09Variation needs constraints and memory

Generative systems

A generative process is not a random-number stream. It is a stable state, an advancing clock, a bounded transformation and a rule for returning or accepting change.

Deterministic motion before randomness

Five hits over sixteenX..X..X..X..X...
12345678910111213141516
gap vector3 · 3 · 3 · 3 · 4
The same spacing, rotated..X..X..X..X..X.
12345678910111213141516
gap vector3 · 3 · 3 · 3 · 4
meeting = LCM(lengthA, lengthB)Different lengths create a long combined cycle without changing either source pattern.
Contextual example

Stable kick, drifting percussion

kick length 16 · percussion length 5 · reset every 80 steps
kickN = 16invariant frame
percussionN = 5phase motion
resetLCM = 80formal convergence
Hear
The kick remains a reference while percussion approaches it from changing phases.
Use
When a scene should evolve without losing pulse or accumulating arbitrary events.
Why it fits
The common return is known in advance and can become a section boundary.

Probability changes confidence, not position

track12345678910111213141516
certainP = 1.0XXXX
optionalP = 0.6xxxx
rareP = 0.1x

Probability answers whether a predefined event occurs. It should not silently choose a new pitch, duration and instrument at the same time. Keep random choices seeded or bounded when reproducibility matters during performance.

safe mutation orderrotate → accent → thin/densify → register → pitch setChange relations that preserve identity before replacing the material itself.

From the neutral pattern to Orca

Build deliberately stops before language-specific code. The stable responsibility chain is frame → cursor → read → bang → MIDI; choose Orca operators for each responsibility after the musical relation is clear.

StageNeutral responsibilityTypical Orca family
FrameChoose cycle length N and rate k.C clock
Cursori = floor(frame / k) mod NC, arithmetic and modulo
ReadRead p[i], g[i], v[i] and rest state without advancing them independently.T / O track and lookup
BangEmit only when the event mask or condition is active.D, U, bang routing
MIDISend note, velocity and duration; fan out simultaneous chord degrees when needed.: MIDI output
rest rulerest advances cursor; it emits nothingOtherwise every silence changes phase and the programmed relationship collapses.
Keep exploring

Terms, relations and sources

Key terms

phaseprobabilitymutation

Related chapters

Time & meterForm & arrangement

Detailed lookup

Cycle geometryNotation legend

Evidence

Editorial sources

Models state their boundary; tradition-specific claims require specialist sources.