Index

Grammars, Music and Formal Languages

This article series explores unusual territory: where formal language theory meets algorithmic music. The common thread is BP2SC, a transpiler that converts musical grammars from Bol Processor into SuperCollider patterns.

Each article is designed to be accessible without academic prerequisites, yet rigorous enough to serve as a reference. The series can be read in order or independently based on your interests.

Series I — Introduction

Before diving into theory, let’s set the scene. Why this project exists, what tools it uses, and what problem it aims to solve.

  • I1) Why I created a bridge between two worlds : Discover why I created BP2SC, the bridge between Bol Processor 3 and SuperCollider. Connect formal musical grammars and real-time synthesis for boundless creativity.
  • I2) Bol Processor : Discover the Bol Processor, Bernard Bel’s musical grammar system. Explore its impact on polymetry, Indian music, and algorithmic composition.
  • I3) SuperCollider : Introduction to SuperCollider, the programming language dedicated to sound. Patterns, live coding, real-time synthesis: discover why we chose it for BP2SC.
  • I4) Introduction to MIDI : Dive into the MIDI protocol: understand its principles, strengths, and limitations. Discover why this 40-year-old standard is the cornerstone of digital music.
  • I5) MusicXML : Discover MusicXML, the standard format for exchanging digital scores. Learn how it encodes notes, measures, and key signatures for software interoperability.

Series L — Formal Languages

The theoretical foundation of the project. From the Chomsky hierarchy to formal semantics, these articles build step by step the foundations needed to understand how a language works.

  • L0) The Map of Formalisms : Explore the map of formal language formalisms. Understand how syntax, semantics, and concurrency apply to BP3. Your essential guide for the L series.
  • L1) Chomsky Hierarchy Explained Simply : Dive into Chomsky’s hierarchy! Discover the 4 types of languages, from regular to recursively enumerable. Essential for understanding language and tool design.
  • L2) Context-Free Grammars : Dive deep into Context-Free Grammars (CFG) and grasp how compilers and parsers interpret the syntax of programming languages. A must-read for every developer!
  • L3) EBNF : What is EBNF? Discover this standard meta-language for describing language syntax (Python, JSON…). Learn its operators and key role. Master EBNF!
  • L4) What is an AST? : Dive into compilers! Discover what an AST (Abstract Syntax Tree) is, how it simplifies your code, and its key role in compilation. Essential for developers.
  • L5) The Three Semantics : Explore the 3 formal semantics: operational, denotational, and axiomatic. Understand how they describe program meaning and choose the right approach for your projects.
  • L6) SOS for Dummies : Structural Operational Semantics (SOS) is crucial for understanding language execution. This detailed guide reveals its principles and practical applications.
  • L7) Denotational Semantics : Denotational semantics interprets programs as mathematical functions. Discover this powerful approach to analyze, prove, and optimize your code’s behavior.
  • L8) Axiomatic Semantics : Axiomatic semantics uses pre/postconditions to prove program correctness. Discover Hoare triples, loop invariants, and practical applications.
  • L9) Beyond Chomsky : Beyond Chomsky, explore mildly context-sensitive languages. Discover TAG, CCG, and their crucial importance for natural language and music. An essential article!
  • L10) Attribute Grammars : Knuth’s attribute grammars enrich syntax trees with computable properties. Explore synthesized and inherited attributes, and their link to BP3 flags.
  • L11) Beyond the Three Semantics : Classical semantics have their limits. Discover advanced semantics: translational, process, and algebraic. Make sense of compilers, concurrent systems, and data types.
  • L12) Petri Nets and Process Algebras : Discover how Petri nets and process algebras (CCS, CSP) model concurrency and musical polymetry. An essential guide for formalizing music.
  • L13) Generate or Recognize : Explore the duality of grammars: generation vs. recognition. Why is producing easier than analyzing? Discover this key asymmetry in linguistics and music.

Series M — Music

The bridge between language theory and music. Formats, paradigms, hierarchical structures: how formal concepts apply to sound.

  • M1) MIDI under the Formal Microscope : Is MIDI a formal language? Explore its place in Chomsky’s hierarchy, the lack of complete specification, and its insights into musical representation. Essential!
  • M2) MusicXML Under the Formal Microscope : Discover why MusicXML, despite its formal XSD grammar and its Chomsky Type 2 position, has no musical generative power. A paradox to explore!
  • M3) The Paradigms of Musical Representation : Explore the six paradigms of musical representation, from wave to meaning. Discover how these abstraction levels stack and why certain tools are more powerful.
  • M4) Generative Grammars and Music : Discover how generative grammars, from Chomsky to GTTM and BP3, have revealed the hidden rules of music. Understand how our brain structures sounds.
  • M5) Polymetry : Polymetry is the superposition of multiple meters. Discover why MIDI and MusicXML struggle to represent it, and its roots in African, Indian, and Western music.
  • M6) Hierarchical Structure in Music : GTTM demystified: explore the hierarchical structure in music according to Lerdahl and Jackendoff. Understand the 4 pillars of our musical perception.
  • M12) From Structure to Sound : Discover how BP3, a unique generative language, manages musical layers of abstraction, from structure to sound. Explore a concrete example with flamenco rumba.

Series B — BP3

A deep dive into BP3 language mechanics: probabilities, alphabets, derivation rules.

  • B1) PCFG : Explore Probabilistic Context-Free Grammars (PCFG): assign probabilities to rules to generate varied, controlled music or text. Essential for BP3!
  • B2) Alphabets, Terminals, and Non-Terminals : Definition of alphabets, terminal and non-terminal symbols in BP3: the essential basic building blocks for understanding Bol Processor grammars.
  • B3) Derivation Rules : Master derivation rules and BP3’s 5 modes (ORD, RND, LIN, SUB, SUB1). Discover how these strategies transform grammar into a unique music generator. Explore now!
  • B4) Flags and Decremental Weights : Discover how BP3’s flags and decremental weights model the progressive exhaustion of a musical pattern and conditional execution. Essential dynamic control!
  • B5) Polymetry and Temporal Structures : BP3’s polymetry: temporal compression, parallel voices, and Indian additive signatures. Discover how a musical grammar encodes cyclic time.
  • B6) Homomorphisms, Variables, and Context : Variables, homomorphisms, wildcards, and context markers: explore BP3’s context-sensitive mechanisms with concrete musical examples.
  • B7) From BP3 to SuperCollider : Explore the BP3 SuperCollider transpiler! Discover how bp2sc transforms your musical grammar into playable code, phase by phase.

Reading Paths

“I want to understand the project” — Start with the Introduction series.

“I’m interested in language theory” — Dive into the Formal Languages series, from L1 to L6.

“I want to understand BP3” — Read the basics first (L1, L2) then the BP3 series.

Additional Resources

Glossary — All technical terms explained.

17 articles published — Last updated: 2026-02-08