rubato-composer - Mazzola's Mathematical Music Theory in Code

Overview

Integrates Rubato Composer - Gérard Milmeister's Java implementation of Guerino Mazzola's mathematical music theory. The software embodies the Topos of Music framework with Forms, Denotators, and a Scheme interpreter.

The Yoneda Package

Rubato Composer implements 40 classes in

org.rubato.math.yoneda

:

Core Structures:
├── Form.java              - Abstract base for musical types
├── Denotator.java         - Musical objects (notes, chords, scores)
├── Morphism.java          - Transformations between forms
├── MorphismMap.java       - Functorial mappings
│
├── LimitForm.java         - Categorical limits (product types)
├── ColimitForm.java       - Categorical colimits (sum types)
├── ListForm.java          - Sequence types
├── NameForm.java          - Named reference types
│
├── LimitDenotator.java    - Instances of limit forms
├── ColimitDenotator.java  - Instances of colimit forms
├── ListDenotator.java     - Sequences of denotators
└── Diagram.java           - Categorical diagrams

Scheme Integration

Rubato includes a full Scheme interpreter with musical primitives:

// From org.rubato.scheme
SDenotator.java  - Denotators as Scheme values
SForm.java       - Forms as Scheme values
SExpr.java       - S-expression base class
Parser.java      - Scheme parser
RubatoPrimitives.java - Musical operations

Denotator as S-Expression

;; In Rubato's Scheme dialect
(define note (make-denotator "Note" pitch-form 60))
(define chord (make-list-denotator "Chord" (list note1 note2 note3)))

;; Morphism application
(apply-morphism transposition chord 7)

Bridge to music-topos

Form ↔ ACSet Schema

# Our ACSets correspond to Rubato Forms
@present SchNote(FreeSchema) begin
    Pitch::Ob
    Duration::Ob
    Onset::Ob
    Note::Ob
    pitch::Hom(Note, Pitch)
    duration::Hom(Note, Duration)
    onset::Hom(Note, Onset)
end

# Rubato equivalent:
# LimitForm("Note", [pitchForm, durationForm, onsetForm])

Denotator ↔ ACSet Instance

# ACSet instance = Denotator
note_acset = @acset Note begin
    Pitch = [60, 64, 67]
    Duration = [1.0, 1.0, 1.0]
    Onset = [0.0, 0.0, 0.0]
    Note = [1, 2, 3]
    pitch = [1, 2, 3]
    duration = [1, 2, 3]
    onset = [1, 2, 3]
end

Morphism ↔ ACSet Homomorphism

# Transposition as ACSet morphism
function transpose(notes::ACSet, semitones::Int)
    map_parts(notes, :Pitch) do p
        p + semitones
    end
end

Rubato Rubettes

Rubato's plugin system (Rubettes) maps to our skills:

Rubette	music-topos Equivalent	Description
ScorePlay	sonic_pi_renderer.rb	Score playback
BigBang	maximum_dynamism.rb	Gestural composition (MVC)
MetroRubette	Free Monad patterns	Metric structure
WallpaperRubette	gay_neverending.rb	Morphism-based tiling
MeloRubette	skill_sonification.rb	Melodic analysis

BigBangRubette (from source)

// BigBangRubette.java - Gestural composition
BigBangModel model;        // Composition state
BigBangController controller;  // User interaction
BigBangSwingView view;     // Visualization
// → maps to MaximumDynamism::DerangementConfig

WallpaperRubette (from source)

// WallpaperRubette.java - Florian Thalmann
// Creates wallpapers using morphisms applied to power denotators
List<ModuleMorphism> morphisms;
PowerDenotator output = getUnitedMappedDenotators(input, morphisms);
// → maps to GayNeverending color spiral

Installation

# Clone (already done)
cd ~/worlds/o
gh repo clone rubato-composer/rubato-composer

# Build
cd rubato-composer
ant

# Run
java -jar rubato.jar

Connecting to Our Stack

Rubato → SuperCollider

Rubato can export to MIDI, which SuperCollider can receive:

;; In Overtone/our stack
(def rubato-midi (midi-in "Rubato"))

(on-event [:midi :note-on]
  (fn [e]
    (play-note (:note e) (:velocity e)))
  ::rubato-handler)

Rubato → Sonic Pi

Export Rubato scores to OSC:

# sonic_pi_rubato_bridge.rb
require 'osc-ruby'

client = OSC::Client.new('localhost', 4560)

def play_rubato_score(denotators)
  denotators.each do |d|
    client.send(OSC::Message.new('/trigger/synth',
      d[:pitch], d[:duration], d[:onset]))
  end
end

TAP State Mapping

Rubato State	TAP	Color
Composing	LIVE (+1)	Red
Analyzing	VERIFY (0)	Green
Archived	BACKFILL (-1)	Blue

Mazzola's Core Concepts in Code

The Topos Structure

TOPOS(Music) = Presheaves over Form Category

Forms = Objects (types)
Denotators = Generalized elements (instances)
Morphisms = Natural transformations

Rubato Formula (from Vol. II)

Performance = Score × Tempo × Dynamics × Articulation

Where:
  Tempo: ℝ⁺ → ℝ⁺ (time deformation)
  Dynamics: ℝ → [0,1] (amplitude envelope)
  Articulation: [0,1] (attack/release shaping)

Commands

just rubato-build        # Build Rubato Composer
just rubato-run          # Launch GUI
just rubato-scheme       # Start Scheme REPL
just rubato-export       # Export to MIDI/OSC

See Also

• MAZZOLA_TOPOS_OF_MUSIC_GUIDE.md

  - Mathematical framework

• GENESIS_QUERY_PATTERN.md

  - How we discovered this

• acsets/SKILL.md

  - ACSet implementation

• OVERTONE_TO_OSC_MAPPING.md

  - Sound bridge
• Encyclospace - Mazzola's concept encyclopedia