Скачать или смотреть Schubert 960 : Circle of Thirds

The path on a circle of diatonic triads ordered by thirds

A passage from the final movement of Franz Schubert’s Piano Sonata in Bb major, D. 960, composed in 1828. The passage, which begins in D minor and ends in F major, consists of a motion through the 1-flat diatonic scale’s cycle of thirds, but with two chromatic alternations (indicated with the grey circles) that first substitute Eb for E, and then reverse the substitution, in both cases to avoid diminished triads.


This video will be part of the coming Book Mathematical Models of Musical Pitch and Time, By R.Cohn, Graphics G.Baroin at MIT Press 20025.
Paper : https://link.springer.com/chapter/10....

The images created for the supplementary website take advantage of the most advanced visualization software currently available, with the intention of meeting students, most of whom have been exposed from an early age to visualizations created for advertising, film, and gaming, at the high level that they have been habituated to expect. The images are designed using virtual reality and CGI .Some of the images pertain to topics that are already represented in some undergraduate and post-graduate courses, including atonal pitch-class theory, theory of musical tuning, and neo-Riemann theory.