Additive Particle Field — User Guide

Analysis-driven additive particle synthesis: the selected Sound supplies pitch and intensity contours, while a new stereo field is synthesized from short harmonic, inharmonic, or noise particles.

Author: Shai Cohen Affiliation: Department of Music, Bar-Ilan University, Israel Version: 0.5.1 (2026) License: MIT License Repo: GitHub

Contents:

What this does What is a particle? Quick start Presets Particle spectrum Pitch & intensity control Time, pan & LFO Parameters Visualization Output & limits

What this does

Additive Particle Field does not cut the source into audio grains and rearrange them. Instead, it analyzes the selected Sound for pitch and intensity, then uses those contours as controllers for a newly synthesized stereo particle field.

At each particle time, a voiced analysis frame produces a short additive micro-spectrum anchored to the detected pitch. An unvoiced frame produces a short broadband noise particle instead of inventing a fallback pitch. Particle amplitude follows the source intensity contour, while panning, time distribution, spectral shape, grain envelope, and optional LFO determine the resulting texture.

Source vs. output: the source provides control information; its waveform is not copied into the particles. The output is synthesized from sinusoidal partials and noise, then mixed to stereo and peak-normalized.

What is a particle?

In this script, a particle is one short synthesized sound event with its own start time, pitch anchor, amplitude, spectrum, envelope, and stereo position.

Voiced particle

A set of sinusoidal partials built above the detected pitch. The partials can follow an integer harmonic series or a stretched, bell-like inharmonic series. Each partial receives a random starting phase.

Unvoiced particle

A windowed broadband noise burst. Its level still follows the source intensity contour, but it has no oscillator pitch. The pitch value shown for it in the visualization is only a display/panning anchor.

Quick start

Select exactly one Sound object in Praat.
Run Additive_Particle_Field.praat.
Choose one of the five presets, or keep Custom.
For Custom, set the particle count and grain duration, then choose the number of partials, spectral brightness, spectrum type, envelope, panning, LFO, and time distribution.
Click OK. The result is created as <source>_particles_<preset>.

Starting point: Custom defaults to 100 particles, 50 ms grains, 10 harmonic partials, spectral brightness 0.78, Hann envelopes, pitch-derived panning, no LFO, and linear timing.

Presets

A named preset replaces the relevant synthesis settings with the values below.

Preset	Particles	Grain	Partials	Spectrum	Brightness	Noise mix	Envelope	Pan	Timing / LFO
Dense Cloud	300	30 ms	9	Harmonic	0.82	0.40	Gaussian	Random	Random / Off
Sparse Field	30	150 ms	10	Harmonic	0.68	0.30	Hann	Pitch-derived	Linear / Off
Rhythmic Pulse	80	40 ms	8	Harmonic	0.90	0.45	Rectangular	Fixed center	Linear / 4 Hz
Shimmer	150	60 ms	18	Bell-inharmonic, B=0.018	0.96	0.25	Gaussian	Random	Exponential / 0.25 Hz
Long Resonance	15	800 ms	14	Bell-inharmonic, B=0.030	0.80	0.18	Hann	Pitch-derived	Exponential / 0.15 Hz

Particle spectrum

Harmonic spectrum

partial ratio h = 1, 2, 3, ... frequency_h = detectedPitch × h

Bell-inharmonic spectrum

ratio_h = h × [1 + Inharmonicity × (h - 1)] frequency_h = detectedPitch × ratio_h

The inharmonic formula progressively stretches upper partials away from the integer harmonic series. Inharmonicity is limited to 0–0.10.

Spectral brightness

Spectral_brightness does not apply a filter. It changes the power-law roll-off of the additive partial amplitudes:

partialDecay = 2.6 - 2.0 × Spectral_brightness weight_h = 1 / h^partialDecay

Brightness 0 gives a steep 1/h^2.6 roll-off; brightness 1 gives a much shallower 1/h^0.6 roll-off. The weights of the partials actually used are summed and the carrier is divided by that sum, so increasing the partial count primarily changes timbre rather than causing uncontrolled level growth.

Nyquist protection and phase

Partials at or above 47.5% of the sample rate — 95% of Nyquist — are omitted. Each retained partial receives an independent random starting phase, reducing phase-locked buildup when many particles overlap.

Unvoiced/noise particles

When the Pitch object is undefined at a particle time, the carrier becomes bounded white noise:

carrier = Unvoiced_noise_mix × randomUniform(-1, 1)

The noise is still multiplied by the particle amplitude and the selected grain envelope. Unvoiced_noise_mix therefore controls the carrier level of unvoiced particles relative to voiced additive particles.

Pitch & intensity control

Pitch

The script creates a Praat Pitch object over a fixed analysis range of 75–600 Hz. At each particle time it queries the Pitch object with linear interpolation. Defined values are clamped to this range; undefined values are classified as unvoiced and rendered as noise.

Intensity

Praat Intensity values are in dB SPL, not dBFS. The script measures the maximum of the Intensity contour and converts each particle's level relative to that maximum into a linear amplitude ratio:

relative_dB = min(0, I(t) - Imax) intensityAmp = 10^(relative_dB / 20) grainAmp = 0.2 × intensityAmp

This means the loudest analyzed region receives a base particle amplitude of 0.2 before LFO and panning. Particle amplitude is not derived from an instantaneous source waveform sample.

Time, panning & LFO

Time distributions

Particle times are scheduled over the range in which a full grain can fit. If the requested grain duration is longer than the source, the effective grain duration is clamped to the source duration.

Mode	Behavior
Linear	Evenly spaced starts from the first valid position to the last. With one particle, it is placed halfway through the valid start range.
Exponential	Uses `(1-exp(-3t))/(1-exp(-3))`. Spacing becomes progressively tighter, so particle density increases toward the end.
Random	Each start is drawn uniformly from the valid start range.

The same scheduled time is used to query the source Pitch and Intensity contours. For Sounds whose time domain does not start at zero, the script adds the source start time for analysis while keeping synthesis and visualization zero-based.

Panning

Mode	Pan rule
Pitch-derived	75 Hz maps to full left, 600 Hz to full right, with a monotonic linear mapping between them. Unvoiced particles use a random display/pan anchor in the same range.
Random	Uniform random pan from 0 to 1 for every particle.
Fixed	All particles use Fixed_pan from 0 (left) to 1 (right).

Stereo gains use constant-power panning: L = sqrt(1-pan), R = sqrt(pan).

LFO

When enabled, the LFO modulates the particle amplitude according to zero-based output time:

lfo(t) = 0.5 × [1 + sin(2π × LFO_frequency × t)] grainAmp = grainAmp × lfo(t)

This is an amplitude controller sampled once per particle; it is not a continuous tremolo applied sample-by-sample to each particle.

Parameters

Parameter	Default	Valid behavior
Preset	Custom	Custom plus five named presets.
Number_of_particles	100	1–10,000.
Grain_duration_s	0.050	Must be positive and at least two samples at the source sampling rate. If longer than the source, it is clamped to the source duration.
Number_of_partials	10	1–32. Combined complexity `particles × partials` must not exceed 50,000.
Spectral_brightness	0.78	0–1; maps to partial roll-off exponent 2.6–0.6.
Spectrum_type	Harmonic	Harmonic or Bell-inharmonic.
Inharmonicity	0.020	0–0.10. Used by Bell-inharmonic spectra.
Unvoiced_noise_mix	0.35	0–1. Scales the carrier of unvoiced/noise particles.
Envelope_shape	Hann	Hann, edge-normalized Gaussian, or Rectangular.
Panning_mode	Pitch-derived	Pitch-derived, Random, or Fixed.
Fixed_pan	0.5	Validated to 0–1 only when Fixed panning is selected.
Apply_LFO	Off	Enables per-particle amplitude modulation.
LFO_frequency	0.5 Hz	Must be greater than zero when LFO is enabled.
Time_distribution	Linear	Linear, Exponential, or Random.
Draw_visualization	On	Draws the process visualization.
Play_result	On	Automatically plays the result.

Visualization

When Draw_visualization is enabled, the Picture window shows:

Source: the input waveform.
Particle field: x = particle time, y = pitch anchor. Voiced particles are colored from blue at the left side of the stereo field toward red at the right; grey markers are unvoiced/noise particles. Marker size follows particle amplitude.
Output: the synthesized stereo result.
Summary: particle count, grain duration, spectrum type, brightness, envelope, voiced/unvoiced counts, time distribution, panning, LFO, and duration.

For unvoiced particles: the plotted y-position is only the random anchor used for display and pitch-derived panning. The actual particle carrier is broadband noise.

Output & limits

The output duration is the same as the source duration.
The output is always stereo, built from separate left and right accumulation buffers.
Overlapping particles are summed directly into those buffers.
The final non-silent result is unconditionally peak-normalized to 0.95.
The result is named <source>_particles_<preset>.
Rectangular particles have abrupt edges and may produce audible clicks; Hann and Gaussian envelopes reach zero at their boundaries.
The fixed pitch-analysis range is 75–600 Hz. Material outside that range may be classified or represented imperfectly.