Messiaen | 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