Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory

which is in accordance with the parallelism between (shortened) dominant seventh chords and (shortened) half-diminished chords. Compared with the consonant case the tone $t = 5$ ( $»B «$ ) is down-graded to the truth value $* C$ , while the tone $t = 2$ ( $»D «$ ) is upgraded to the truth value $* L$ . Similar observations for other tones can be made with reference to the table above.

5 Experiments with the Program jMorph

A java-program called $jM orph$ has been developed by the second author of this paper⁶

⁶: Some components of $jMorph$ are reused from Christopher Dyer’s tool $jMidi$

. It enables the user to explore the variety of harmonic morphems and to investigate their presence in musical pieces. The user-interface is divided into three parts, namely a pianola sequencer, an analysis window (based on a score of chord slices) and a morpheme browser (see figure 2).

Figure 2:

Screen Snapshot of a $jM orph$ session with the pianola sequencer (low right window), the chord slices and their self-perspectives (upper right window) and the morpheme browser (left window)