Example 1.18

Alois Hába, Suite für vier Posaunen im Vierteltonsystem, Mvt. V, Allegro risoluto, mm. 1-3

ERRATUM: I let a misprint find its way into the dissertation: in the fourth beat of the second mesure, the third trombone should have an E-flat instead of an E-natural. The audio reflects this mistake. (You can hear the mistake easily; the wrong note is quite dissonant.)

In my dissertation, I used this short passage to demonstrate T-operators, which are a fancy way of describing transpositions. You can see the lower three voices moving in parallel motion (pretend the mistake isn't there), spelling out a succession of major triads in identical voicing. We can describe each successive triad as a transposition of the one that comes before it. For more detail about T-operators and how they work in a mod-24 pitch space, I would recommend the full text of Chapter 1.