Spectral Smearing Reverb — v0.2 User Guide

Frequency‑dependent delays simulating acoustic dispersion. Lower frequencies get longer delays (bass “hangs”), higher frequencies shorter. Uses an inverse‑square‑root dispersion model with a Lorentzian frequency response (peak around 600 Hz) and cosine modulation for textural richness.

Author: Shai Cohen Affiliation: Department of Music, Bar‑Ilan University, Israel Version: 0.2 (2025) – Stereo, wet/dry, visualisation License: MIT License Repo: GitHub

Contents:

What it does Quick start Presets (4 archetypes) The physics model Parameters Visualization FAQ / troubleshooting

What this does

Spectral Smearing Reverb creates a reverb where the delay time depends on frequency. Low frequencies are delayed more, high frequencies less – mimicking the dispersive behaviour of acoustic materials (e.g., sound travelling through a plate or a room with frequency‑dependent propagation speed). The effect is built from a bank of frequency bands (default 20), each with its own delay, amplitude (shaped by a Lorentzian curve peaking around 600 Hz), and a slow cosine modulation for evolving texture.

Key features v0.2:

Inverse‑sqrt dispersion: delay(f) ∝ 1/√f (bass hangs longer).
Lorentzian frequency response: gain peaks at a user‑controlled centre frequency (default 600 Hz).
Per‑band cosine modulation (0.3 + 0.7·cos(2π·f_mod·t)) for evolving, non‑static texture.
Stereo decorrelation: right channel uses slightly different parameters (base frequency, stretch, peak).
Wet/dry mix control and visualisation of dispersion curve and Lorentzian response.

Quick start

In Praat, select exactly one Sound object (mono or stereo).
Run script… → Spectral_Smearing_Reverb.praat.
Choose a Preset:
- Subtle Smear, Medium Smear, Heavy Smear, Extreme Smear
For custom mode (preset = Custom), adjust parameters as desired.
Set Wet_dry_percent (0 = dry only, 100 = wet only).
Click OK. The script adds a silent tail, processes each frequency band with its own delay and modulation, applies wet/dry mix and fadeout, and imports the result as originalname_smear_preset.

Tip: Start with Medium Smear (20 bands, stretch 0.6) to hear the characteristic frequency‑dependent smear. For a more pronounced effect, try Heavy or Extreme. The visualisation shows both the dispersion curve and the Lorentzian gain shape.

Important: This reverb is implemented entirely in Praat – no Python required. It uses the Formula command to add delayed, modulated copies of the signal. For many bands (e.g., 45) on long files, processing can be slow; the script scales the signal every 10 bands to prevent overload.

The 4 presets (+ Custom)

Preset	Bands	Stretch	Base amp	Peak freq	Description
Subtle Smear	12	0.4	0.20	600 Hz	Light, gentle smearing.
Medium Smear	20	0.6	0.35	600 Hz	Balanced, clear smearing.
Heavy Smear	30	0.85	0.50	600 Hz	Dense, prominent smear.
Extreme Smear	45	1.2	0.65	600 Hz	Extreme, cavernous smear.

Each preset also sets response_width_Hz = 800 and fadeout_duration_s appropriately.

The physics model

📐 Dispersion (delay vs. frequency)

delay(f) = time_stretch × 1 / √(f / f_base)

where f_base = 80 Hz (the lowest band).

Lower frequencies → longer delay (bass “hangs”).
Higher frequencies → shorter delay.
This approximates the dispersive behaviour of plates and certain acoustic materials.

📐 Lorentzian frequency response (gain)

gain(f) = 1 / [1 + ((f – f_peak) / width)²]

This bell‑shaped curve peaks at f_peak (default 600 Hz) and rolls off symmetrically. The gain determines how much each band contributes to the overall smear.

📐 Cosine modulation (time‑varying texture)

mod(t) = 0.3 + 0.7·cos(2π·f_mod·t)

where f_mod = centre_freq / 15. This creates a slow, evolving amplitude ripple that prevents the reverb from sounding static.

The right channel uses slightly different parameters:

Base frequency ≈ 85 Hz (instead of 80 Hz)
Stretch scaled by 0.92
Peak frequency shifted by +50 Hz
Width reduced by 50 Hz
Modulation frequency centre_freq / 18

This decorrelates the left and right signals, creating a wide, immersive stereo image.

Parameters & defaults

Smearing parameters

Parameter	Range	Default	Description
Tail_duration_s	any positive	1.5 s	Length of silent tail added after the original sound (allows smears to ring out).
Frequency_bands	integer ≥1	20	Number of discrete frequency bands (each gets its own delay and modulation).
Time_stretch	any positive	0.6	Multiplier for the dispersion delay. Higher = longer delays.
Base_amplitude	0–1	0.35	Base amplitude for the bands (further shaped by Lorentzian response).

Frequency response

Parameter	Range	Default	Description
Peak_frequency_Hz	any positive	600 Hz	Centre frequency of the Lorentzian peak (where the smear is strongest).
Response_width_Hz	any positive	800 Hz	Width of the Lorentzian curve (larger = broader peak).

Mix & output

Parameter	Range	Default	Description
Wet_dry_percent	0–100	60	0 = dry only, 100 = wet only.
Fadeout_duration_s	any positive	1.2 s	Cosine fade‑out applied at the end of the tail to avoid clicks.
Draw_visualization	yes/no	yes	Show waveforms, dispersion curve, Lorentzian response, and summary.
Play_result	yes/no	yes	Auto‑play after processing.

Visualization (Praat picture)

When Draw_visualization = 1, the script draws:

Original waveform (grey).
Result waveform (purple) with wet/dry percentage.
Dispersion curve (left panel) – delay (ms) vs. frequency (kHz). The blue line shows the theoretical 1/√f law, with dots marking the actual frequency bands.
Lorentzian frequency response (right panel) – gain vs. frequency. The pink line shows the Lorentzian curve, with a vertical dashed line at the peak frequency. Dots mark the actual band gains.
Parameter summary – band count, frequency range, stretch, peak frequency.

Tip: The two plots give a complete picture of the smearing engine. The dispersion curve shows how delays increase as frequency decreases. The Lorentzian response shows which frequencies are emphasised (near 600 Hz). Together, they explain the character of the reverb.

FAQ / troubleshooting

Output is silent / no smear heard

Check that Wet_dry_percent is not 0. Also verify that Frequency_bands is ≥5 and Base_amplitude is not too low. The script prints the first few band frequencies and delays in the Info window – if they seem reasonable, the effect should be audible.

Processing is slow

Each band adds a Formula pass. For 45 bands on a long file, this can be slow. Reduce Frequency_bands for faster preview. The script scales the signal every 10 bands to prevent overload, but this doesn't speed it up.

Modulation sounds too obvious / “wobbly”

The cosine modulation is applied per band with a frequency proportional to the band’s centre frequency. If it sounds too pronounced, reduce the modulation depth by editing the script: change 0.3 + 0.7*cos(...) to 0.5 + 0.5*cos(...) or even 0.8 + 0.2*cos(...).

Understanding the dispersion formula

The inverse‑sqrt law delay ∝ 1/√f is chosen because it produces a strong bass‑hang effect without being extreme. At 80 Hz, delay = time_stretch × 1.0; at 640 Hz, delay = time_stretch × 0.35; at 2560 Hz, delay = time_stretch × 0.18. This means bass frequencies decay much more slowly than highs, creating a warm, evolving tail.

Stereo decorrelation

The right channel uses slightly different base frequencies and stretch factors to ensure the left and right smears are not identical. This creates a wider, more immersive image. If you need a narrower image, you can reduce the differences in the script.