Wave Terrain Synthesis — User Guide

What this does

The script generates sound from a two-dimensional Matrix terrain z(x,y). Two normalized control signals, x(t) and y(t), define a path across the surface. At every audio sample, the terrain height underneath that path becomes the raw audio value.

No input Sound is required. The final result is mono.

The terrain is a discrete Matrix, but the trajectory is not restricted to Matrix cell centers. Version 0.4 and later use bilinear interpolation so motion across the surface is continuous between neighboring terrain samples.

Quick start

1. Choose Custom or one of the eight named presets.
2. Set the total Duration.
3. In Custom mode, choose Terrain type plus X and Y trajectory waveforms and their base rates.
4. Enable Edit details to change terrain resolution/scale, spans, offsets, phases, phase-modulation rates/index, Sample rate, Output peak, or Random seed.
5. Run the script. A mono Sound named waveTerrain_<terrain name> is created.

Terrain construction

The terrain occupies normalized coordinates x,y ∈ [0,1]. It is first filled according to the selected terrain equation, then globally centered by subtracting the Matrix mean. Finally, the entire terrain is divided by its largest absolute value so that its largest positive or negative height reaches magnitude 1 whenever the terrain is nonzero.

This terrain normalization happens before the trajectory scans the surface. It is separate from the final Sound normalization.

1 — Sine product

2 — Chebyshev product

Coordinates are first centered to approximately −1…1 and stretched by Terrain spatial scale:

3 — Random smoothed

Every Matrix cell starts as an independent Gaussian random value. The script then performs one periodic cross-neighbor smoothing pass:

The smoothing wraps across Matrix boundaries for this terrain-construction step only.

4 — Multi-scale harmonic

This is a deterministic sum of three spatial harmonic layers. It replaces the earlier “Fractal” label.

5 — Spiral

Trajectory controls

X and Y each have an independent base rate, waveform, phase, span, offset, and phase-modulation rate. Both axes share one modulation-index value.

Span means terrain coverage

Version 0.4 redefines span directly as a fraction of the terrain dimension:

With Offset = .5, Span = 1.0 covers the full 0…1 range. Span = .8 covers .1….9.

The script validates span against offset so the trajectory remains inside the terrain instead of relying on clipping.

Trajectory waveforms

These waveforms describe motion through the terrain; they are not directly used as oscillator audio waveforms.

Trajectory phase modulation

The modulation controls perturb trajectory phase, not the coordinate after the offset/span mapping.

For a sine trajectory, for example:

Y uses the same modulation index β but its own modulation rate.

For Triangle, Saw, and Square, the equivalent phase perturbation is applied before the periodic waveform is evaluated.

Bilinear terrain lookup

The normalized X/Y controls are converted to continuous Matrix indices:

The script takes the four neighboring terrain values and blends them according to the fractional X/Y positions:

This interpolated z is the raw audio sample value. Edge lookups are clamped to the last valid Matrix row/column.

Presets

Presets are applied before the Details page opens, so enabling Edit details lets you inspect and modify the preset's actual advanced settings.

Controls

Main page

Details page

Validation and safety

Terrain-size guard

Version 0.4.2 limits Terrain size before Matrix allocation:

The upper bound prevents accidental very large Matrix allocation and the associated nested Praat loops.

Bounded trajectory validation

Span and offset are validated together. For each axis:

This guarantees the generated path stays within normalized terrain coordinates 0…1.

Trajectory-rate / Nyquist guard

The script estimates the largest instantaneous trajectory phase rate as:

The larger of these must remain below 45% of Sample rate.

Random terrain and seed

Random seed affects the Gaussian values used by Random smoothed terrain.

If Random seed is positive, the script calls Praat's predictable seeded RNG before terrain creation, so the same terrain parameters and seed reproduce the same initial random Matrix and therefore the same result.

When Random seed = 0, the script does not replace Praat's current random state with a fixed seed.

Output and level

The earlier Output gain control is no longer present because a single fixed gain applied before unconditional target normalization would not alter the final peak.

Visualization and QC

The visualization is organized as a direct representation of the synthesis process rather than as a decorative terrain display.

A — Terrain surface + actual trajectory excerpt

The normalized terrain Matrix is painted in the same 0…1 coordinates used by synthesis. A white line overlays the actual generated X/Y trajectory for a short excerpt.

The excerpt length is chosen automatically: up to two cycles of the slower base trajectory, bounded to 30–500 ms and never longer than the Sound.

Manual plot queries are clamped to the first and last actual Sound sample-center times. This is the v0.4.1 visualization hotfix that prevents undefined endpoint queries at nominal time 0 or exactly Duration.

B — X/Y trajectory controls

The same excerpt is shown as normalized x(t) and y(t) curves, making span, offset, waveform, rate, phase, and phase modulation directly visible.

Bilinear equation strip

A separate strip states the four-neighbor interpolation law used by the audio engine.

C — Sampled terrain height → conditioned audio

The raw interpolated terrain-height signal is plotted against the final DC-removed and peak-normalized output over the same excerpt.

D — Full measured output

The final mono waveform is drawn over the complete requested Duration.

QC

The bottom grid reports:

• terrain type, N×N size, and bilinear lookup;
• X waveform, base rate, and span;
• Y waveform, base rate, and span;
• shared phase-modulation index and the two modulation rates;
• raw terrain-height RMS and sample rate;
• measured final peak and RMS.