cusses on the detailed combinatorial analysis of symmetry patches, i.e., subsets of a melody occuring at least two times up to symmetry transformations. He provides several measures for the amount of symmetry and complexity and describes analytical experiments with authentic and artificial choral melodies. The programs MeloPatchRubette³ and jMelo allow experimental verification of this approach.
Three concluding papers are concerned with different aspects of experimental harmonic analysis. Thomas Noll and Monika Brand present a Morphology of Chords which is dedicated to the study of subsets of the twelve-tone-system on the basis of tone perspectives (affine transformations). The Java program jMorph allows to edit harmonic morphemes and to localize their presence in musical pieces. Thomas Noll and Jörg Garbers use Rubato’s HarmoRubette as a basis to reconsider its motivations and possibilities and situate several recent approaches in a widened common experimental frame-work of Harmonic Path Analysis. In Correspondence Analysis for Visualizing Interplay of Pitch Class, Key, and Composer, Hendrik Purwins and his co-authors apply statistical methods to investigate the presence of pitch classes and keys in various musical compositions.


Berlin, Mexico City, and Zürich, February 2004


The Editors