rubato-composer

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])