Module: Musa::Markov

Included in:: All

Defined in:: lib/musa-dsl/generative/markov.rb

Overview

Markov chain generator for stochastic sequence generation.

Implements Markov chains that generate sequences of states based on probabilistic transition rules. Each state transitions to the next based on defined probabilities, creating pseudo-random but structured sequences.

Theory

A Markov chain is a stochastic model describing a sequence of possible events where the probability of each event depends only on the state attained in the previous event (memoryless property).

Transition Types

Array: Equal probability between all options
- { a: [:b, :c] } → 50% chance of :b, 50% chance of :c
Hash: Weighted probabilities
- { a: { b: 0.2, c: 0.8 } } → 20% :b, 80% :c
- Probabilities are normalized (don't need to sum to 1.0)
Proc: Algorithmic transitions based on history
- { a: proc { |history| history.size.even? ? :b : :c } }
- Proc receives full history and returns next state

Musical Applications

Generate melodic sequences with style-based transitions
Create rhythmic patterns with probabilistic variation
Produce chord progressions with weighted likelihood
Build dynamic musical structures with emergent behavior

Examples:

Equal probability transitions

markov = Musa::Markov::Markov.new(
  start: :a,
  finish: :x,
  transitions: {
    a: [:b, :c],      # 50/50 chance
    b: [:a, :c],
    c: [:a, :b, :x]
  }
).i

markov.to_a  # => [:a, :c, :b, :a, :b, :c, :x]

Weighted probability transitions

markov = Musa::Markov::Markov.new(
  start: :a,
  finish: :x,
  transitions: {
    a: { b: 0.2, c: 0.8 },  # 20% b, 80% c
    b: { a: 0.3, c: 0.7 },  # 30% a, 70% c
    c: [:a, :b, :x]         # Equal probability
  }
).i

Algorithmic transitions with history

markov = Musa::Markov::Markov.new(
  start: :a,
  finish: :x,
  transitions: {
    a: { b: 0.2, c: 0.8 },
    # Transition based on history length
    b: proc { |history| history.size.even? ? :a : :c },
    c: [:a, :b, :x]
  }
).i

Musical pitch transitions

# Create melodic sequence with style-based transitions
melody = Musa::Markov::Markov.new(
  start: 60,  # Middle C
  finish: nil,  # Infinite
  transitions: {
    60 => { 62 => 0.4, 64 => 0.3, 59 => 0.3 },  # C → D/E/B
    62 => { 60 => 0.3, 64 => 0.4, 67 => 0.3 },  # D → C/E/G
    64 => [60, 62, 65, 67],                      # E → C/D/F/G
    # ... more transitions
  }
).i.max_size(16).to_a

Defined Under Namespace

Classes: Markov