Harmonic Resonance Processor — User Guide

Exponential harmonic processing: applies iterative bidirectional time-shifts with exponentially increasing offsets, weighted amplitude decay, creating metallic resonances and harmonic reverb textures.

Author: Shai Cohen Affiliation: Department of Music, Bar-Ilan University, Israel

What this does

This script creates harmonic resonance effects through iterative bidirectional time-shift processing with exponential scaling. Each iteration applies formula mixing forward and backward delays at harmonically-related intervals (base^iteration), with amplitude decay proportional to iteration depth. Result: metallic, resonant textures with harmonic overtone structure and reverberant tail.

Quick start

Select one Sound object in Praat.
Run script… → Load this harmonic processing script.
Choose Preset: Subtle/Medium/Heavy/Extreme or Custom.
If Custom: Set num_iterations (4-15), harmonic_base (1.5-6.0), decay_factor (0.4-0.85).
Adjust Tail_duration (reverb length) and Fadeout_duration.
Click OK — processing completes instantly, auto-plays result.

Quick tip: Start with Medium Harmonics preset — balanced resonance without overwhelming source. Subtle for gentle shimmer, Heavy/Extreme for radical metallic transformation.

How It Works

Exponential Harmonic Scaling

For each iteration k (1 to num_iterations): 1. Calculate shift factor: shiftFactor = harmonicBase ^ k Example: base=2.5, k=3 shiftFactor = 2.5³ = 15.625 2. Calculate delay offset: b = total_samples / shiftFactor Example: 44100 samples, factor=15.625 b = 44100 / 15.625 = 2822 samples (~64ms) 3. Apply bidirectional formula: output = (forward_delay - backward_delay) × (1/k) forward_delay = self[position + b] backward_delay = self[position - b/2] Weighting: 1/k (iteration 1 = 100%, iteration 7 = 14%) 4. Apply amplitude decay: output = output × (1 - k/iterations × decay_factor) Result: Exponentially increasing delays create harmonic series

Key Characteristics

Exponential scaling: Delays grow exponentially (base^k), creating harmonic relationships
Bidirectional processing: Forward + backward delays create complex interference
Iteration weighting: Earlier iterations stronger (1/k decay)
Amplitude decay: Progressive reduction prevents explosion

Presets

Preset	Iterations	Base Range	Decay	Character
Subtle Harmonics	4	1.3-2.2	0.4	Gentle shimmer, transparent
Medium Harmonics	7	1.5-4.0	0.6	Balanced resonance (recommended)
Heavy Harmonics	10	2.0-4.8	0.75	Dense metallic texture
Extreme Harmonics	15	2.5-6.0	0.85	Radical transformation, cascading

🎵 Medium Harmonics (Default)

Settings: 7 iterations, base 1.5-4.0, decay 0.6, tail 2s

Effect: Clear harmonic resonance, noticeable but musical

Best for: General use, adding harmonic richness without overwhelming

Parameters

Parameter	Type	Default	Description
Preset	choice	Custom	Preset configuration or manual
Tail_duration	positive	2.0s	Silent tail for reverb decay
num_iterations	natural	7	Number of harmonic layers (4-15)
harmonic_base_min/max	positive	1.5 / 4.0	Random base range (exponential factor)
use_fixed_base	boolean	no	Use fixed base instead of random
fixed_harmonic_base	positive	2.5	Fixed exponential base value
decay_factor	positive	0.6	Amplitude decay rate (0.4-0.85)
scale_peak	positive	0.95	Final peak normalization
Fadeout_duration	positive	1.0s	Cosine fade at end
play_after_processing	boolean	yes	Auto-play result

Parameter Tuning

Harmonic Base (1.5-6.0):

Low (1.5-2.5): Tight harmonic spacing, dense texture
Medium (2.5-4.0): Balanced, musical intervals
High (4.0-6.0): Wide spacing, sparse harmonics, extreme effect

Iterations (4-15):

Few (4-6): Simple resonance, clear
Medium (7-10): Rich harmonic structure
Many (11-15): Complex, dense, potentially chaotic

Decay Factor (0.4-0.85):

Low (0.4-0.5): Gentle decay, maintains energy
Medium (0.6-0.7): Balanced reduction
High (0.75-0.85): Aggressive decay, cleaner but less dense

Applications

Sound design:

Metallic resonances and shimmers
Harmonic reverb tails
Sci-fi/experimental textures

Music production:

Add harmonic richness to sounds
Create resonant pads from short samples
Experimental processing for creative effects

Best source material: Percussive sounds (bells, metallic hits), sustained tones with clear pitch, short impulsive sounds. Less effective: noise, very complex material.

Output

New Sound object: "originalname_harmonics"

Duration: Original + tail_duration
Processing: Harmonic resonance applied
Fadeout: Smooth cosine fade at end
Normalized: Scaled to scale_peak value

Processing: Instant execution regardless of duration. Stereo sounds processed preserving channels. Original file preserved.