Global Classification

Summary

Global classification relies on two concepts: affine functions and resolutions of global compositions. These constructs are discussed and exemplified. We derive classifying spaces and compare them to the situation in the Dreiding-Dress-Haegi theory of molecules: The latter are deduced from global compositions by additional structures concerning orientation, distances and angles (bilinear and exterior forms). It is therefore possible to view “molecules” as being global compositions with additional constraints; their musical meaning is discussed.

Wir sehen also, daft in der Musik die Mehrzahl der sogenannten “wissenschaftlichen” Geister fast so naiv ist wie Monsieur Achras - eine Figur von Jarry der eine Sammlung von Polyedern anlegte. Nun, es mag dahinstehen, ob in unserem Fall Polyeder wirklich von unerschöpflichem Interesse sind. Mir jedenfalls will die Notwendigkeit solcher pataphysikalischer Spekulationen nur schwerlich einleuchten.

Pierre Boulez [60, II, p.19]