  In the Pythagorean tuning system, the fifth is used to generate a scale of 12
notes per octave. In this paper, we use the octave to generate a scale of 19
notes per tritave; one can play this scale on a traditional piano. In this
system, the octave becomes a proper interval and the 2:3:4 chord a proper
chord. We study harmonic properties obtained from the 2:3:4 chord, in
particular composition elements using dominants, subdominants, higher
dominants, associated minor chords, inversions, and diminished chords. The
Tonnetz (array notation) turns out to be an effective tool to visualize the
harmonic development in a composition based on these elements. 2:3:4-harmony
may sound pure, yet sparse, as we illustrate in a short piece.
