’s Tonal System
The 6400 part of Bernstein’s Tonal System is an array of tonal centers or nodes representing different levels of composition or “organismic” entities in music. Each node is divided into a hierarchy of four levels, consisting of 16 initial tonal centers, 64 second-level tonal centers, 256 third-level tonal centers and 1024 fourth-level tonal centers. Taken together, these 6400 nodes form a large, highly structured and interconnected tonal system. This system is based in part on the concept of Tonal Centroid Focus (TCF) developed by Bernstein, which explores the center of gravity of a musical passage by analyzing its harmonic content. By creating this musical grid and providing access to musical material across multiple levels of structure, Bernstein sought to provide musicians, composers and theorists with a powerful tool to explore the nature of tonal music and its expressive potential.