general-lachenmann-machine time-grid generator

A generalized algorithmic time-grid generator for music composition, based on the system used by Helmut Lachenmann in Mouvement (– vor der Erstarrung).

The generator takes a 12-tone row, permutation pattern, and duration list as input and produces a complete multi-stage compositional scaffold as MusicXML scores.

Installation

Requires Python 3.9+ and music21.

pip install music21

Usage

Generate (full pipeline)

# Default inputs (Lachenmann's Mouvement)
python -m zeitnetz generate --output-dir ./output

# Custom inputs
python -m zeitnetz generate \
  --pitches "0 1 2 3 4 5 6 7 8 9 10 11" \
  --perm "1 5 0 6 2 7 11 8 3 10 4 9" \
  --durations "-11 6 9 7 6 6 4 3 10 6 3 1 10" \
  --output-dir ./output

# With auto-generated time signatures
python -m zeitnetz generate --auto-ts --output-dir ./output

# With custom time signature sequence
python -m zeitnetz generate --ts-sequence "7 6 5 4 3 2 1 1 2 3 4 5 6 7" --output-dir ./output

Validate (check inputs before generating)

python -m zeitnetz validate \
  --pitches "cis h c gis a dis fis e d ais f g" \
  --perm "1 5 0 6 2 7 11 8 3 10 4 9" \
  --durations "-11 6 9 7 6 6 4 3 10 6 3 1 10"

If inputs fail, the validator suggests repairs (rotations, transpositions).

Discover (find viable input combinations)

# Test 100 random combinations
python -m zeitnetz discover --trials 100 --seed 42

# Find combinations with many families
python -m zeitnetz discover --trials 200 --min-families 50

Pipeline Stages

Stage	Description	Output
1	Row Generation — permutation matrix, onsets, rhythm row	Internal
2	Zeitnetz V1 — 12 rows via circular scanning	Internal
3	Klangfamilien — sound families (dynamic count)	Internal
4	Full Score — cyclic Zeitnetz + families, uniform 3/8	zeitnetz_stage4_score.musicxml
V2	Variable time signatures (7 types, cyclic sequence)	zeitnetz_v2.musicxml
Final	Duration-as-count transformation	zeitnetz_final.musicxml

Time Signature Types

Type	Time Sig	Unit	Tuplet
1	3/8	32nd note	No
2	4/8	16th-note triplet	Yes (3:2)
3	3/4	16th note	No
4	4/4	8th-note triplet	Yes (3:2)
5	3/2	8th note	No
6	4/2	quarter-note triplet	Yes (3:2)
7	12/4	quarter note	No

Input Parameters

Parameter	Format	Example
Pitch row	12 pitch classes (0–11 or German names)	cis h c gis a dis fis e d ais f g
Permutation	12 integers (0-indexed permutation of 0–11)	1 5 0 6 2 7 11 8 3 10 4 9
Durations	13 integers (first may be negative)	-11 6 9 7 6 6 4 3 10 6 3 1 10

Architecture

zeitnetz/
  cli.py              — Command-line interface (generate, validate, discover)
  constants.py         — Fixed system constants
  pitch.py             — Pitch class utilities
  validate.py          — Input validation + repair suggestions
  discover.py          — Discovery mode (random search)
  stages/
    stage1_rows.py     — Permutation matrix + rhythm row
    stage2_zeitnetz_v1.py — Circular scanning
    stage3_families.py — Sound family derivation (dynamic count)
    stage4_score.py    — Full score computation
    stage5_final.py    — Duration-as-count transformation
  core/
    zeitnetz_grid.py   — Shared grid construction + cyclic extension
    family_scan.py     — Sequential activation scan
    time_signatures.py — 7 TS types + sequence generation
    staff_assignment.py — Round-robin + greedy assignment
  export/
    musicxml.py        — MusicXML generation via music21

References

• Pena, Luís Antunes. Lachenmann: Mouvement (– vor der Erstarrung). Eine analytische Betrachtung. Diplomarbeit, Universität für Musik und darstellende Kunst Graz, 2004.
• Cavallotti, Pietro. Differenzen. Poststrukturalismus und Neue Musik. Schliengen: Edition Argus, 2006.

License

Research and educational use.