Evolving Grain Mass — User Guide

An evolving stochastic granular synthesizer. Grain onsets follow a time-varying Poisson event field; the selected evolution mode then controls whether only density changes, whether the pitch center also sweeps, or whether pitch spread and grain duration morph as well.

Author: Shai Cohen Affiliation: Department of Music, Bar-Ilan University, Israel Version: 0.4 (2026) License: MIT License Repo: Praat AudioTools

Contents:

What this does Event density Evolution modes Presets Grain statistics Spatial modes Rendering & output Visualization Further Reading

What this does

Evolving Grain Mass builds a cloud from many short sine-wave grains. The grains do not sit on a fixed grid: their onset times are stochastic, their frequencies are sampled in log-frequency space, their phases are random, and each grain has a Hann envelope.

Signal process:
time-varying event density → Poisson onset times → evolving pitch statistics → Hann-windowed grains → grain-level spatialization → short edge fade → optional peak normalization

The important distinction is between event density and spectral evolution. Initial Density and Final Density always control how frequently grains are expected to occur. The three Evolution modes then decide what else changes over time.

This is best described as a stochastic granular mass. It is not a breakpoint-based dynamic-stochastic waveform generator: the stochastic process here schedules and parameterizes grains.

Event density: target versus realization

The requested grain rate changes linearly from Initial density to Final density over the duration:

lambda(t) = d0 + (d1 - d0) * t / T

This is the target intensity in grains per second, not a deterministic event count. Onsets are generated as a genuine inhomogeneous Poisson process. The expected total number of grains is:

expected grains = T * (d0 + d1) / 2

The actual number is random and normally differs from that expectation. The visualization therefore shows both the target density line and the realized event density measured in time bins.

Density is not used as a loudness envelope. Per-grain amplitude is reduced according to expected local overlap. Higher density therefore mainly increases occupancy and texture thickness rather than simply making the output louder.

The three evolution modes

Mode	Density	Pitch center	Pitch spread	Grain duration
Density Only	Moves from Initial to Final density	Fixed at Base frequency	Fixed at Initial pitch spread	Uniform random between Min and Max duration
Density + Pitch Sweep	Moves from Initial to Final density	Moves exponentially in octave space	Fixed at Initial pitch spread	Uniform random between Min and Max duration
Density + Distribution Morph	Moves from Initial to Final density	Moves exponentially in octave space	Morphs continuously from Initial to Final spread	Distribution moves continuously from longer toward shorter grains

Pitch-center trajectory

Modes 2 and 3 interpret Pitch evolution directly in octaves:

center(t) = BaseFrequency * 2^(PitchEvolutionOctaves * t / T)

For example, +1 means one octave upward by the end, -1 means one octave downward, and 0 keeps the center frequency stationary.

Distribution Morph

Mode 3 changes more than the center frequency. Its pitch spread moves linearly from the Initial to the Final pitch-spread value. At the same time, the center of the grain-duration distribution moves from the maximum duration toward the minimum duration. Each grain receives additional random duration variation around that moving center, then is clipped to the user-defined Min/Max limits.

In modes 1 and 2, Final pitch spread is not used; the pitch spread remains at Initial pitch spread for the whole sound.

Presets

Each non-Custom preset is a complete configuration: it overrides Duration, densities, Base frequency, Pitch evolution, Evolution mode, grain-duration range, pitch spread, and Spatial mode. Sample rate, random seed, edge fade, normalization, visualization, and playback are not preset-specific.

Preset	Duration	Density	Base / pitch evolution	Mode	Grains	Spread	Spatial
Low Cloud Growth	6 s	10 → 45/s	80 Hz / 0 oct	Density Only	45–120 ms	0.22 oct	Mono
Rising Fine Sweep	6 s	7 → 32/s	140 Hz / +1.1 oct	Pitch Sweep	30–90 ms	0.12 oct	Rotating Cloud
Dense Low Build	8 s	18 → 110/s	95 Hz / 0 oct	Density Only	15–55 ms	0.28 oct	Stereo Evolution
Slow Wide Sweep	10 s	8 → 35/s	60 Hz / +1.7 oct	Pitch Sweep	60–160 ms	0.20 oct	Rotating Cloud
Short-Grain Cascade	5 s	28 → 130/s	170 Hz / +1.2 oct	Pitch Sweep	8–35 ms	0.25 oct	Wide Field
Broadening Bloom	8 s	12 → 55/s	105 Hz / +0.55 oct	Distribution Morph	30–110 ms	0.08 → 0.55 oct	Stereo Evolution
High Digital Morph	5 s	30 → 95/s	200 Hz / +0.8 oct	Distribution Morph	7–32 ms	0.12 → 0.70 oct	Wide Field
Narrow Rising Band	6 s	18 → 55/s	130 Hz / +1.25 oct	Pitch Sweep	25–70 ms	0.08 oct	Mono
Dense Swarm	5 s	55 → 170/s	150 Hz / +0.35 oct	Distribution Morph	5–28 ms	0.30 → 0.65 oct	Rotating Cloud

Because the presets explicitly set Spatial mode, the Spatial-mode choice in the main form is retained only for Custom. The same applies to the main synthesis parameters that a preset overrides.

Grain statistics and randomness

Enable Edit grain statistics to open the second compact page after preset application. It provides:

Control	Baseline	Meaning
Min grain duration	20 ms	Lower duration bound.
Max grain duration	80 ms	Upper duration bound.
Initial pitch spread	0.18 octaves SD	Standard deviation of the log-frequency offset at the beginning.
Final pitch spread	0.45 octaves SD	End spread used only by Distribution Morph.
Random seed	0	0 = unpredictable; positive integer = reproducible realization.
Edge fade	0.02 s	Short global protection fade at the two outer edges.

Frequency draw

Each grain frequency is drawn in octave space, not directly in Hz:

z = clipped Gaussian(0,1), limited to ±2.5
frequency = center * 2^(spreadOctaves * z)

This means the distribution is symmetric around the center in log-frequency space. The script uses a practical upper limit of 0.45 × sample rate and a lower limit of 20 Hz. It also reduces Base frequency in advance when the requested upward trajectory plus maximum spread would otherwise exceed practical sampling headroom.

Grain waveform

Every grain is a sinusoid with a random starting phase and a full Hann envelope:

grain = amplitude
      * sin(2*pi*frequency*age + phase)
      * 0.5*(1 - cos(2*pi*age/duration))

A grain beginning near the end of the requested duration is shortened so that the final Sound keeps the requested overall duration.

Spatial modes

Stereo positioning happens per grain. For stereo modes, a pan value from 0 to 1 is converted to equal-power gains:

left  = cos(pi/2 * pan)
right = sin(pi/2 * pan)

Mode	Pan model
Mono	One-channel output; pan metadata is centered but no stereo rendering occurs.
Stereo Evolution	Global left-to-right trajectory `pan ≈ t/T` plus random ±0.10 deviation, clipped to 0.02–0.98.
Rotating Cloud	Sinusoidal pan trajectory whose rotation rate rises from 0.06 to 0.24 Hz over the sound.
Wide Field	Each grain is placed randomly near one edge: 0.03–0.25 or 0.75–0.97.

There is no post-mix complementary filtering or synthetic stereo widening stage: the stereo image comes directly from grain positions.

Rendering, chunking, and output

The stochastic event list is generated once in chronological order. Rendering then uses local chunks of at most 1 second to keep Praat formulas manageable.

A grain that crosses a chunk boundary is not restarted or truncated at that boundary. The next chunk evaluates the same grain using its original onset-relative age, duration, frequency, phase, and Hann envelope. The chunks are therefore only a rendering strategy, not a change to the musical timeline.

The script does not silently discard grains when a chunk becomes dense. If more than 400 grain terms would be required in one one-second chunk, it stops with an explicit message asking for lower density or shorter grains.

Property	Behavior
Duration	The requested/preset duration.
Sample rate	Direct synthesis at the selected Sample rate, 8–192 kHz.
Channels	Mono for Mono; stereo for the three spatial modes.
Edge fade	Linear fade-in/out, capped at 20% of total duration.
Normalize output	If enabled, every non-zero result receives target peak normalization to 0.90.
Output name	`evolving_grain_mass_<preset>`.

The Info window reports expected versus actual grain count, realized mean density, realized frequency range, mean grain duration, pre/post-normalization levels, maximum terms used by any one-second chunk, and any low/high-frequency corrections.

Visualization and QC

Panel	What it shows
A — Event Density	Linear target intensity against actual binned Poisson density.
B — Actual Grain Field	Rendered grain onset-to-end segments on a log-frequency axis. In stereo modes, colour indicates broad pan region. The target pitch-center trajectory is overlaid.
C — Model → Measurement	Measured spectrogram of a representative final-output channel with sampled actual grain-frequency guides overlaid.
D — Actual Pitch Statistics	Binned geometric mean frequency with ±1 log-standard-deviation bars, compared with the target pitch center.

For stereo output, the representative channel used for the measured spectrogram is whichever channel has the higher whole-file RMS. The QC strip summarizes expected/actual events, seed state, realized frequency and duration statistics, spatial mode, and output levels.