Applications of random walks for the analysis of graphs, musical compositions and language phylogeny

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Random walks provide us with a powerful tool for studying the structure of graphs and databases in details. We analyze the structure of undirected graphs by random walks. We have analyzed transition matrices aggregated for the MIDI representations of 804 pieces of classical music written by 29 composers. The successful understanding of tonal music calls for an experienced listener, as entropy- contrary to human languages - dominates over information redundancy, in classical music. Large pieces of tonal music might contain just a few types of melodic lines translated over the entire diapason of pitches by chromatic transposition as complexity typically decreases rapidly with the number of pitches used in a classical composition. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes in musical scores can be used to reliably resolve tonality of a piece and feat
Original languageEnglish
Title of host publicationApplications of random walks for the analysis of graphs, musical compositions and language phylogeny
Pages443-508
StatePublished - Jan 1 2013

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