counterpoint-engine

🎵 Species counterpoint as constraint satisfaction — every rule returns SAT/UNSAT, voices form a Laman graph.

What It Does

Generates multi-voice counterpoint against a cantus firmus using backtracking search over musical constraints, then outputs the result as Tensor-MIDI events. Each contrapuntal rule is a predicate returning "SAT" or "UNSAT"; each voice is a vertex in a Laman graph; every constraint is an edge.

Why It Exists

Species counterpoint has been taught as a set of prohibitions for centuries. This library treats those prohibitions as constraint predicates and proves that the constraint graph on N voices is a Laman graph (2N−3 edges, minimally rigid). That guarantees no voice is redundant and every rule is load-bearing. If you remove any edge, the structure gains a degree of freedom — a voice can drift unconstrained.

The math: a set of N points in the plane is rigid iff the bar-and-joint framework on those points is Laman. Counterpoint voices are the points; interval constraints are the bars.

Quick Start

pip install -e .

from counterpoint_engine.generator import CounterpointGenerator, Species, Scale, VoiceRange

# Define a cantus firmus (C major, 8 notes)
cantus = [60, 62, 64, 65, 67, 69, 71, 72]  # C D E F G A B C

gen = CounterpointGenerator(
    cantus_firmus=cantus,
    species=Species.FIRST,
    scale=Scale(tonic=0, mode="major"),
    voice_range=VoiceRange(min_pitch=48, max_pitch=67),
)

counterpoint = gen.generate()
print(counterpoint)
# → [48, 53, 52, 50, 48, 48, 50, 48]

# Multi-voice — Laman graph guarantees independence
voices = gen.generate_n_voices(n_voices=4)
# voices[0] = cantus firmus, voices[1..3] = generated

# Tensor-MIDI output
from counterpoint_engine.tensor_output import voices_to_tensor_events
tensor_events, midi_events = voices_to_tensor_events(voices)
print(tensor_events[0].to_bytes())  # b'\x3c\x00\x00\x0c'

API Overview

Rules (counterpoint_engine.rules)

Every rule returns the string "SAT" or "UNSAT".

from counterpoint_engine.rules import (
    no_parallel_fifths, no_parallel_octaves, proper_resolution,
    max_leap_seventh, consonant_interval, voice_independence, SAT, UNSAT
)

voice_a = [60, 62, 64, 65]
voice_b = [67, 69, 67, 69]
beats = [0, 1, 2, 3]

assert no_parallel_fifths(voice_a, voice_b, beats) == SAT
assert consonant_interval(voice_a, voice_b, 0) == SAT

Laman Graphs (counterpoint_engine.laman_counterpoint)

from counterpoint_engine.laman_counterpoint import (
    CounterpointGraph, henneberg_construct, verify_rigidity
)

graph = CounterpointGraph(n_voices=4)
print(graph.edges)              # [(0,1), (0,2), (1,2), ...]
print(graph.verify_rigidity())  # True
print(graph.edge_count())       # 5 (= 2*4 - 3)
print(graph.is_minimally_rigid())  # True

edges = henneberg_construct(4, seed=42)
assert verify_rigidity(4, edges)

Generator (counterpoint_engine.generator)

from counterpoint_engine.generator import CounterpointGenerator, Species, Scale, VoiceRange

gen = CounterpointGenerator(
    cantus_firmus=[60, 62, 64, 65, 67, 69, 71, 72],
    species=Species.FIRST,
    scale=Scale(tonic=0, mode="major"),
    voice_range=VoiceRange(min_pitch=48, max_pitch=72),
)

# Single voice
counterpoint = gen.generate()

# Multi-voice
voices = gen.generate_n_voices(n_voices=4)

Tensor-MIDI Output (counterpoint_engine.tensor_output)

from counterpoint_engine.tensor_output import (
    voices_to_tensor_events, voice_leading_to_sidechannels,
    interval_to_flux_vector, voice_intervals_to_flux_vectors,
    TensorMIDIEvent
)

tensor_events, midi_events = voices_to_tensor_events(voices)
raw = tensor_events[0].to_bytes()  # 4 bytes: cos, sin, beat, state

gestures = voice_leading_to_sidechannels(voices, beat=2)
# {(0,1): "Smile", (0,2): "Nod", (1,2): "Frown"}

fv = interval_to_flux_vector(7)  # perfect fifth → FluxVector

Architecture

┌─────────────────────────────────────────────────────┐
│                   counterpoint-engine                │
│                                                     │
│  rules.py          laman_counterpoint.py             │
│  ┌──────────┐      ┌──────────────────┐             │
│  │ SAT/UNSAT│◄─────│ CounterpointGraph│             │
│  │ kernels  │      │ henneberg_construct│            │
│  └────┬─────┘      └────────┬─────────┘             │
│       │                     │                        │
│       ▼                     ▼                        │
│  generator.py                                         │
│  ┌──────────────────────────────────┐               │
│  │ CounterpointGenerator            │               │
│  │  .generate() → List[int]         │               │
│  │  .generate_n_voices() → voices   │               │
│  └──────────────┬───────────────────┘               │
│                 │                                    │
│                 ▼                                    │
│  tensor_output.py                                    │
│  ┌──────────────────────────────────┐               │
│  │ voices_to_tensor_events()        │               │
│  │ voice_leading_to_sidechannels()  │               │
│  │ interval_to_flux_vector()        │               │
│  └──────────────────────────────────┘               │
│                                                     │
├─────────────────────────────────────────────────────┤
│  Dependencies                                       │
│  constraint-theory-core ─ Laman rigidity, A₂ lattice│
│  flux-tensor-midi ─ FluxVector, MidiEvent types     │
└─────────────────────────────────────────────────────┘

Data flow: cantus firmus → generator (backtracking) → voices → tensor_output → TensorMIDIEvent stream

Documentation

• User Guide — Complete usage documentation
• Developer Guide — Contributing and internals
• Examples — Working code examples

Ecosystem

• constraint-theory-core — Laman rigidity, A₂ lattice, dodecet directions
• flux-tensor-midi — FluxVector, MidiEvent, tensor-midi event stream
• plato-room-musician — Music theory room in the PLATO knowledge system

Requirements

• Python ≥ 3.10
• constraint-theory-core (from ../constraint-theory-core, add to PYTHONPATH)
• flux-tensor-midi (Tensor-MIDI event types)

Installation

pip install counterpoint-engine

Or install from source with dependencies:

pip install constraint-theory-core flux-tensor-midi
git clone https://github.com/SuperInstance/counterpoint-engine.git
cd counterpoint-engine
pip install -e ".[dev]"
pytest

Status

All 78 tests pass.

License

Apache 2.0