algorithmic pitch sequencers - deterministic processes that unfold rule-based, evolving patterns from compact parameter seeds.
the generative domain lives in the pitch layer, parallel to tonal and atonal.
while those domains expose static pitch sets, generative produces time-extended sequences whose internal logic is encoded entirely in two parameters a, b ∈ [0,1].
all sequences are pre-computed*: once a and b are fixed, the full pitch stream is deterministically known.
four irreducible forms cover the major algorithmic archetypes:
markov_chainbehavior:* generates a first-order markov walk over a pitch class set synthesised from parameters.
parameters*
a → state count* (2 – 12). defines how many pitch classes are in the chain.
b → directional bias* (0 = always downward, 1 = always upward). interpolates the transition matrix between descending and ascending tendencies.
state_machinebehavior:* steps through a finite deterministic state graph whose edges add fixed pitch intervals.
parameters*
a → node count* (2 – 8). sets the graph size.
b → edge rule* (0 = left-rotate, 1 = right-rotate). chooses one of two canonical traversal patterns.
grammar_expandbehavior:* expands an l-system–style rewrite grammar and maps each symbol to a pitch offset.
parameters*
a → branching factor* (1 – 4). controls the number of production alternatives.
b → expansion depth* (1 – 6). sets how many rewrite generations are performed.
chaos_mapbehavior:* iterates a logistic map and quantises the resulting orbit to pitch indices, yielding quasi-chaotic but repeatable melodies.
parameters*
a → map parameter* r (2.5 – 4.0). governs orbit complexity.
b → initial value* x₀ (0 – 1). selects the starting point on the attractor.
markov_chain*
a: how many distinct pitch states exist.b: skew of transition probabilities toward ascending vs. descending motion.
state_machine*a: size of the state set.b: choice between two deterministic edge-rotation patterns.
grammar_expand*a: number of symbols introduced at each rewrite.b: total generations before the sequence is frozen.
chaos_map*a: non-linear growth rate r controlling orbit stability or chaos.b: seed value determining which branch of the orbit is taken.archetypal breadth:* the four forms cover stochastic-looking walks (markovchain), rule-driven state cycling (statemachine), recursive grammar growth (grammarexpand), and deterministic chaos (chaosmap).
irreducibility:* each algorithm embodies a distinct generative principle that cannot be reproduced by parameter tuning of another form.
compact control:* despite rich output, every form remains fully navigable with exactly two normalized parameters, sustaining the project's parametric purity.
deterministic expressivity:* long, intricate pitch sequences emerge without runtime randomness, aligning with the engine's requirement for full pre-computation and repeatability.
higher-order stochastic models or adaptive learning:* would require runtime probability updates, violating determinism.
input-reactive or feedback-driven algorithms:* excluded by the “no post-processing, no side-effects” rule.
rhythmic or onset generation:* handled in the onset layer (grid, field, etc.), not here.
pitch-to-frequency mapping:* deferred to the tuning domain.
generative supplies the system with an expandable palette of algorithmic pitch engines.
by capturing four fundamental paradigms - markov, finite-state traversal, recursive grammar, and chaotic mapping - the domain supports evolving melodic and harmonic behaviors that remain wholly deterministic, parameter-driven, and stylistically unbound, fulfilling the project's mandate to construct the full space of structured sonic possibility.