Complexity and Time Scales in Music Theory and Literary Analysis

The multiplicity of time scales is seen from new twelve-tone theory and from literary semantical analysis. Common for these is the use of finite groups as a heuristic tool. Part 1. Any twelve-tone row is represented by a unique permutation. Schönberg’s Method of twelve-tone composition (1922) with 48 “forms” of any row used only a subgroup of a group of permutations giving 48 × 48 combinations. The group of new dodecaphony gives 288 × 288 forms. But as composers want to hear about music intervals and not about groups, we can talk about the 288 × 24 interval rows of the 288 × 288 tone rows. Examples from works of Stravinsky and Bartok show structures, which theoretically imply our new dodecaphony. The practice of composers often precedes the theory. Part 2. Many time scales are interwoven in literature: scales in the fiction and scales of the reading creating semantical structures in the reader. In James Joyce’s novel Ulysses (1922), each chapter corresponds with some episode(s) in Homer’s Odyssey. And one page in the novel itself let us follow the stream of consciousness of the protagonist Mr Bloom on his morning stroll, with multiple shifts of time periods. In a Danish poem by the (fictive) authoress, Alma, we find a complicated interplay between the “occurrence” and “system” of linguistics. This is shown through projecting sections of the poem on the elements of the group D4 × C2 of order 16.