Music-Theory | Sebastian Spicker

2023

1 article

19 Apr 2023 The Charm of Impossibilities: Group Theory and Messiaen’s Modes of Limited Transposition 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. musicmathgroup-theory

2022

1 article

8 Nov 2022 Spiral Out: Tool’s Lateralus, the Fibonacci Sequence, and the Mathematics of Musical Structure 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. musicmathematicsfibonacci