Spiral Segmentation — User Guide

Spiral-based temporal and pitch transformation: divides sound into segments, applies exponential duration scaling and incremental pitch shifting to create a spiral trajectory through time-pitch space.

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 Spiral Concept Spiral Presets Parameters Explained Visualization

What this does

This script implements Spiral Segmentation — a time and pitch transformation that creates spiral trajectories through audio material. Process: (1) Segmentation: Divide sound into equal-duration segments. (2) Duration spiral: Apply exponential scaling to segment durations (expanding or contracting). (3) Pitch spiral: Apply incremental pitch shifts to each segment. (4) Jitter addition: Add stochastic timing variations for non-metric feel. (5) Resynthesis: Recombine transformed segments via PSOLA (Pitch-Synchronous Overlap-Add). Result: Audio material returns repeatedly, but each return occurs at transformed temporal and spectral levels — never identical, never metrically fixed.

Key Features:

12 Spiral Presets: Gentle Expansion, Accelerating Collapse, Pitch Ascent, Pitch Descent, Drunken Spiral, Tight Coil, Wide Orbit, Reverse Time Feel, Glitch Scatter, Meditative Stretch, Anxious Compression, Cosmic Drift
Exponential Duration Scaling: Segments grow/shrink by multiplier^n
Incremental Pitch Shifts: Linear pitch changes across segments
Stochastic Jitter: Gaussian timing variations for non-metric feel
PSOLA Resynthesis: High-quality time and pitch modification
6-Panel Visualization: Waveforms, duration factors, pitch shifts, spiral diagram
Preset System: 12 artistic presets + custom manual settings

What is spiral transformation? Traditional time-stretch/pitch-shift: Uniform transformations. Spiral transformation: Segmented, exponential, incremental changes creating perceptual spirals. Philosophical basis: Material returns but transformed — "eternal return" with variation. Musical applications: (1) Formal structure: Creates perceivable large-scale shape. (2) Perceptual interest: Systematic yet variable transformations. (3) Algorithmic composition: Generates complex structures from simple materials. (4) Sound design: Creates evolving, spiraling textures. (5) Analytical tool: Reveals material through systematic variation. The spiral is both a formal structure and a perceptual metaphor: expansion, return, displacement.

Technical Implementation: (1) Segmentation: Divide sound into N equal segments. (2) Duration factors: Calculate multiplier^n for each segment (n = segment index). (3) Jitter application: Multiply duration factors by (1 + Gaussian random). (4) Pitch shifts: Calculate pitch_step_Hz × segment_index (with direction options). (5) Manipulation object: Create Praat Manipulation object for PSOLA. (6) Duration tier: Build duration tier with segment-specific tempo factors. (7) Pitch tier: Extract original pitch, add spiral offsets, create new pitch tier. (8) Resynthesis: Replace tiers in manipulation, resynthesize via overlap-add. (9) Visualization: Create 6-panel plot showing waveforms, factors, shifts, spiral diagram.

Quick start

In Praat, select exactly one Sound object.
Run script… → Spiral_Segmentation.praat.
Choose Preset (12 options) or Custom for manual settings.
Set Number_of_segments (how many times material repeats).
Adjust Duration_multiplier (1.0 = no change, >1 = expansion, <1 = contraction).
Choose Spiral_direction: Expanding or Contracting.
Set Pitch_step_Hz (pitch change per segment).
Choose Pitch_direction: Rising, Falling, or Alternating.
Add Jitter_amount (0.0 = precise, 0.2 = noticeable variation).
Enable Show_visualization to see spiral trajectory.
Click OK — spiral transformation applied, visualization shown.

Quick tip: Start with Gentle Expansion preset (segments gradually lengthen, pitch rises slightly). Use 8-16 segments for clear spiral perception. Duration_multiplier 1.1-1.3 creates noticeable expansion; 0.7-0.9 for contraction. Pitch_step_Hz 5-15 creates clear pitch spiral. Enable visualization to understand the transformation — shows original vs spiral waveforms, duration factors, pitch shifts, and spiral diagram. Jitter_amount 0.05-0.15 adds natural, non-mechanical feel. For voice/speech, use subtle settings; for sound design, experiment with extreme values. Output named [original]_spiral appears in Objects window.

Important: PSOLA REQUIREMENTS: Works best with voiced sounds (speech, singing, monophonic instruments). Unvoiced/noisy sounds may produce artifacts. Extreme duration factors (>3× or <0.3×) can cause quality degradation. Large pitch shifts (>±50 Hz) may exceed PSOLA's natural range. Segment boundaries occur at equal time intervals — musically significant boundaries not detected. Jitter is applied multiplicatively to duration factors — large jitter can create extreme variations. Visualization may be complex for many segments (>20). Processing time scales with sound duration and number of segments. Original sound preserved unless "Preserve_original" disabled.

Spiral Concept

The Spiral as Formal Structure

🌀 Philosophical & Musical Basis

Core idea: Material returns repeatedly, but transformed

Musical precedents: Minimalism (Reich, Glass), spiral forms in non-Western music

Perceptual effect: Familiar yet novel, predictable yet variable

Time-pitch space: Two-dimensional transformation creates spiral trajectory

Mathematical Spiral Formulation

TIME DIMENSION (duration spiral): durationFactor[i] = multiplier ^ i WHERE i = segment index (0-based) PITCH DIMENSION (pitch spiral): pitchShift[i] = stepHz × i × direction COMBINED SPIRAL: Each segment i has coordinates: timeCoordinate = Σ durationFactor[j] for j=0 to i-1 pitchCoordinate = basePitch + pitchShift[i] VISUALIZATION: Points (timeCoordinate, pitchCoordinate) trace spiral

Segment Processing Pipeline

🔄 From Original to Spiral

Step 1: Equal segmentation

Original duration: D Number of segments: N Segment duration: d = D / N Segment boundaries: start[i] = (i - 1) × d end[i] = i × d

Step 2: Duration factor calculation

Base multiplier: m Direction: expanding (1) or contracting (2) IF expanding: factor[i] = m ^ (i - 1) [first segment unchanged] ELSE (contracting): factor[i] = m ^ (N - i) [last segment unchanged] Jitter application: jitter[i] = randomGauss(0, jitter_amount) factorJittered[i] = factor[i] × (1 + jitter[i])

Step 3: Pitch shift calculation

Pitch step: p (Hz) Direction: rising (1), falling (2), alternating (3) IF rising: shift[i] = p × (i - 1) ELSE IF falling: shift[i] = -p × (i - 1) ELSE (alternating): shift[i] = p × floor((i - 1) / 2) × (-1)^(i - 1)

PSOLA Resynthesis

🎵 High-Quality Time-Pitch Modification

Praat Manipulation object: PSOLA (Pitch-Synchronous Overlap-Add) algorithm

PROCESS: 1. Create Manipulation object (analysis) 2. Extract original pitch contour 3. Build DurationTier with segment factors 4. Build PitchTier with spiral shifts 5. Replace tiers in Manipulation 6. Resynthesize via overlap-add ADVANTAGES: - Preserves formants (voice quality) - High quality for moderate modifications - Smooth transitions between segments LIMITATIONS: - Works best with voiced sounds - Extreme modifications cause artifacts - Requires pitch detection (may fail on noise)

Jitter: Breaking Metric Regularity

🎲 Stochastic Timing Variations

Purpose: Prevent mechanical, predictable timing

Implementation: Gaussian-distributed multiplicative factors

jitter_amount = standard deviation parameter (0.0 to 0.5+) FOR each segment i: jitter[i] = randomGauss(0, jitter_amount) factorJittered[i] = factor[i] × (1 + jitter[i]) EFFECTS: jitter_amount = 0.0: precise, mechanical jitter_amount = 0.1: subtle humanization jitter_amount = 0.3: noticeable variations jitter_amount = 0.5+: extreme, unpredictable CONSTRAINTS: Clamped to [0.1, 10.0] to prevent extreme values

Philosophical rationale: Imperfection as humanizing element, escape from perfect metric grid

Spiral Presets

Preset 1: Gentle Expansion

🌱 Gradual Growth

Settings: 8 segments, multiplier=1.12, expanding, pitch+3Hz, rising, jitter=0.05

Character: Subtle, natural expansion with slight pitch rise

Use: Gentle evolution, meditative textures, gradual intensification

Musical analogy: Breathing exercise, sunrise, gradual awakening

Preset 2: Accelerating Collapse

💥 Implosive Compression

Settings: 16 segments, multiplier=1.25, contracting, pitch-8Hz, falling, jitter=0.06

Character: Rapid shortening with pitch descent, accelerating feel

Use: Dramatic tension, collapsing structures, downward spirals

Musical analogy: Black hole, vortex, downward spiral

Preset 3: Pitch Ascent

⬆️ Upward Trajectory

Settings: 10 segments, multiplier=1.05, expanding, pitch+15Hz, rising, jitter=0.03

Character: Strong pitch rise with minimal time expansion

Use: Ascending lines, lifting effects, upward motion

Musical analogy: Elevator, rocket launch, climbing

Preset 4: Pitch Descent

⬇️ Downward Trajectory

Settings: 10 segments, multiplier=1.05, expanding, pitch-15Hz, falling, jitter=0.03

Character: Strong pitch fall with minimal time expansion

Use: Descending lines, sinking effects, downward motion

Musical analogy: Falling object, descent, subsidence

Preset 5: Drunken Spiral

🥴 Unstable Orbit

Settings: 12 segments, multiplier=1.18, expanding, pitch±7Hz, alternating, jitter=0.25

Character: High jitter creates unstable, wavering feel

Use: Disorientation, instability, drunken/wobbly effects

Musical analogy: Drunken walk, unstable orbit, wavering

Preset 6: Tight Coil

🌀 Dense Winding

Settings: 24 segments, multiplier=1.08, expanding, pitch+2Hz, rising, jitter=0.02

Character: Many segments with small increments, tight spiral

Use: Dense textures, intricate patterns, detailed evolution

Musical analogy: Watch mechanism, tight spring, precise clockwork

Preset 7: Wide Orbit

🌌 Broad Sweep

Settings: 6 segments, multiplier=1.35, expanding, pitch+20Hz, rising, jitter=0.1

Character: Few segments with large increments, broad spiral

Use: Grand gestures, sweeping motions, large-scale forms

Musical analogy: Planetary orbit, broad sweep, grand gesture

Preset 8: Reverse Time Feel

⏪ Backward Expansion

Settings: 12 segments, multiplier=1.2, contracting, pitch+5Hz, rising, jitter=0.08

Character: Time contracts while pitch rises — contradictory motion

Use: Temporal paradox, contradictory cues, unusual perceptions

Musical analogy: Time running backward, paradoxical motion

Preset 9: Glitch Scatter

💥 Digital Fragmentation

Settings: 32 segments, multiplier=1.1, expanding, pitch±12Hz, alternating, jitter=0.4

Character: Many segments with high jitter, glitchy texture

Use: Glitch art, digital corruption, fragmented textures

Musical analogy: CD skip, digital corruption, data error

Preset 10: Meditative Stretch

🧘 Extreme Expansion

Settings: 6 segments, multiplier=1.5, expanding, pitch-1Hz, falling, jitter=0.02

Character: Extreme time expansion with minimal pitch change

Use: Meditation, time dilation, extreme slow motion

Musical analogy: Time dilation, deep meditation, extreme slow motion

Preset 11: Anxious Compression

😰 Tense Contraction

Settings: 20 segments, multiplier=1.3, contracting, pitch+10Hz, rising, jitter=0.15

Character: Rapid shortening with pitch rise and moderate jitter

Use: Anxiety, tension building, accelerating pressure

Musical analogy: Pressure building, anxiety attack, accelerating tension

Preset 12: Cosmic Drift

🌠 Space-Time Drift

Settings: 8 segments, multiplier=1.4, expanding, pitch±25Hz, alternating, jitter=0.12

Character: Large increments in both time and pitch with oscillation

Use: Cosmic effects, space-time distortion, large oscillations

Musical analogy: Space-time distortion, cosmic drift, gravitational wave

Preset 13: Custom

🔧 Manual Settings

Settings: User-defined parameters

Character: Tailored to specific needs

Use: Experimentation, specific applications, fine control

Flexibility: Full control over all parameters

Parameters Explained

Segmentation Parameters

Parameter	Default	Range	Description
Number_of_segments	12	2-100	How many times material repeats

Duration Spiral Parameters

Parameter	Default	Range	Description
Duration_multiplier	1.15	0.5-3.0	Factor applied exponentially across segments
Spiral_direction	Expanding	Expanding/Contracting	Whether segments get longer or shorter

Pitch Spiral Parameters

Parameter	Default	Range	Description
Pitch_step_Hz	5.0	0.1-100.0	Pitch change per segment (Hz)
Pitch_direction	Rising	Rising/Falling/Alternating	Direction of pitch change

Temporal Jitter Parameters

Parameter	Default	Range	Description
Jitter_amount	0.08	0.0-1.0	Standard deviation of timing variations

Output Parameters

Parameter	Default	Description
Preserve_original	yes	Keep original sound in Objects window
Play_result	yes	Automatically play output
Show_visualization	yes	Display 6-panel visualization

Parameter Interactions

How parameters work together:

Number_of_segments × Duration_multiplier: Determines total output duration
Duration_multiplier ^ Number_of_segments: Ratio of last/first segment durations
Pitch_step_Hz × Number_of_segments: Total pitch change from first to last segment
Jitter_amount × Duration_multiplier: Combined effect on timing irregularity
Spiral_direction + Pitch_direction: Creates coherent or contradictory motion

Effect of Parameter Values

Duration_multiplier effects:

1.0: No duration change (segments equal length)
1.05-1.15: Gentle expansion/contraction
1.2-1.4: Strong expansion/contraction
1.5+: Extreme expansion/contraction
0.5-0.9: Opposite direction (contraction/expansion)

Pitch_step_Hz effects:

1-3 Hz: Subtle, barely perceptible changes
5-10 Hz: Clear but moderate changes
15-30 Hz: Strong, obvious pitch spiral
50+ Hz: Extreme, possibly unnatural changes

Jitter_amount effects:

0.0: Precise, mechanical timing
0.05-0.1: Subtle humanization
0.15-0.25: Noticeable rhythmic variation
0.3+: Highly irregular, unpredictable

Visualization

Six-Panel Display

📊 Understanding the Visualization

Panel	Content	Purpose
Title	Script name, input file, preset	Context and identification
Original Waveform	Input sound with segment boundaries (red dotted lines)	Show segmentation of original material
Result Waveform	Output spiral-transformed sound	Show effect of spiral transformation
Duration Factor Plot	Bars showing duration factor for each segment	Visualize duration spiral (blue bars = planned, black line = jittered)
Pitch Shift Plot	Line graph of pitch shift per segment	Visualize pitch spiral (red line with markers)
Spiral Diagram	Parametric spiral with numbered segment markers	Conceptual representation of spiral trajectory
Parameters & Results	Text display of settings and outcomes	Reference information
Time Axis	Timeline showing original and output durations	Compare time scales

Interpreting the Spiral Diagram

🌀 Reading the Conceptual Diagram

Spiral equation: r = a + b×θ (Archimedean spiral)

Radius (r): Represents cumulative duration factor
Angle (θ): Represents segment number/position
Marker position: Shows segment's place in spiral
Marker size: Proportional to segment duration factor
Marker number: Segment index (1, 2, 3...)

Interpretation: Movement outward = expansion; movement around = progression through segments

Duration Factor Plot Details

⏱️ Understanding Duration Changes

Blue bars: Planned duration factor (multiplier^n)

Black horizontal lines: Actual jittered duration factor

Dotted line at 1.0: Reference (no change)

Pattern: Shows exponential growth/decay across segments

Jitter effect: Black lines deviate from blue bars

Pitch Shift Plot Details

🎵 Understanding Pitch Changes

Red line: Pitch shift trajectory across segments

Square markers: Pitch shift for each segment

Dotted line at 0 Hz: Reference (no change)

Pattern: Shows linear/alternating pitch changes

Direction: Upward slope = rising, downward = falling, oscillation = alternating

Practical Examples of Visualization

What to look for with different presets:

Gentle Expansion: Slightly upward blue bars, gradual red line rise
Accelerating Collapse: Steeply downward blue bars, falling red line
Drunken Spiral: Black lines far from blue bars (high jitter), oscillating red line
Tight Coil: Many small blue bars, gradual red line
Wide Orbit: Few large blue bars, steep red line
Reverse Time Feel: Downward blue bars (contracting) with upward red line (rising pitch)

Advanced Applications

Compositional Techniques

Layering spirals: Apply different spirals to same material, mix results

Spiral chains: Use spiral output as input for another spiral transformation

Multi-voice spirals: Apply same spiral to different sounds, create spiral counterpoint

Sound Design Applications

Evolving textures: Create slowly evolving pads from short samples

Riser/downer effects: Use pitch ascent/descent with time expansion/contraction

Glitch generation: High segment count + high jitter = glitch textures

Analytical Applications

Material study: Hear material transformed systematically, reveal hidden characteristics

Formal analysis: Test different segmentations, hear formal implications

Perceptual experiments: Study perception of time-pitch relationships

Performance Applications

Live processing: Apply spiral transformations in real-time (with adaptation)

Interactive composition: Let parameters be controlled by performers/sensors

Algorithmic improvisation: Use spiral as generative structure

Troubleshooting

Problem: Artifacts/distortion in output
Causes: Extreme duration/pitch modifications, unvoiced input, PSOLA limitations
Solutions: Use more moderate settings, ensure input has clear pitch, try different source material

Problem: No pitch change detected (pitch tier empty)
Causes: Unvoiced/noisy input, Praat pitch detection failure
Solutions: Script adds reference points, but results may be artificial; use voiced input

Problem: Output much longer/shorter than expected
Causes: Extreme duration_multiplier, many segments, jitter accumulation
Solutions: Check formula: total_duration = segment_duration × Σ(multiplier^i × (1+jitter[i]))

Problem: Visualization missing/corrupted
Causes: Many segments (>30), complex plot, Praat drawing limits
Solutions: Reduce number_of_segments, disable visualization, use simpler preset

Mathematical Formulas Reference

SEGMENT BOUNDARIES: segStart[i] = (i - 1) × totalDuration / N segEnd[i] = i × totalDuration / N DURATION FACTORS (expanding): factor[i] = multiplier^(i - 1) factorJittered[i] = factor[i] × (1 + randomGauss(0, jitter_amount)) DURATION FACTORS (contracting): factor[i] = multiplier^(N - i) factorJittered[i] = factor[i] × (1 + randomGauss(0, jitter_amount)) PITCH SHIFTS (rising): shift[i] = stepHz × (i - 1) PITCH SHIFTS (falling): shift[i] = -stepHz × (i - 1) PITCH SHIFTS (alternating): shift[i] = stepHz × floor((i - 1) / 2) × (-1)^(i - 1) TOTAL OUTPUT DURATION: totalOut = Σ(segmentDuration × factorJittered[i]) for i=1 to N

Creative Combinations

Experiment with these combinations:

Contradictory spirals: Expanding time + falling pitch, or contracting time + rising pitch
Micro-spirals: Many segments (30+) with tiny increments
Macro-spirals: Few segments (3-6) with huge increments
Jitter experiments: Same spiral with different jitter amounts
Alternating extremes: Extreme expansion then extreme contraction
Nested spirals: Apply spiral to already-spiraled material