other applications
Cause: Too many segments, insufficient RAM
Solution: Process shorter files, increase system memory, close other applications
Problem: Unexpected parameter behavior
Cause: Invalid row values, incorrect row formatting
Solution: Verify rows contain values 0-11 exactly once, check space separation
Cause: Invalid row values, incorrect row formatting
Solution: Verify rows contain values 0-11 exactly once, check space separation
Technical Reference
Complete Parameter Reference
| Parameter | Type | Default | Description |
|---|---|---|---|
| Preset | optionmenu | 1 | Pre-configured serial row sets |
| mod_rate_row | sentence | "0 3 7 11 2 6 9 1 5 8 4 10" | Modulation rate row (0-11) |
| mod_depth_row | sentence | "5 9 2 11 0 7 3 10 1 6 8 4" | Modulation depth row (0-11) |
| mod_shape_row | sentence | "2 8 5 0 11 3 7 1 9 4 10 6" | Waveform shape row (0-11) |
| duration_row | sentence | "6 2 9 1 11 4 8 0 7 3 10 5" | Segment duration row (0-11) |
| panning_row | sentence | "4 8 1 10 3 7 0 11 5 9 2 6" | Stereo panning row (0-11) |
| speed_row | sentence | "6 5 7 4 8 3 9 2 10 1 11 0" | Playback speed row (0-11) |
| min_rate | positive | 0.5 | Minimum modulation rate (Hz) |
| max_rate | positive | 50 | Maximum modulation rate (Hz) |
| min_depth | positive | 0.05 | Minimum modulation depth |
| max_depth | positive | 0.95 | Maximum modulation depth |
| min_duration | positive | 0.1 | Minimum segment duration (s) |
| max_duration | positive | 3.0 | Maximum segment duration (s) |
| perceptual_rate_scaling | boolean | 1 | Use logarithmic rate mapping |
Output Characteristics
Generated Sound Properties
Technical specifications:
Output object: "originalname_AM"
Type: Stereo Sound (always converted to stereo)
Duration: Approximately original duration (varies with speed changes)
Sampling frequency: Same as original
Content: 48 sequentially processed segments
Segment properties:
Each segment has unique parameter combination
AM applied with one of four waveform types
Stereo panning applied
Pitch may be shifted ±6 semitones
Duration varies 0.1-3.0 seconds
Quality considerations:
Resampling may introduce slight artifacts
Extreme parameters may cause distortion
Segment boundaries are abrupt (rectangular window)
Performance Characteristics
Processing Time Factors
Major time consumers:
1. Segment extraction: 48× O(n) with segment length
2. Resampling: 48× O(n) when speed changes needed
3. AM processing: 48× O(n) with sound length
4. Panning: 48× O(n) with sound length
5. Concatenation: O(n) with total length
Dominant factors:
Number of segments (always 48)
Original audio length
Complexity of parameter combinations
Typical performance:
1-minute audio: 2-5 minutes processing
5-minute audio: 10-25 minutes processing
30-minute audio: 1-2 hours processing
Memory usage:
Peak: 48× segment size in memory
Final: only original and result preserved