| Random | Exponentially-distributed random inter-onset intervals within the density range. No periodicity, no pattern — pure stochastic time points. | Xenakis, Formalized Music (1963). Poisson processes applied to temporal distribution of sound events. |
| Polyrhythm | Superimposes two periodic cycles at ratio A:B, producing composite rhythms from their intersections. Three sub-modes: Sum (all pulses from both streams), Difference (faster stream only), and Fractioned (subdivides each resultant interval). Uses LCM-based cycling for proper Schillinger resultant patterns. | Schillinger, The Schillinger System of Musical Composition, Book I: Theory of Rhythm. Resultant rhythms from interference of generators. |
| Phasing | Two pulse streams at different rates create gradually shifting phase relationships. Events fire when either stream pulses, producing evolving polyrhythmic patterns that cycle through alignment and divergence. | Steve Reich, phasing technique (Piano Phase, 1967). Messiaen’s rhythmic canons. Mathematical phase interference. |
| Grouping | Notes cluster into groups of varying sizes (e.g., 5-3-2), then disperse. Creates rhythmic cells with internal acceleration and deceleration. Configurable group pattern. | Messiaen, added values and non-retrogradable rhythms. The Technique of My Musical Language (1944). Rhythmic grouping as structural unit. |
| Cloud | Stochastic density field modulated by overlapping sine waves at incommensurate frequencies. Creates regions of rhythmic concentration and rarefaction — dense clusters dissolving into sparse scatter. | Xenakis, stochastic clouds (Pithoprakta, 1956). Golden ratio frequency relationships for maximal non-periodicity. |
| Euclidean | Distributes N pulses as evenly as possible across M steps using the Bjorklund algorithm. Produces maximally-even rhythmic patterns found across world music traditions. | Bjorklund (2003), Toussaint, “The Euclidean Algorithm Generates Traditional Musical Rhythms” (2005). Connects Euclid’s GCD algorithm to West African bell patterns, Afro-Cuban clave, and Balkan aksak meters. |
| Harmonic | Maintains multiple pulse streams at overtone-series ratios (1:2:3:…N). Each harmonic h has period fundamental/h. Events fire when any harmonic pulses, creating rhythms derived from the physics of vibrating bodies. | Hindemith, The Craft of Musical Composition (1937). Harmonic series as rhythmic generator — temporal analogue of spectral structure. |
| Power Seq | Group sizes follow mathematical progressions — squares (1,4,9,16), powers of 2 (1,2,4,8,16), or triangular numbers (1,3,6,10,15). Creates accelerating or decelerating rhythmic arcs. Reversible. | Schillinger’s numerical progressions applied to rhythmic grouping. Mathematical series as compositional determinant. |
| Counterpoint | Two independent pulse generators with synchrony detection. When both streams coincide within a configurable window, a synchrony event is produced — creating rhythmic consonance/dissonance analogous to pitch intervals. | Species counterpoint (Fux, Gradus ad Parnassum, 1725). Two-voice rhythmic independence with controlled convergence points. |
| Additive | Each duration equals the sum of the two previous durations, following a Fibonacci-like growth pattern. Seed pair (a,b) → a, b, a+b, a+2b, 2a+3b… Wraps back to seeds when duration exceeds a threshold. Reversible (longest to shortest). | Fibonacci sequence. Bartók’s proportional structures. Lendvai’s analysis of golden section in musical form. |
| L-System | Lindenmayer system string rewriting generates fractal rhythmic sequences. Axiom ‘A’ with rules A→AB, B→A produces Fibonacci-word rhythms. ‘A’ maps to a long duration, ‘B’ to a short duration (golden ratio by default). | Lindenmayer (1968), biological growth models. Prusinkiewicz, The Algorithmic Beauty of Plants. Self-similar structures applied to musical time. |
| Beat Grid | A 16-step binary seed pattern (drum machine style) is expanded by a first-order Markov chain each bar. Low density stays close to the seed; high density produces wilder variations. Combines grid-based familiarity with stochastic evolution. | Markov chains applied to pattern variation. Step sequencer tradition meets probabilistic generation. |
