Does it integrate with other musical software?

Yes, it features a Rubato Bridge that allows for naturality tracking within Rubato-based musical morphisms and score processing.

Which mathematical systems does it support?

It supports several systems including GF(3) (triadic), Z/12Z (chromatic), Diatonic (scale degrees), Parity (XOR), and standard Integers.

What does the Naturality Factor measure?

It measures how well a transformation (like a musical transposition) preserves underlying conservation laws, such as interval distances or triadic balance, on a scale of 0 to 1.

How is this skill used in music theory?

It implements Guerino Mazzola's 'Topos of Music' insights, treating musical transformations as functors and checking if the naturality square commutes.

Naturality Factor

Name: Naturality Factor
Author: plurigrid

byplurigrid

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数据科学与机器学习

Measures structural conservation and naturality in musical and categorical transformations.

关于

The Naturality Factor skill provides a rigorous framework for evaluating how well transformations—such as musical transpositions or mathematical morphisms—preserve underlying structural properties. By implementing category theory concepts like natural transformations and the Yoneda lemma, it allows developers and researchers to quantify 'defect' in conservation laws across chromatic, triadic, and diatonic systems. It is particularly useful for users of the Rubato musical framework or those working with topological data structures to ensure compositional coherence.

主要功能

Integrates with Rubato morphisms for advanced musical structure analysis
Supports multiple conservation laws including GF(3), Z/12Z chromatic, and Diatonic
Quantifies transformation naturality on a 0.0 to 1.0 scale
Calculates mathematical defect to identify where structural conservation fails
2 GitHub stars
Provides Yoneda conservation checks for object relationship analysis

使用场景

Validating if a musical transformation preserves interval structures across a score
Testing triadic balance in complex transformations using GF(3) logic
Analyzing structural coherence in category-theoretic models of music or data

关于

主要功能

Integrates with Rubato morphisms for advanced musical structure analysis
Supports multiple conservation laws including GF(3), Z/12Z chromatic, and Diatonic
Quantifies transformation naturality on a 0.0 to 1.0 scale
Calculates mathematical defect to identify where structural conservation fails
2 GitHub stars
Provides Yoneda conservation checks for object relationship analysis

使用场景

Validating if a musical transformation preserves interval structures across a score
Testing triadic balance in complex transformations using GF(3) logic
Analyzing structural coherence in category-theoretic models of music or data