Abstract
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, inversions, major and minor chords, 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.
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