Harmonic Resonance Boost — User Guide

Matrix-based spectral enhancement: selectively boosts harmonic frequencies while attenuating non-harmonic content, with optional stereo widening through asymmetric processing.

Author: Shai Cohen Affiliation: Department of Music, Bar-Ilan University, Israel Version: 0.1 (2025) License: MIT License Repo: https://github.com/ShaiCohen-ops/Praat-plugin_AudioTools

Contents:

What this does Quick start Harmonic Theory Preset Configurations Parameters & Effects Stereo Processing Applications

What this does

This script implements harmonic resonance boosting — a spectral processing technique that enhances harmonic frequencies based on a specified fundamental while attenuating non-harmonic content. Process: (1) Converts audio to frequency domain via FFT, (2) Identifies harmonic frequencies (multiples of fundamental), (3) Applies gain boost to harmonic regions, (4) Attenuates non-harmonic frequencies, (5) Separates treatment for low/mid vs high frequencies, (6) Optionally processes left/right channels with slight frequency variations for stereo width, (7) Reconstructs enhanced audio with emphasized harmonics.

Key Features:

5 Built-in Presets — From subtle to extreme harmonic enhancement
Matrix-Based Processing — Optimized for speed using Praat matrix operations
Harmonic Detection — Identifies frequencies at integer multiples of fundamental
Dual-Band Processing — Separate treatments for low/mid vs high frequencies
Stereo Width Option — Asymmetric L/R processing creates natural stereo image
Customizable Parameters — Full control over harmonic selection and enhancement

What is harmonic resonance enhancement? Natural sounds contain harmonics — integer multiples of a fundamental frequency. This script: (1) Identifies harmonics: Using modulo operation on FFT bin indices relative to fundamental. (2) Enhances harmonics: Applies gain boost to frequency regions around harmonics. (3) Attenuates other content: Reduces non-harmonic frequencies to make harmonics stand out. (4) Creates resonance: The result emphasizes tonal/pitched elements while reducing noise and non-harmonic components. Applications: Vocal enhancement (emphasize formants), musical instrument processing (bring out tone), noise reduction (attenuate non-harmonic noise), creative sound design (artificial resonances), audio restoration (enhance degraded harmonics).

Technical Implementation: (1) Input preparation: Convert to mono if stereo input (for consistent processing). (2) Frequency domain conversion: Convert to Spectrum with windowing ("yes" for FFT). (3) Matrix representation: Convert spectrum to Matrix for fast mathematical operations. (4) Harmonic detection: Use modulo operation: (col mod fundamental_frequency) identifies harmonic bins. (5) Spectral manipulation: Apply different multipliers: harmonic_boost for harmonic regions, low_mid_attenuation for frequencies below cutoff, high_freq_attenuation for frequencies above cutoff. (6) Stereo processing: Process left and right channels separately with slightly different harmonic_bandwidth for stereo width. (7) Reconstruction: Convert modified matrices back to spectra, then to time-domain sounds. (8) Stereo combination: Merge L/R channels if stereo output requested.

Quick start

In Praat, select exactly one Sound object.
Run script… → harmonic_resonance_boost.praat.
Choose preset (Strong Harmonic Boost recommended for first try).
Or select Custom and adjust parameters manually.
Enable create_stereo for stereo output (recommended).
Set scale_peak to prevent clipping (default 0.88).
Click OK — harmonic enhancement applied.
Output named "originalname_HB_presetname_STEREO" appears in Objects window.
Output automatically played if play_after_processing enabled.

Quick tip: Start with Strong Harmonic Boost preset for clear effect. Use fundamental_frequency matching your audio (440Hz for A4, 261.6Hz for C4, etc.). For speech/vocals, try fundamental around 100-200Hz (male) or 200-300Hz (female). harmonic_bandwidth controls how wide the harmonic regions are — wider includes more adjacent frequencies. harmonic_boost > 1.0 enhances harmonics; <1.0 would attenuate them. low_mid_attenuation and high_freq_attenuation < 1.0 reduce non-harmonic content. Enable create_stereo for more natural sound with width. Processing is fast due to matrix optimization.

Important: FUNDAMENTAL MUST MATCH CONTENT — if fundamental doesn't align with audio harmonics, effect will be wrong. EXCESSIVE BOOST can cause distortion and clipping — use scale_peak < 1.0. VERY HIGH ATTENUATION can remove too much audio content. STEREO WIDENING may cause mono compatibility issues. HARMONIC DETECTION uses simple modulo — may misidentify harmonics in complex signals. FFT RESOLUTION affects accuracy — short sounds have poor frequency resolution. CHECK RESULTS on both harmonic and non-harmonic material to understand effect. PRESERVE ORIGINAL — script doesn't modify original sound.

Harmonic Processing Theory

Harmonic Series Fundamentals

What Are Harmonics?

Physical definition:

Harmonic frequencies: integer multiples of a fundamental frequency Fundamental: f₀ (base frequency) Harmonics: f₁ = 2·f₀, f₂ = 3·f₀, f₃ = 4·f₀, ... Example: f₀ = 100Hz Harmonic 1: 100Hz (fundamental) Harmonic 2: 200Hz Harmonic 3: 300Hz Harmonic 4: 400Hz Harmonic 5: 500Hz etc. In music: harmonics create timbre Different instruments have different harmonic strengths Sine wave = only fundamental (no harmonics) Complex tones = fundamental + harmonics

FFT Bin Identification

Detecting harmonics in digital domain:

FFT produces frequency bins: bin k represents frequency f_k = k·Fs/N Where: Fs = sample rate N = FFT size k = 0...(N/2) (DC to Nyquist) Harmonic detection algorithm: For each bin k, compute: k mod f₀ Where mod operation finds remainder after division If (k mod f₀) is small → near harmonic frequency If (k mod f₀) ≈ f₀/2 → between harmonics Script uses: if (col mod fundamental_frequency) < harmonic_bandwidth "col" represents bin index in matrix Checks if bin is within bandwidth of a harmonic

📐 Visualizing Harmonic Detection

Fundamental = 100Hz, Bandwidth = 10Hz:

Boost regions: 90-110Hz, 190-210Hz, 290-310Hz, ...

Attenuate regions: 110-190Hz, 210-290Hz, ...

Result: Comb-filter-like enhancement at harmonic multiples

FFT bin alignment example:

Fs=44100, N=65536 → bin width ≈ 0.673Hz

100Hz corresponds to bin ≈ 148.6

Mod 148.6 operation detects harmonics at bins ≈ 148.6, 297.2, 445.8, ...

Spectral Processing Strategy

Three-Region Processing

Different treatment for different frequency ranges:

REGION 1: Harmonic Regions
Condition: (col mod fundamental_frequency) < harmonic_bandwidth
Treatment: Multiply by harmonic_boost (e.g., 1.5-5.0)
Effect: Enhance harmonic frequencies

REGION 2: Low/Mid Non-Harmonic
Condition: x < mid_freq_cutoff AND not in harmonic region
Treatment: Multiply by low_mid_attenuation (e.g., 0.2-0.75)
Effect: Attenuate non-harmonic content in lower frequencies

REGION 3: High Frequency Non-Harmonic
Condition: x ≥ mid_freq_cutoff AND not in harmonic region
Treatment: Multiply by high_freq_attenuation (e.g., 0.05-0.6)
Effect: Attenuate non-harmonic content in higher frequencies

Rationale: Different frequency ranges need different treatment
Low frequencies: often harmonic fundamentals, gentle attenuation
High frequencies: often noise/hiss, stronger attenuation
Mid frequencies: transition region

Matrix Optimization

Why matrix processing is fast:

Traditional approach: Process each frequency bin individually Slow: millions of operations for typical audio Matrix approach: Apply single formula to entire matrix Fast: Praat optimizes matrix operations Single evaluation handles all bins Matrix structure: 2 rows × n frequency bins Row 1: real components Row 2: imaginary components Formula syntax: "if condition then self * boost else self * attenuation fi" Applied to all matrix cells simultaneously Performance gain: 10-100x faster than loop-based processing Especially noticeable with long audio files

Mathematical Implementation

Complete Processing Formula

Matrix formula breakdown:

Left channel formula: if (col mod fundamental_frequency) < harmonic_bandwidth then self * harmonic_boost else if x < mid_freq_cutoff then self * low_mid_attenuation else self * high_freq_attenuation fi fi Where: col = matrix column index (0-based, relates to frequency bin) x = frequency value in Hz (continuous, not discrete bin) self = original complex spectrum value mod = modulo operation (remainder after division) Interpretation: 1. Check if current bin is near a harmonic 2. If yes: apply harmonic boost multiplier 3. If no: check frequency range 4. Apply appropriate attenuation multiplier

Modulo Operation for Harmonic Detection

How modulo identifies harmonics:

Given: fundamental_frequency = f₀ Bin index: k (0 to N/2) Frequency represented: f = k·Fs/N Ideal harmonic: f = n·f₀ for integer n In practice: f ≈ n·f₀ (due to FFT discretization) Modulo operation: (k mod f₀) Computes remainder when k divided by f₀ For harmonics: remainder should be small For non-harmonics: remainder ≈ f₀/2 Example: f₀ = 100, bin k=150 150 mod 100 = 50 (not harmonic) Example: f₀ = 100, bin k=200 200 mod 100 = 0 (harmonic!) Check: if remainder < harmonic_bandwidth → harmonic region harmonic_bandwidth in bins, not Hz (conversion happens internally)

Frequency Response Profile

Visualizing the processing effect:

Frequency: 0Hz ──────────────────────────────→ Nyquist

Example: f₀=440Hz, bandwidth=50, cutoff=6000Hz

│ ▲ │ ▲ │ ▲ │ ▲ │ ▲ │ ▲ │
│ │ │ │ │ │ │ │ │ │ │ │ │
│ 440 │ 880 │ 1320 │ 1760 │ 2200 │ 2640 │ ...
│boost │boost │boost │boost │boost │boost │
│ ▲ │ ▲ │ ▲ │ ▲ │ ▲ │ ▲ │
│ 1.5x │ 1.5x │ 1.5x │ 1.5x │ 1.5x │ 1.5x │
│───────│───────│───────│───────│───────│───────│
│atten │atten │atten │atten │atten │atten │
│0.6x │0.6x │0.6x │0.6x │0.6x │0.4x │
│<6000Hz│<6000Hz│<6000Hz│<6000Hz│<6000Hz│>6000Hz│

Result: Comb-filter-like response with periodic boosts
Low/mid frequencies: moderate attenuation between harmonics
High frequencies: stronger attenuation between harmonics

Preset Configurations

Preset Overview

Custom

User-defined parameters

Use: Full manual control

Strong Harmonic Boost

Boost: 3.0x

Attenuation: 0.4x / 0.3x

Subtle Harmonic Boost

Boost: 1.2x

Attenuation: 0.75x / 0.6x

Wide Harmonic Bandwidth

Bandwidth: 150 bins

Boost: 2.0x

Deep Attenuation

Attenuation: 0.2x / 0.1x

Boost: 2.5x

Extreme Resonance

Boost: 5.0x

Attenuation: 0.15x / 0.05x

Preset Details

🎵 Strong Harmonic Boost (Preset 2)

Character: Clear harmonic enhancement with moderate attenuation

Parameters:

fundamental_frequency: 440 Hz
harmonic_bandwidth: 50 bins
harmonic_boost: 3.0×
low_mid_attenuation: 0.4×
high_freq_attenuation: 0.3×

Best for: General purpose, music enhancement, vocal clarity

Effect: Harmonics clearly emphasized, background reduced

🎵 Subtle Harmonic Boost (Preset 3)

Character: Gentle enhancement, minimal processing artifacts

Parameters:

fundamental_frequency: 440 Hz
harmonic_bandwidth: 50 bins
harmonic_boost: 1.2×
low_mid_attenuation: 0.75×
high_freq_attenuation: 0.6×

Best for: Subtle enhancement, preserving natural sound

Effect: Slight harmonic emphasis, minimal coloration

🎵 Wide Harmonic Bandwidth (Preset 4)

Character: Broad harmonic regions, less precise but fuller sound

Parameters:

fundamental_frequency: 440 Hz
harmonic_bandwidth: 150 bins (3× default)
harmonic_boost: 2.0×
low_mid_attenuation: 0.5×
high_freq_attenuation: 0.35×

Best for: Complex signals, rich harmonic content

Effect: Wide frequency regions boosted, smoother response

🎵 Deep Attenuation (Preset 5)

Character: Strong suppression of non-harmonic content

Parameters:

fundamental_frequency: 440 Hz
harmonic_bandwidth: 50 bins
harmonic_boost: 2.5×
low_mid_attenuation: 0.2×
high_freq_attenuation: 0.1×

Best for: Noise reduction, isolating pitched elements

Effect: Harmonics stand out clearly from suppressed background

🎵 Extreme Resonance (Preset 6)

Character: Very strong harmonic emphasis, dramatic effect

Parameters:

fundamental_frequency: 440 Hz
harmonic_bandwidth: 30 bins (narrow)
harmonic_boost: 5.0×
low_mid_attenuation: 0.15×
high_freq_attenuation: 0.05×

Best for: Sound design, extreme effects, experimental music

Effect: Very strong harmonic peaks, most other content suppressed

Parameters & Effects

Core Parameters

Parameter	Type	Default	Range	Description
fundamental_frequency	positive	440	20-5000 Hz	Base frequency for harmonic detection
harmonic_bandwidth	positive	50	10-500 bins	Width of harmonic regions in FFT bins
harmonic_boost	positive	1.5	1.0-10.0	Multiplier for harmonic frequencies
mid_freq_cutoff	positive	6000	100-20000 Hz	Transition between low/mid and high freq treatment
low_mid_attenuation	positive	0.6	0.05-1.0	Multiplier for non-harmonic frequencies below cutoff
high_freq_attenuation	positive	0.4	0.05-1.0	Multiplier for non-harmonic frequencies above cutoff

Output Parameters

Parameter	Type	Default	Description
create_stereo	boolean	1 (yes)	Create stereo output with L/R differences
stereo_bandwidth_offset	positive	10	Right channel bandwidth offset for stereo width
scale_peak	positive	0.88	Output normalization level (prevent clipping)
play_after_processing	boolean	1 (yes)	Auto-play result after processing

Parameter Interaction Guide

🔧 fundamental_frequency

Purpose: Sets the base frequency for harmonic detection

Typical values:

Male speech: 85-180 Hz
Female speech: 165-255 Hz
Musical A4: 440 Hz
Bass guitar: 41-196 Hz
Violin: 196-2637 Hz

Tip: Use Praat's pitch analysis to find actual fundamental

🔧 harmonic_bandwidth

Purpose: Controls how wide harmonic regions are

Effects:

Small (10-30): Precise harmonic targeting, comb-filter sound
Medium (30-80): Natural enhancement, includes some adjacent frequencies
Large (80-200): Broad enhancement, smoother sound
Very large (200+): Almost broadband processing

Note: In bins, not Hz — depends on FFT size

🔧 harmonic_boost vs attenuation

Balance is key:

High boost + low attenuation: Overall louder, harmonics emphasized
High boost + high attenuation: Strong contrast, harmonics isolated
Low boost + low attenuation: Subtle effect, slight enhancement
Low boost + high attenuation: Background reduction, harmonics preserved

Rule of thumb: attenuation = 1/boost for balanced processing

Stereo Processing

Stereo Width Technique

🎧 Asymmetric Harmonic Processing

Method: Process left and right channels with slightly different harmonic_bandwidth

Left channel: Uses harmonic_bandwidth

Right channel: Uses harmonic_bandwidth + stereo_bandwidth_offset

Effect: Different harmonic regions emphasized in each ear

Result: Psychoacoustic stereo widening without time delays

Stereo Processing Workflow

STEREO PROCESSING PIPELINE:

1. Mono Input Preparation
Original sound → Convert to mono (if stereo)
Single channel for consistent processing

2. Left Channel Processing
Mono → Spectrum → Matrix
Apply formula with harmonic_bandwidth
Matrix → Spectrum → Sound

3. Right Channel Processing
Mono → Spectrum → Matrix (fresh conversion)
Apply formula with (harmonic_bandwidth + offset)
Matrix → Spectrum → Sound

4. Stereo Combination
Left Sound + Right Sound → Combine to stereo
Rename, normalize, output

Key insight: Same mono source processed twice
Different parameters create stereo differences
No artificial delays or panning

Stereo Width Control

stereo_bandwidth_offset	Stereo Effect	Mono Compatibility	Recommended Use
0	Mono (identical L/R)	Perfect	Mono output needed
5-15	Natural width	Good	General stereo enhancement
15-30	Wide stereo	Moderate	Creative effects, headphones
30-50	Very wide	Poor	Experimental, check mono
50+	Extreme separation	Problematic	Special effects only

Mono Compatibility Considerations

Stereo width vs mono compatibility trade-off:
Issue: When L and R have different frequency responses, summing to mono causes comb filtering
Cause: Different harmonic regions emphasized in each channel
Result in mono: Some frequencies may cancel or be overemphasized
Solution: Use moderate stereo_bandwidth_offset (5-15), check mono sum
Testing: Always verify important material in mono

Applications

Vocal Enhancement

Use case: Bring out vocal clarity, reduce background noise

Technique: Set fundamental to vocal pitch (100-300Hz), use moderate boost

Example: Speech with background noise → harmonics emphasized, noise reduced

Musical Instrument Processing

Use case: Enhance specific instruments in mix

Technique: Match fundamental to instrument pitch

Workflow:

Guitar: 82-988 Hz fundamentals
Piano: 27.5-4186 Hz
Brass: 62-932 Hz
Strings: 196-3136 Hz

Noise Reduction

Use case: Reduce broadband noise while preserving pitched content

Technique: Deep attenuation presets (0.1-0.3×), moderate boost

Application: Historical recordings, field recordings, noisy speech

Sound Design

Use case: Create artificial resonances, metallic sounds

Technique: Extreme settings, experiment with fundamentals

Example: White noise + harmonic boost → tuned noise, metallic textures

Audio Analysis

Use case: Visualize harmonic content

Technique: Process then view spectrum

Application: See which harmonics are present in complex sounds

Practical Workflow Examples

🎤 Vocal Clarity Enhancement

Goal: Make vocals stand out in busy mix

Settings:

Preset: Strong Harmonic Boost
fundamental_frequency: 200 Hz (adjust to vocal pitch)
create_stereo: Yes
stereo_bandwidth_offset: 8

Result: Vocal harmonics enhanced, instruments slightly reduced

Tip: Blend processed with dry signal (50/50 mix)

🎸 Guitar Tone Enhancement

Goal: Add richness to acoustic guitar

Settings:

Preset: Wide Harmonic Bandwidth
fundamental_frequency: 164 Hz (E3) or song key
harmonic_boost: 1.8
low_mid_attenuation: 0.7

Result: Warmer, richer guitar tone with enhanced harmonics

Tip: Process different takes with different fundamentals for layered sound

🔇 Noise Reduction for Speech

Goal: Reduce room noise while preserving speech

Settings:

Preset: Deep Attenuation
fundamental_frequency: 150 Hz (male) or 220 Hz (female)
create_stereo: No (mono for speech)

Result: Cleaner speech with reduced background noise

Tip: Combine with gentle compression after processing

Advanced Techniques

Multi-fundamental processing:

Serial processing: Apply multiple times with different fundamentals
Parallel processing: Process copies with different settings, then mix
Automation: Change fundamental over time to follow melody
Key-based: Set fundamental to song key frequency

Combine techniques for complex harmonic enhancement

Creative sound design:

Non-musical fundamentals: Try 55 Hz (power hum), 1000 Hz (whine)
Extreme settings: Boost 10.0×, attenuate 0.01× for dramatic effects
Inverted processing: Attenuate harmonics, boost non-harmonics
Frequency sweeps: Automate fundamental from 20 to 2000 Hz

Troubleshooting Common Issues

Problem: No audible effect
Cause: fundamental doesn't match audio, boost too low, attenuation too high
Solution: Analyze audio pitch first, use stronger settings

Problem: Distortion/clipping
Cause: harmonic_boost too high, scale_peak too high
Solution: Reduce boost, lower scale_peak to 0.7-0.8

Problem: Metallic/ringing artifacts
Cause: harmonic_bandwidth too narrow, extreme settings
Solution: Increase bandwidth, use more moderate presets

Problem: Phase issues in stereo
Cause: Large stereo_bandwidth_offset, different L/R processing
Solution: Reduce offset, check mono compatibility

Problem: Too much content removed
Cause: attenuation too low (0.1-0.3)
Solution: Increase attenuation values (0.5-0.8)

Technical Notes

FFT Considerations

Frequency Resolution Impact

How FFT size affects harmonic detection:

FFT frequency resolution: Δf = Fs / N Where: Fs = sample rate (typically 44100 Hz) N = FFT size (power of 2, determined by Praat) For N = 65536 (typical): Δf ≈ 0.673 Hz Harmonic detection precision: ± harmonic_bandwidth × Δf Example: harmonic_bandwidth = 50 bins Width in Hz = 50 × 0.673 ≈ 33.65 Hz So harmonic region is ±16.8 Hz around exact harmonic Short audio files → smaller N → poorer resolution N may be as low as 1024 for very short sounds Δf = 44100/1024 ≈ 43 Hz (poor for harmonic work) Implication: Use reasonably long audio for good results At least 1-2 seconds for decent frequency resolution

Windowing Effects

Hann window impact on processing:

To Spectrum: "yes" applies Hann window:
Pros:
- Reduces spectral leakage
- Smoother frequency response
- Better harmonic isolation

Cons:
- Smears transients
- Reduces time resolution
- Affects start/end of signal

For harmonic processing:
Windowing is beneficial
Reduces artifacts from sharp spectral edits
Makes harmonic regions blend better
Recommended: keep "yes" (default)

Performance Optimization

Matrix vs Loop Processing

Speed comparison:

Loop-based approach (slow): for bin from 1 to nBins if is_harmonic(bin) spectrum[bin] *= boost else spectrum[bin] *= attenuation endif endfor Operations: ~nBins × (check + multiply) For 32768 bins: ~65,000 operations Matrix-based approach (fast): Formula: "if condition then self*boost else self*attenuation fi" Operations: Single evaluation optimized by Praat Internal C++ implementation 10-100× faster depending on audio length Memory usage: Matrix holds entire spectrum in memory Efficient for modern computers Allows complex formulas without performance hit

Mathematical Precision

Modulo Operation Details

Implementation in Praat Formula:

Praat's Formula language: "col mod fundamental_frequency" Where: col = column index (0-based in matrix) fundamental_frequency = parameter in Hz But: col represents bin number, not frequency So: col mod f₀ checks bin alignment, not frequency alignment Conversion: bin k represents frequency f = k·Fs/N We want: f mod f₀ (frequency modulo) But using: k mod f₀ (bin modulo) Approximation works because: k = f·N/Fs So k mod f₀ ≈ (f·N/Fs) mod f₀ For constant N/Fs ratio, detects harmonic frequencies Imperfect but practical for audio processing Exactness less important than perceptual effect