2:3:4-Harmony within the Tritave
This work addresses a niche problem in music theory for composers and theorists interested in alternative tuning systems, but it appears incremental as it adapts existing concepts to a new scale.
The paper tackles the problem of generating a 19-note scale per tritave using the octave instead of the fifth, making the 2:3:4 chord a proper chord, and studies harmonic properties like dominants and subdominants, resulting in a system that can be played on a traditional piano and visualized using Tonnetz.
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.