### Describing and Interpreting Music in Haskell

**Speaker:**
Paul Hudak
**When & Where:** 12:30pm, Wednesday, Sept 18, 2002, Room 400 AKW

**Abstract:**

Musicologists have long noted subtle and complex relationships between
musical compositions and mathematical structures. Indeed, some well
known composers deliberately exploited this relationship in their
compositions. This talk explores a slightly different relationship:
that between **musical expression** and **computer languages**.
Specifically, two results are described:

First, Haskell is used to **describe** musical structures. These
structures consist of primitive entities (notes and rests), operations
to transform musical structures (transpose and tempo-scaling), and
operations to combine musical structures to form more complex ones
(concurrent and sequential composition). From these simple roots,
much richer musical ideas can be developed.

Second, an **interpretation** of these musical structures is defined in
terms of an abstract notion of **performance**. This interpretation
gives meaning to music (even if not as grandiose as the meaning given
by a musician), and allows one to prove certain **laws** that
collectively form an **algebra of music**.

The ideas presented are similar to the speaker's previous work on
Haskore [1] and MDL [2], two domain-specific languages for computer
music. But this talk focuses more on the algebraic properties of
music. For that purpose the design of the musical structures is
simplified and changed slightly to enhance its symmetry and the
applicability of algebraic methods.

Familiarity with Haskell and very basic musical concepts are all that
is expected; the talk is otherwise accessible to a broad audience.

**References:**

[1] Paul Hudak, Tom Makucevich, Syam Gadde, and Bo Whong, "Haskore
Music Notation -- An Algebra of Music", Journal of Functional
Programming, 6(3), May 1996, pp 465--483.

[2] Paul Hudak, "The Haskell School of Expression -- Learning
Functional Programming through Multimedia", Cambridge University
Press, New York, 2000.