What are PLR operations in this skill?

PLR operations refer to Neo-Riemannian triad transformations: P (Parallel) changes the third, L (Leading-tone) changes the root or fifth to move to a neighbor triad, and R (Relative) moves to the relative major/minor.

What is a Klumpenhouwer network (K-net)?

A K-net is a graph-theoretical representation of musical pitch-class sets where nodes are pitches and edges are labeled with transposition (T) or inversion (I) operations.

What is the Topos of Music framework?

The Topos of Music is a comprehensive mathematical theory developed by Guerino Mazzola that uses category theory to model musical objects as forms, denotators, and morphisms.

How does color integration work with music?

The skill utilizes Gay.jl to map specific hue values to pitch classes (e.g., 12 pitch classes mapped to 30-degree increments on the color wheel), enabling synesthetic or color-based composition.

Topos of Music

Name: Topos of Music
Author: plurigrid

byplurigrid

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数据科学与机器学习

Implements Guerino Mazzola's categorical music theory framework for advanced mathematical analysis and transformation of musical structures.

关于

The Topos of Music skill brings Guerino Mazzola's sophisticated mathematical music theory to the Claude Code environment. It utilizes category theory to define musical 'Forms' and 'Denotators,' allowing for rigorous modeling of notes, chords, and scores as structure-preserving morphisms. Users can perform complex Neo-Riemannian PLR (Parallel, Leading-tone, Relative) operations, navigate Tonnetz networks, and verify Klumpenhouwer (K-net) structures. Integrated with Gay.jl for color-pitch mapping and GF(3) Galois connections, this skill is an essential tool for algorithmic composition, scientific musicology, and developers working at the intersection of mathematics and sound.

主要功能

Categorical modeling of musical forms (Simple, Limit, Colimit, and List types)
Klumpenhouwer (K-net) verification and network analysis
2 GitHub stars
Color-to-pitch integration using Gay.jl and HSL-based mapping
Tonnetz navigation for parsimonious voice-leading and harmonic mapping
Neo-Riemannian PLR group operations for triad transformations

使用场景

Automating complex harmonic transformations in algorithmic composition
Scientific research into the relationship between category theory and musical performance
Validating mathematical properties of musical sets and structural morphisms

关于

主要功能

Categorical modeling of musical forms (Simple, Limit, Colimit, and List types)
Klumpenhouwer (K-net) verification and network analysis
2 GitHub stars
Color-to-pitch integration using Gay.jl and HSL-based mapping
Tonnetz navigation for parsimonious voice-leading and harmonic mapping
Neo-Riemannian PLR group operations for triad transformations

使用场景

Automating complex harmonic transformations in algorithmic composition
Scientific research into the relationship between category theory and musical performance
Validating mathematical properties of musical sets and structural morphisms