Perforation Engine
The Perforation Engine is PERF’s defining feature. After the Rhythm Engine generates a stream of events, the Perforation Engine decides which events are kept and which are removed — creating holes, gaps, and silence within the texture.
This is not random muting. Each perforation method uses a distinct mathematical structure to determine its pattern of presence and absence, producing characteristic textural signatures.
Perforation Methods
| Method | What It Does | Lineage |
|---|
| Euclidean | Distributes gaps as evenly as possible across the event stream using the Bjorklund/Bresenham algorithm. Produces maximally-even perforation patterns — the most uniform distribution of silence achievable for a given density. | Bjorklund (2003). The same algorithm that generates traditional rhythms also generates their inverse — maximally-even rest patterns. |
| Prime Sieve | Removes events at positions divisible by prime numbers, using the Sieve of Eratosthenes. Configurable prime basis (2–13). Creates quasi-periodic patterns with long-range structure determined by prime factorization. | Eratosthenes (3rd century BC). Xenakis, sieves (Nomos Alpha, 1966) — logical operations on periodic sets applied to pitch and time. |
| Fibonacci | Filters events based on their Zeckendorf representation — the unique decomposition of each event’s index into non-consecutive Fibonacci numbers. Events with fewer Fibonacci terms are more protected from removal, creating genuine self-similar filtering at all scales. | Zeckendorf’s theorem (1972). Fibonacci structure applied to musical filtering — events whose positions have “simpler” Fibonacci representations persist longer. |
| Modular | Keeps events whose index satisfies a modular congruence (index mod N = offset). Creates perfectly periodic patterns with configurable modulus and phase offset. | Modular arithmetic, number theory. Regular intervallic sieving — the simplest deterministic perforation pattern. |
| Golden Ratio | Quasiperiodic lattice based on phi (1.618…). Two modes: Phi mode creates beating patterns between irrational and integer ratios; Golden Angle mode uses the golden angle fraction (2−φ ≈ 0.382) for maximally uniform distribution — the same phyllotactic spiral that arranges sunflower seeds. | Golden ratio in nature and architecture. Phyllotaxis — the mathematics of leaf arrangement. Aperiodic tiling (Penrose). |
| Cellular | 1D elementary cellular automaton (Wolfram rules 0–255) generates binary patterns. The automaton state evolves each cycle, producing complex emergent perforation structures from simple local rules. Rule 30 (default) generates chaotic, non-repeating patterns. | Wolfram, A New Kind of Science (2002). Elementary cellular automata as generators of complex behavior from minimal rules. |
| Corpus Density | Rest patterns derived from MusicBERT analysis of 3.44 million MIDI files. Uses phrase-level density curves extracted from the pre-trained model to bias perforation decisions toward musically natural rest placement. Context-aware — considers note length, pitch direction, and repetition. Falls back to Euclidean behavior if no corpus data is loaded. | MusicBERT (Zeng et al., 2021). Statistical learning of rest patterns from large-scale musical corpora. |
Parameters
| Parameter | ID | Range | Default | Description |
|---|
| Perforation | perforation | 0.0–1.0 | 0.3 | Gap density — 0 = no gaps, 1 = maximum removal |
| Perforation Method | perfType | 0–6 | 0 | Algorithm selection |
| Spiral Holes | goldenAngle | On/Off | Off | Golden Ratio mode: Phi vs Golden Angle |
| Corpus Bias | corpusBias | 0.0–1.0 | 0.7 | How strongly corpus data influences decisions (Corpus Density only) |
Layer Interaction Modes
Perforation can operate independently per layer or coordinate across layers:
| Mode | What It Does | Lineage |
|---|
| Independent | Each layer’s perforation pattern is unrelated to other layers. Maximum textural complexity. | Free counterpoint — each voice follows its own logic. |
| Inverse | Layers become more active when other layers are quiet, and quieter when others are busy. Creates natural breathing between voices. | Complementary motion in orchestration. Density compensation. |
| Complementary | Layers actively fill each other’s gaps, producing interlocking patterns where silence in one voice is filled by another. | African hocket technique — melodic lines distributed across multiple performers. Machaut’s isorhythmic motets. |
| Synchronized | Perforation holes appear at similar times across all layers. Creates collective silence — the entire texture breathes together. | Tutti rests in orchestral writing. Collective phrasing. |
coordMode parameter.
The Perforation amount of 0.3 (30%) means roughly 30% of generated events are removed. At 0.0, every event plays; at 1.0, maximum removal is applied (the exact amount depends on the method — some methods are inherently denser than others at the same setting).
