Lejaren A. Hiller, Jr. describes one of the earliest experiments in...
Lejaren Hiller (1924-1994) was an American chemist and composer, re...
The ILLIAC I (Illinois Automatic Computer) was a pioneering early c...
Early digital computers like ILLIAC I lacked modern displays, so re...
A pupil of Aristotle, Aristoxenus was one of the first thinkers to ...
Timbre is the quality of a sound that lets you distinguish which in...
### Warren Weaver
A mathematician, scientist, and administrator at...
At the time of this article, information theory was a new mathemati...
The Sonata Form is a common structure in Classical-era composition,...
In information-theoretic terms, the G7 chord is highly redundant—it...
Here’s one of the probability tables derived by Richard Pinkerton i...
### Mozart’s Musikalisches Würfelspiel (Musical Dice Game)
Around ...
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The ILLIAC I (Illinois Automatic Computer) was a pioneering early computer built at the University of Illinois Urbana-Champaign. Following the influential von Neumann architecture, it became operational on September 1, 1952, and holds the distinction of being the first computer to be built and owned entirely by a U.S. university.
Constructed with 2,800 vacuum tubes and weighing five tons, the ILLIAC I was a powerhouse for its time, providing reliable computing for a wide range of university research for a decade. It was a general-purpose machine used for complex scientific and engineering calculations, such as designing particle accelerators and radio telescopes. In 1957, astronomers at the university famously used it to calculate the orbit of the Sputnik 1 satellite just two days after its launch.
ILLlAC I operated until 1962, when it was retired and replaced by ILLIAC II. Parts of the original machine are preserved at the University of Illinois, marking its legacy as a bridge between early computing and creative experimentation.
Lejaren A. Hiller, Jr. describes one of the earliest experiments in computer-generated music, using the ILLIAC I computer at the University of Illinois. Drawing on information theory, probability, and classical counterpoint, he and Leonard Isaacson programmed the machine to compose the Illiac Suite for String Quartet (1956), the first substantial musical work created by a computer.
The paper reframed composition as a process that could be formalized, analyzed, and automated, linking artistic intuition with algorithmic structure and foreshadowing modern approaches to generative and AI-assisted music.
Early digital computers like ILLIAC I lacked modern displays, so results were printed or punched mechanically. The teletype machine converted the computer’s paper-tape output - a stream of holes encoding data - into alphanumeric printouts.
*Teletype Machine*
At the time of this article, information theory was a new mathematical framework, introduced by Claude Shannon in 1948 (roughly 10 years prior to this paper) to quantify information and communication. Initially developed for telecommunications, it quickly influenced other disciplines - biology, linguistics, psychology, and here, music theory.
Its key idea is that any message (or melody) can be described in terms of choices and probabilities, allowing researchers to analyze how order and randomness shape structure and meaning.
The Sonata Form is a common structure in Classical-era composition, especially for the first movement of symphonies. Sonata form organizes musical ideas through contrast and return, typically in three main sections:
- **Exposition** – presents the main themes, usually in two contrasting keys.
- **Development** – explores and transforms those themes, moving through different keys.
- **Recapitulation** – returns to the original material, now resolved in the home key.
The form balances predictability and variation, giving listeners both familiarity and surprise - making it a natural example for discussions of redundancy and information in music.
Timbre is the quality of a sound that lets you distinguish which instrument or source produced it, even when the frequency and amplitude are the same.
It’s often described as the sound’s “color” or texture — what makes a violin’s note feel different from a flute’s, even at the same frequency.
Technically, timbre depends on the waveform’s shape, its harmonic spectrum (the mix of overtones), and how those components change over time (the sound’s attack, sustain, and decay).
In information-theoretic terms, the G7 chord is highly redundant—its movement to C major is so common that it carries little informational surprise. Listeners familiar with tonal harmony almost always expect G7 → C, so the chord conveys less new information.
Musically, this comes from its strong dominant function within the C major scale (C–D–E–F–G–A–B). The dominant is the fifth degree (G), which naturally leads back to the tonic (C), creating a sense of resolution.
A dominant 7th chord is built on that fifth degree and includes:
- G (root) – the foundation
- B (major third) – defining its major quality
- D (perfect fifth) – reinforcing tonal stability
- F (minor seventh) – adding tension that pulls toward resolution
The F, a minor seventh above the root G, introduces the instability that drives the chord to resolve to C major (C–E–G). This predictable resolution is what makes the G7 chord both structurally central and informationally low in traditional Western harmony.
### Mozart’s Musikalisches Würfelspiel (Musical Dice Game)
Around 1792, Mozart devised a system that allowed a player to assemble a short minuet (a graceful 18th-century dance in triple meter) by rolling dice. Each dice throw selected one measure from a table of pre-composed options, guaranteeing a musically coherent result no matter the combination.
Similar “musical chance” systems circulated in Vienna, and Mozart’s version became a popular parlor activity, admired for blending mathematical curiosity with musical order.
If you want to see an example of Mozart’s musical dice game you can go here: https://www.youtube.com/watch?v=WJwJEZ5uaL4
*Mozart's Musical Dice Game*
Here’s one of the probability tables derived by Richard Pinkerton in his paper. It shows how frequently any note follows any other in the nursery tunes he surveyed.
### Warren Weaver
A mathematician, scientist, and administrator at the Rockefeller Foundation, Weaver played a key role in popularizing Claude Shannon’s work on information theory. In their joint 1949 publication, The Mathematical Theory of Communication, Weaver extended Shannon’s technical ideas to broader questions about language, meaning, and communication.
When Weaver wrote that information “relates not so much to what you do say as to what you could say,” he meant that information measures possibility, not content. A message drawn from a wide range of possible alternatives carries more information than one from a narrow set. In other words, information theory quantifies choice and uncertainty, rather than meaning or intent.
*Warren Weaver*
A pupil of Aristotle, Aristoxenus was one of the first thinkers to treat music as a science of perception rather than pure mathematics. In his treatise *Elementa harmonica*, he argued that musical structure arises from ordered relationships.
His observation that “the voice does not place intervals at random” reflects an early understanding of pattern and selection in composition: music gains coherence not from chance, but from structured choices that distinguish the melodious from the unmelodious.
Lejaren Hiller (1924-1994) was an American chemist and composer, recognized as a pioneer in computer-composed music. His unique path into this field began with a doctorate in chemistry from Princeton. While working as a research chemist at DuPont, he developed an interest in the creative potential of emerging computer technology.
In 1952, he joined the University of Illinois, where he gained access to the ILLIAC I (Illinois Automatic Computer), one of the earliest computers built and owned by a university. Collaborating with mathematician Leonard Isaacson, Hiller applied his scientific background to musical composition. He theorized that a computer could be programmed with fundamental rules of musical theory and then use a random number generator (a Monte Carlo method) to create novel compositions that adhered to those rules. This process moved from generating simple melodies to complex four-voice counterpoint in the style of Palestrina.
This research culminated in the 1957 "Illiac Suite for String Quartet," the first significant piece of music composed by a computer. The work demonstrated that algorithmic processes could produce aesthetically interesting results, effectively launching the field of computer music.
*Lejaren Hiller*