Ben Johnston: String Quartet No. 7, 3rd movement: Superposition of the different scale types

In his theoretical work “Rational Structure in Music” (1976), ben Johnston explains how scales of varying degrees of density are structurally connected. Johnston names four levels for the size of the intervals:1. triadic2. diatonic3. chromatic4. ultrachromatic 

The final movement of the seventh string quartet is designed as a superposition of different scales, analogous to this description. On the one hand, these are used to generate the tonal material; on the other, the formal proportions correspond to those of the ratios used. This translation process gives the scales a structure-forming effect and they become the blueprint of the movement.