Spectral Echo Cascade — User Guide

Fibonacci-based delay cascade: applies iterative multi-tap delays with Fibonacci-progression timing, exponential decay, and cosine-modulated spectral coloring for organic, mathematical echo patterns.

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

What this does

This script creates cascading echo effects using Fibonacci sequence for delay timing (1, 1, 2, 3, 5, 8, 13...), exponential amplitude decay per level, and cosine-modulated spectral coloring that varies across the sample. Result: organic-sounding delays with mathematical structure and frequency-dependent intensity variations.

Quick start

Select one Sound object in Praat.
Run script… → Load Spectral Echo Cascade script.
Choose Preset: Default/Gentle/Dense/Long Tails or Custom.
If Custom: Set cascade_levels (4-8), decay_rate (0.7-0.9), delay_base (4-9).
Adjust coloring_center (0.5) and coloring_depth (0.5) for spectral modulation.
Click OK — processing instant, auto-plays result.

Quick tip: Start with Default preset (6 levels, 0.75 decay) for balanced cascade. Gentle Echoes for subtle effect, Dense Cluster for complex textures.

How It Works

Fibonacci Delay Progression

Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34...
Each number = sum of previous two

Delay calculation:
delayShift = samples / (delay_base + fibonacci_number)

Example: 44100 samples, delay_base=5
Level 1: 44100 / (5+1) = 7350 samples (~167ms)
Level 2: 44100 / (5+1) = 7350 samples
Level 3: 44100 / (5+2) = 6300 samples (~143ms)
Level 4: 44100 / (5+3) = 5512 samples (~125ms)
Level 5: 44100 / (5+5) = 4410 samples (~100ms)
Level 6: 44100 / (5+8) = 3392 samples (~77ms)

Result: Delays get progressively shorter, creating accelerating echo pattern

Processing Formula

For each cascade level: output = input + delayed_input × decay × spectral_coloring Where: delayed_input = self[position - delayShift] decay = decay_rate ^ level (exponential decay) spectral_coloring = center + depth × cos(level × 2π × position/total) Example: Level 3, decay_rate=0.75 decay = 0.75³ = 0.422 (42% amplitude) Spectral coloring oscillates: Creates frequency-dependent intensity Varies across the sound's timeline Center controls baseline, depth controls variation

Spectral Coloring

Cosine modulation creates frequency-dependent echoes:

coloring_center (0.5): Baseline echo intensity
coloring_depth (0.5): Modulation amount (0 = flat, 1 = full range)
Cosine wave: Varies intensity across sample position
Result: Some frequency regions emphasized, others reduced

Presets

Preset	Levels	Decay	Base	Character
Default (balanced)	6	0.75	5	Balanced cascading echoes
Gentle Echoes	4	0.85	7	Subtle, smooth decay
Dense Cluster	8	0.7	4	Many echoes, tight spacing
Long Tails	7	0.9	9	Extended reverberant decay

🌊 Default (Balanced)

Settings: 6 levels, decay 0.75, base 5, coloring center/depth 0.5

Effect: Natural-sounding cascade with organic decay pattern

Best for: General use, musical applications, adding depth

Parameters

Parameter	Type	Default	Description
Preset	choice	Default	Preset configuration
cascade_levels	natural	6	Number of echo layers (4-8)
decay_rate	positive	0.75	Exponential decay per level (0.7-0.9)
delay_base	positive	5	Base offset for Fibonacci delays (4-9)
coloring_center	positive	0.5	Baseline spectral intensity
coloring_depth	positive	0.5	Spectral modulation amount (0-1)
scale_peak	positive	0.88	Final peak normalization
play_after_processing	boolean	yes	Auto-play result

Parameter Tuning

Cascade levels (4-8):

4-5: Simple, clear echoes
6-7: Rich cascade, balanced complexity
8+: Dense, potentially cluttered

Decay rate (0.7-0.9):

0.7-0.75: Quick decay, distinct echoes
0.75-0.85: Balanced (recommended)
0.85-0.9: Slow decay, long tails, reverberant

Delay base (4-9):

4-5: Short initial delays, fast rhythm
6-7: Medium delays, balanced spacing
8-9: Long delays, spacious echoes

Spectral coloring:

Center 0.5, Depth 0: No spectral variation (flat)
Center 0.5, Depth 0.5: Moderate variation (balanced)
Center 0.3, Depth 0.7: Dramatic frequency sweeps

Applications

Music production:

Natural-sounding delay effects with mathematical structure
Rhythmic echo patterns based on golden ratio proportions
Add depth and space to sounds

Sound design:

Organic cascading effects
Fibonacci-inspired rhythmic textures
Spectral-shifting echoes

Why Fibonacci? Creates naturally pleasing delay patterns. Ratios approximate golden ratio (1.618...) which appears throughout nature. Results in organic-sounding, non-mechanical echo spacing.

Output

Modified Sound object: "soundObj" (overwrites working copy)

Processing: Multi-tap cascade delays applied
Normalized: Scaled to 0.88 peak (prevents clipping)
Original: Preserved (script works on copy)

Processing: Instant execution. Each cascade level adds delays iteratively. Spectral coloring creates frequency-dependent intensity variations throughout the sound.