"The Complexity of Songs"

[Mike]

In a short paper called "The Complexity of Songs", a famous computer scientist named Donald Knuth argued that popular songs are becoming less and less complex with time (with "That's the way - uh huh, uh huh - I like it" representing the global minimum): Baroque music was characterized by multiple polyphonic lines of melody interacting and weaving in and out with one another. This was gradually phased out in the Classical and Romantic periods in favor of homophonic ("melody + chords") harmony. The orchestration grew as new instruments were made available, but the melodic and harmonic complexity of the songs ultimately decreased. Modernism abolished the concept of tonal harmony altogether, and movements such as minimalism subsequently constructed entire songs out of a few simple recurring patterns, but these were eclipsed as popular music came into its own: first with Jazz, which gave performers a rough skeleton of a piece and required them to fill in the rest, then with rock, pop, and rap, the latter of which may sometimes lack melody entirely.

Has Knuth hit on something? Have we "left the symphony behind"? What would result from a fusion of the harmonic structure of popular music with the complexity of classical music?

[Leif]

Interestingly, the "quadrivium" of Classical Educational Theory (which has its roots in medieval education) consists of the "4 ways": arithmetic, music, geometry, and astronomy. Medieval scholars considered these 4 cornerstones of secondary education to represent quantities at rest (arithmetic), quantities in motion (music), magnitudes at rest (geometry), and magnitudes in motion (astronomy). In modern terms this has been described as "pure (arithmetic), stationary (geometry), moving (astronomy) and applied (music) number".

This is a reminder to me that music was recognized even as early as the Middle Ages as a mathematical expression. Music, like arithmetic, is a branch of mathematics, but it differs from the latter by its dynamicism. In a sense, music is arithmetic at play. I would argue that as educational theory diverged from the Classical Theory, the emphasis on music as mathematics declined, most rapidly in the 20th century. Today, we are largely left with a structurally infantile medium that struggles to say anything worthwhile because its practitioners are no longer literate in the language of music: mathematics.

Contrary to what Michael suggested however, I would argue that the minimalists are perhaps more aware than most of the mathematical roots of music, and are striving to re-learn those roots from first principles.

[Mike]

Contrary to what Michael suggested however, I would argue that the minimalists are perhaps more aware than most of the mathematical roots of music, and are striving to re-learn those roots from first principles.

You're absolutely right - I was just noting that it was less complex that what had preceded it. I'm not making value judgments on any particular form of music (I listen to almost everything, including minimalist music), but just observing the trend towards simplicity. Building music from the ground up often entails a break from a system perceived as having excess complexity, if anything.