Computational Musicology, ????, Profit

This year I had the pleasure of attending FARM at ICFP. As well as demoing Klangmeister, I gave a paper on what computational musicology means for the study of music. The abstract is as follows:

In this paper I examine the relationship that complexity theory and
disjunctive sequences have to music, music-generating programs
and literary works. I then apply these ideas by devising a program
to generate an infinite ‘Copyright Infringement Song’ that contains
all other songs within it. I adopt literary modes of analysis and
presentation, which I motivate by arguing that music is a cultural
and artistic phenomenon rather than a natural one.

The full paper is available online via the ACM.

Most of the FARM papers focused more on general analysis of the structure of music than the interpretation of the meaning of specific pieces. I find the general analytic approach fascinating, but as I argue in my paper, I think computational musicology can be more than that.

I'm grateful to the FARM organisers for accepting a work that is a little loose with the genre conventions of a computer science paper. ICFP is a great conference, but its usual standard of worthwhile research is inherited from mathematics and the sciences. With notable exceptions like James Noble's work on postmodern programming, I don't see many examples of academics employing computational thinking for humanities research.

The paper is based on a talk I gave at Strange Loop last year called Kolmogorov Music.

Music as code talks

I've been giving talks about music theory and code for a few years now, so I thought I'd collect them all together in one place. They are based on Overtone and my Leipzig music composition library.

1. Functional Composition, about music theory from sine waves through to canons, given at Lambda Jam 2013 (code).
2. Kolmogorov Music, about music and complexity theory, given at Strange Loop 2015 (code).
3. Dueling Keyboards, about temperament and tuning systems, given at Clojure eXchange 2015 (code).
4. Klangmeister, about my online live coding environment, given at FlatMap 2016 (code).
5. African Polyphony and Polyrhythm, about music from the Central African Republic, given at Strange Loop 2016 (code). Slides are online.
6. It Ain't Necessarily So, about the psychology of musical perception, given at Curry On 2018 (code). Slides and demo are online.
7. Birdsong-as-code, about the music theory of birdsong, given at Strange Loop 2023 (code).

 If you're interested in my personal music, check out Whelmed (code) or this performance with keytar accompaniment.

Falsehoods programmers believe about music

In the spirit of Patrick McKenzie's great post on falsehoods programmers believe about names, I am trying to write an equivalent one for music. Any false assumption that might be made in codifying music is a candidate for inclusion. Suggestions are very welcome.

1. Music can be written down.
2. Okay, maybe not with European notation, but there'll be a specialist notation for that kind of music.
3. Music is finite in duration.
4. Music has a composer.
5. Music is about harmony.
6. Music uses scales.
7. Music uses equal temperament.
8. Music uses tones and semitones.
9. Music and dance are separate activities.
10. Playing and listening to music are separate activities.
11. Musicians can play their part separately from the overall composition.
12. Music is performed by professional musicians.

GEB

Douglas Hofstadter's Godel, Escher, Bach is one of my favourite books. Commonly referred to as GEB, this book is a mesmerising meditation on consciousness, mathematics and creativity. The central idea is that of a "strange loop", in which the same message is interpreted on multiple semantic levels.

GEB was the first place I came across the idea of a musical canon. A canon is a beautifully austere form of composition that was popular in the Baroque period. A canon consists of a dux part which sets out the base melody accompanied by a comes part which is some kind of transformation of the dux.

Here is the structure of a canon described using the programming language Clojure. f stands for the transformation selected by the composer.

(defn canon [f notes]
  (->> notes
       (with (f notes))))

For example, the comes might be formed by delaying the dux by a bar and raising every note by a third. In my talk Functional Composition I show how computer code can be used to explain music theory, focussing on JS Bach's Canone alla Quarta from the Goldberg Variations. Canone alla Quarta is an unusually complex and beautiful canon where the transformation is composed of a delay of three beats (a simple canon), a reflection (a mirror canon) and a pitch transposition down a fourth (an interval canon).

Here is the transformation from Canone alla Quarta written in Clojure. comp is a Clojure function for composing multiple transformations together.

(defn canone-alla-quarta [notes]
  (->> notes
       (canon
         (comp (interval -3) mirror (simple 3)))))

I was working on a talk for last year's Strange Loop programming conference (itself a reference to Hofstadter's work) and I decided that I wanted to create my own canon as a tribute to GEB as a finale. Rather than use an ordinary musical transformation for my comes, I wanted to pick something that spoke to the idea of composing music with computer code. I also wanted to incorporate GEB's theme of interpreting messages on multiple levels.

I took the letters G, E and B, and used the ASCII codes that represent these letters as though they were MIDI pitch codes. This gave me my dux. I then took the same three letters and interpreted them as the musical notes G, E and B. This gave me my comes. I had obtained a canon based not on musical concepts like delay or transposition, but on encoding schemes used in computer programming.

(defn canone-alla-geb [notes]
  (->> notes
       (canon
         #(where :pitch ascii->midi %))))

I elaborated the harmonies provided by this canon into a complete track, composed via computer code. The dux and the comes are joined by various other parts, some using polyrhythms to generate apparent complexity from underlying simplicity.

Eventually, the dux and the comes are accompanied by a third canonic voice, in which the names of Godel, Escher and Bach are read out by a text-to-speech program. So the theme of three notes G, E and B becomes a canon of three voices musical, technical and allusive to the three great creative spirits Godel, Escher and Bach.

Listen to the recording.

Read the code.

Watch the talk.