Hierarchical multi-scale set-class analysis

Abstract

This work presents a systematic methodology for set7class surface analysis using temporal multi7scale techniques; The method extracts the set7class content of all the possible temporal segments2 addressing the representational problems derived from the massive overlapping of segments; A time versus time7 scale representation2 named class7scape2 provides a global hierarchical overview of the class content in the piece2 and it serves as a visual index for interactive inspection; Additional data structures summarize the set7class inclusion relations over time and quantify the class and subclass content in pieces or collec7 tions2 helping to decide about sets of analytical interest; Case studies include the comparative subclass characterization of diatonicism in Victoria's masses Iin Ionian modeB and Bach's preludes and fugues Iin major modeB2 as well as the structural analysis of Webern's Variations for piano op; :72 under different class7equivalences;

A comparative statistical analysis of music styles (seventeenth–nineteenth centuries)

“…A vast number of studies closely related to the examination of the relationship between mathematics and music exist in the world practice (Edelson and Johnson 2012; Roberts 2016). Classical music, which is the most examined from a mathematical point of view, is also analysed in detail by multiple research (Shafer 2010; Martorell and Gomez 2014).…”