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 used probability distributions, Markov processes, and game structures as compositional tools. Pithoprakta maps a Gaussian law derived from kinetic theory to glissando slopes; the orchestra is an analogy to a gas, not a thermodynamic system with measured temperature.
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, produces patterns that can be compared with timelines documented in several musical traditions. The mathematical similarity does not establish a shared origin, cultural equivalence or historical transmission.
The Kuramoto model explains how heterogeneous phase oscillators can develop collective synchrony. It is a useful analogy for ensemble timing, applause, and delayed feedback, but it does not by itself predict a universal networked- music latency limit or prove neural coupling between musicians.
A regular heptagon is not constructible by classical compass and straightedge. That theorem can illuminate seven-fold imagery, but it does not document Danny Carey’s compositional or symbolic intent.
Why has twelve-tone equal temperament become so useful? Continued fractions explain its unusually good fifth; cyclic-group structure explains some pitch-class symmetries. Neither fact makes it the only musical possibility.
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. The subgroup lattice constrains the possible symmetry types; it does not select Messiaen’s seven scales.
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 frequently analysed through Fibonacci numbers, including reported lyric counts and a 9/8–8/8–7/8 metre grouping. This post separates checked arithmetic from listening analysis and authorial interpretation.