I love concerts. I love setlists. I hate building the playlist manually afterward. But do I really? A small automation project, a Deftones show in Dortmund, and the question of whether you should automate something you kind of enjoy.
Iannis Xenakis applied the Maxwell-Boltzmann velocity distribution, Markov chains, and game theory to orchestral composition. In Pithoprakta (1955–56), 46 string parts are molecules of a gas, each following the kinetic theory distribution. In Duel and Stratégie (1959–62), two conductors play a zero-sum game with payoff matrices on stage. This post works through the physics and mathematics, and asks what it means when a composer treats an orchestra as a thermodynamic system.
The {7/2} heptagram is not only a symbol. It is a traversal algorithm over seven beat positions. Because 7 is prime, that traversal never gets trapped in a sub-orbit.
Euclid’s algorithm for computing greatest common divisors, applied to the problem of distributing k drum beats as evenly as possible among n time slots, generates rhythmic patterns that match traditional timelines from West Africa, Cuba, Brazil, Turkey, and the Balkans. An algorithm devised in Alexandria around 300 BCE encodes the rhythmic structure of musical cultures that had no contact with ancient Greek mathematics.
Every ensemble faces the same physical problem: N oscillators with slightly different natural frequencies trying to synchronise through a shared coupling channel. The Kuramoto model — developed by a statistical physicist to describe fireflies, neurons, and power grids — applies directly to musicians. It predicts a phase transition between incoherence and synchrony, quantifies why latency destroys networked ensemble performance, and connects to recent EEG studies of inter-brain synchronisation.
Danny Carey calls it sacred geometry. Gauss proved it non-constructible. They are, unexpectedly, describing the same object.
Why does the octave divide into twelve? The answer lies not in aesthetics but in the continued-fraction convergents of log₂(3/2) — and the same group structure that gives Messiaen his modes.
Messiaen’s seven modes of limited transposition cannot be fully transposed through all twelve keys — not by convention, but because of group theory. The modes are pitch-class sets whose stabiliser subgroups in ℤ₁₂ are non-trivial. The orbit–stabiliser theorem gives the exact count of distinct transpositions for each mode, and the subgroup lattice of ℤ₁₂ maps directly onto the hierarchy of the seven modes.
Alongside physics and astronomy, two other things have occupied an unreasonable share of my attention since adolescence: mathematics and music. Lateralus by Tool — released 2001, still in rotation — is the piece that most conspicuously occupies the intersection. The song is structurally built around the Fibonacci sequence, from the syllable counts in Maynard Keenan’s vocals to the time signature pattern that concatenates to F(16). This post works through the mathematics in some detail and asks why it works musically.