The Shadow Tonnetz, from Genesis to Generation, Moscow Conservatory 2021

Premiere of the Shadow Tonnetz : the latest evolution of Neo Riemanian Tonnetz
at Moscow Conservatory, Euromac International Music Analysis Congress


Short History
2011 Colorized Tonnetz provides Symbols with 2 Parameters that fit 2 notes Parameters
part of my PhD (G.Baroin)

2012 Polarized Tonnetz by H.Seress, can describe modal orientation polarization and intensity
2014 Spinnen Tonnetz with H.Seress, adds the concept of Tonal Center



2020 Shadow Tonnetz with I.Khannanov, keeps trace and quantisize the harmonic paths



The Shadow Tonnetz

In order to reveal other essential or distinctive features related to a musical composition, we propose a new visualization technique, the Shadow-Tonnetz. Its goal is to unveil the “Harmonic Rhythm” of a musical piece, that is commonly understood as the rate at which the chords progress in a musical composition.


The Shadow-Tonnetz keeps traces of the chords employed and helps displaying the “musical weight” of a specific chord and paths within a composition. It enables the spectator to better apprehend the key points and harmonic structure of a composition.

In comparison with many current approaches, the visualization of harmonic progression including Speed and Weight is innovative and provides new horizons for the understanding of musical structures. Since these concepts work fine with the pieces that we have studied, we envision to use these principles for Tonal Center variations (see Spinnen-Tonnetz) [5]