"Now art is the contrary of chaos." - this statement made by Igor Stravinsky in his "Poetics of Music" emphasizes the fundamental problem of music, which is organizing sound into a coherent logical whole. This problem of opposing chaos has been up until till now only partially solved, hence many different music composition methods and styles. We propose structure theory, which is a system for organizing sounds by means of a mathematical graph model, that can form the basis of any musical piece, independent of style. The foundations of the model are two sets of rules for modeling: the perception of time and the perception of sound in the horizontal and vertical contexts. To provide a tool for composers and music theoreticians to experiment with structure theory, we further propose the Forte Framework for Music Composition. The framework consists of two embedded domain-specific languages: the Forte DSL and the Graph DSL. The domain of the former is the music analysis theory of Allen Forte which we describe, systematize and enhance with several generalizations. Besides proposing a DSL for this domain we contribute by showing how to use the knowledge of the domain itself, indexed type families and phantom types to achieve: (1) implementation swapping, (2) self-optimizing library code and (3) boilerplate code reduction. We provide the aforementioned features in a purely functional setting and without building an abstract syntax tree (we use a shallow embedding). Our second proposal, the Graph DSL, is an implementation of our structure theoretic graph model. To materialize our ideas for music organizing we describe an algebra for directed acyclic graph manipulation and show how structure theory can be translated onto this algebra. The Graph DSL itself is general enough to be used for creating and transforming graphs from other domains, but we focus on presenting our DSL in the context of the Forte Framework, with the Forte DSL being the drop-in language for node specification. We also show an extended example of music analysis that demonstrates one of the two possible applications of our framework, with the other major use being music composition. We chose Haskell to implementent both the Forte DSL and Graph DSL of the Forte Framework.

1. The Forte Framework for Music
Composition
Jakub Korczyński
Lambda Days 2015

2. – Igor Stravinsky
„Now art is the contrary of chaos.”

3. The Problem
Frederic Chopin playing for prince Radziwiłł in 1887,
Henryk Siemiradzki

4. How to grasp music?
"Etude in A minor" (Op. 10, No. 2) by Fryderyk Chopin

5. A partial solution
"Etude in A minor" (Op. 10, No. 2) by Fryderyk Chopin

6. What we would like instead?
"Etude in A minor" (Op. 10, No. 2) by Fryderyk Chopin

7. Even better …
"Etude in A minor" (Op. 10, No. 2) by Fryderyk Chopin

8. Wow!
"Etude in A minor" (Op. 10, No. 2) by Fryderyk Chopin

9. Structure Theory

11. Forte DSL

12. Forte DSL
Allen Forte (born December 23, 1926) is a music theoretician
and musicologist best known for his work “The Structure of
Atonal Music” published by Yale University Press.
What is Forte theory?
• A mapping of pitches to pitch classes
• A mapping of intervals to interval classes
• A grouping of pitch classes with pitch class sets
• Pitch class set normalization
• Various pitch class set relations
• Analysis with interval vectors and basic interval patterns
• Complexes and subcomplexes

13. Mapping music to numbers
Claude Debussy at the piano

14. Pitches to Pitch Class Sets
Forte mapping - "Clair de lune" C. Debussy

15. Contributions
What we propose:
• Forte theory systematization and enhancement
• A EDSL instead of a batch processor for manipulating
• Forte-theoretic entities
• Techniques for domain abstraction, interpretation swapping
and self-optimizing library implementation
• A method for boilerplate code reduction

16. Graph DSL

17. Graph DSL
Basic concepts:
• Modeling music as a graph
• Time axis and musical time windows
• Vertical plane
• Musical paths and the horizontal plane

18. Graph DSL example

19. Musical Time Window

20. Musical Time Window

21. Musical Time Window

22. Musical Time Window

23. Vertical Plane

24. Vertical Plane

25. Vertical Plane

26. Vertical Plane
Quarter Note Time Window

27. Horizontal Plane

28. Horizontal Plane

29. Horizontal Plane

30. Horizontal Plane
Two Horizontal Planes

31. Graph DSL operations

32. Function application code example

33. Function Application Intuition

34. Split code example

35. Split intuition

36. Merge code example

37. Merge Intuition

38. Cut and Inject code example

39. Cut and Inject Intuition

40. Helper code example

41. Helper Intuitions

42. Forte Framework =
Forte DSL + Graph DSL

43. Getting real

44. Final result …

45. … and with a little more work

46. Thank you!