| 0 | Stochastic | 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. |
| 1 | Polyrhythm | Superimposes two periodic cycles at ratio A:B, producing composite rhythms from their intersections. Multiple sub-modes (Sum, Difference, Fractioned, Superimpose, Paired) plus optional phasing and synchrony detection. 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. Steve Reich phasing (Piano Phase, 1967) when phasing is enabled. |
| 2 | 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 and grouping mode (by product, by generator). | Messiaen, added values and non-retrogradable rhythms. The Technique of My Musical Language (1944). Schillinger Ch 3, grouping by ratio. |
| 3 | 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. |
| 4 | 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. |
| 5 | 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. |
| 6 | Multigenerator | Three or more concurrent periodic generators (3-Generator, Fibonacci, Series II, Series III) whose combined attacks form composite rhythms more intricate than any two-generator polyrhythm. | Schillinger Ch 6, multi-generator resultants. Extension of two-voice interference into higher-dimensional periodic structure. |
| 7 | Attack Groups | Time-rhythm × instrumental-rhythm product: a base meter is partitioned into attack/rest “places” producing dance-form templates (Polka, Fox-trot, Waltz, Rhumba) and free custom configurations. | Schillinger Ch 7, instrumental rhythm. The product of a time rhythm and an instrumental rhythm — choreographic time articulated through orchestral attack distributions. |
| 8 | Lattice | Distributes duration groups across attack groups via PL (place-length) coordination. Three procedures: PL Distribution, Attack Sync, Full Coordination. Produces interlocking grids of pulse and rest. | Schillinger Ch 8, coordination of time structures. Two-dimensional rhythmic grid where time and attack generators index into each other. |
| 9 | Permutation | Cycles a small alphabet of durations, rests, or accents through every ordering (circular, retrograde, higher-order permutations). Produces predictable variation that exhausts a finite combinatorial space. | Schillinger Ch 9–10, permutation of durations and rests. Combinatorial enumeration as compositional engine — Boulez’s serial extension of the same idea. |
| 10 | Continuity | Subdivides a source rhythm by divisor, by bar, or by attack, producing homogeneous continuity from a sparse seed. The deeper the split, the more uniform the resulting flow. | Schillinger Ch 11, homogeneous rhythmic continuity. Subdivision as a way of converting articulated material into continuous textural flow. |
| 11 | Power Series | Group sizes follow mathematical progressions — squares (1,4,9,16), powers (1,2,4,8,16), triangular numbers (1,3,6,10), or binomial/trinomial squares. Creates accelerating or decelerating rhythmic arcs. | Schillinger Ch 12, distributive powers. Mathematical series as compositional determinant of grouping size. |
| 12 | Growth Series | Each duration is the sum of the two previous, following a Fibonacci-like growth pattern with selectable seed pair (Fibonacci, Series II, Series III, Interference Groups, Swing Hybrid). | Schillinger Ch 13, rhythm families. Fibonacci sequence, Bartók’s proportional structures, Lendvai’s analysis of golden section in musical form. |
| 13 | Acceleration | Inter-onset intervals change continuously over a cycle using one of seven curves: Harmonic (1, 1/2, 1/3…), Arithmetic, Geometric, Power, Summation, Primes, Rubato. Configurable accelerate/decelerate/bounce direction. | Schillinger Ch 14, variable velocities. Continuous transformation of pulse rate as compositional gesture. |
| 14 | 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. |
| 15 | 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. |
| 16 | NOMN Drum Computer | A 4-axis pad (Swing / Kick Push / Snare / Hi-hat) navigates a stylist-space learned from an open source corpus of drum patterns. The pad position blends the top-3 nearest cluster centroids via inverse-distance weighting; per-instrument probability matrices then sample the active 16-step grid each bar. Five voicing sliders (Hi-hat Boost, Cymbal Wash, Dynamics, Backbeat Accent, Wander) shape the output after blending. | Genre-seeded probabilistic groove generation. The pad selects a momentary groove signature in latent style space; the engine emits the corresponding pattern across the active layers. |
| 17 | Subdivision Grid | Strictly metronomic emitter for arp-style workflows. Two parameters: Subdivision (1/4 down to 1/128, → 1..32 attacks per beat) and Tuplet (Straight, 3:2, 5:4, 7:4, 9:8, 11:8) multiplier. The grid itself contains no holes — perforation patterns it. | Classical step-sequencer / arpeggiator architecture exposed as a first-class rhythm engine for use under the Monophonic layer mode or as a base for perforation-driven texture. |
