Random Walk Rhythm — User Guide

Scope

Random Walk Rhythm separates timing from pitch-state evolution:

The rhythm itself is not random. Event onsets occur on a regular metric lattice. The stochastic process controls only which frequency state is assigned to each grid event.

The frequency states are equally spaced in Hz, not in semitones or logarithmic pitch distance.

Quick start

1. Run Random_Walk_Rhythm.praat. No input Sound is required.
2. Choose Custom or one of the eight presets.
3. Set Duration, Tempo, Steps per beat, Base frequency, Frequency step, Probability up/down, and Spatial mode.
4. Enable Edit details to set Sample rate, frequency bounds, Event fill, Decay rate, Rotation speed, Output peak, and Random seed.
5. Run the script. The random-walk state sequence is generated first, then the complete event stream is synthesized and spatialized.

Deterministic timing grid

Tempo and Steps per beat determine the exact grid spacing:

The number of events is:

The final step may therefore begin before the requested end time but have less than one complete grid step remaining. The event itself is clipped to the remaining output duration.

There are no random onset offsets, no swing, and no tempo drift.

Event fill

Each event occupies:

Because Event fill is restricted to 0 < fill ≤ 1, one event never extends past the onset of the following grid event. Thus there is no intentional event overlap within the mono source stream.

Random walk on a linear-Hz lattice

The base state has index 0 and frequency Base frequency. Reachable neighboring states are spaced by the selected Frequency step:

The usable integer-index range is derived from Minimum frequency, Maximum frequency, Base frequency, and Frequency step. The resulting lattice can begin slightly above the requested minimum or end slightly below the requested maximum because only exact integer steps around the base are retained.

Categorical transition rule

At every transition, one random number determines the requested direction:

The two user probabilities must each lie between 0 and 1, and their sum cannot exceed 1.

An up or down request changes the state by exactly one frequency lattice step. There are no multi-step jumps.

Boundary reflection

The walk does not clamp an illegal move to the edge state.

If an up request occurs at the highest lattice index, it is applied as one step downward. If a down request occurs at the lowest lattice index, it is applied as one step upward.

The script counts these events as boundary reflections. This prevents an outward random request from becoming an artificial repeated edge state.

A genuine hold occurs only when the categorical draw selects the hold category.

Percussive event kernel

Each grid event is a sine oscillator with local phase, exponential decay, and a cosine closure:

where D is the realized event duration.

Local phase

The carrier uses τ, so phase restarts at zero for every event. Consecutive events are therefore separate pulses even if the random walk holds the same frequency state.

Envelope

The exponential term creates the percussive decay. The cosine term begins at 1 and reaches zero at the event boundary, ensuring a zero-valued closure at the end of a complete pulse.

The final event is shortened when necessary so the output ends exactly at Duration.

For implementation stability, synthesis is accumulated in chunks of 20 events. Chunking does not alter the timing or random-walk sequence.

Spatial modes

Mono

The synthesized pulse stream remains mono without additional spatial processing.

Stereo Ping-Pong

Complete events alternate between channels:

Because Event fill never exceeds one grid step, this grid-index routing does not split overlapping events.

Rotating Panorama

The same mono pulse stream is distributed with a continuous constant-power pan trajectory.

The rotation rate is:

A value of 0.5 cycles per beat therefore completes one L→R→L excursion every two beats.

Dual-Band AM

This mode starts from the same mono pulse stream, creates two copies, filters them differently, and applies slow independent amplitude modulation:

Controls

Main page

Details page

Presets

Presets override Tempo, Steps per beat, Base frequency, Frequency step, Probability up, and Probability down. Duration, Spatial mode, and Details-page controls remain user-controlled.

Safety and derived limits

Frequency lattice

The base frequency must lie inside the requested min/max bounds. The Frequency step must allow at least two reachable integer lattice states.

The highest reachable lattice frequency must remain below:

The scale is not compressed or rescaled automatically. Unsafe settings stop with an error.

Minimum event resolution

The nominal Event duration must contain at least eight samples at the selected sample rate.

Runtime guard

Version 0.4.1 limits the metric grid to:

If Duration, Tempo, and Steps per beat would create more than 12,000 grid events, the script stops before allocating the event arrays or beginning synthesis.

Randomness and reproducibility

The random walk uses one categorical draw per transition. Timing, event-envelope shape, spatial formulas, and level normalization are deterministic.

Random seed = 0 uses Praat's unpredictable random state. A positive seed makes the requested direction sequence reproducible.

After a fixed-seed walk is complete, the script restores Praat's global RNG to an unpredictable state.

Output and level

Visualization and QC

The visualization explains the generating mechanism first and shows the measured waveform only at the end.

The QC bar reports Tempo, step duration, Event fill, event count, target and realized requested up/down/hold probabilities, reflection count, lattice range, realized frequency range, event duration, Decay rate, local-phase status, spatial mode, and final peak/RMS.