Surprisingly, Skriabin actually avoids the two tones with the >lowest< truth value troughout the piece. The highest >non-true< truth-value corresponds to the tritone (relative to the local fundament considered), i.e., the paradigmatic tritone pendulum between the opening halfbars can also be interpreted as a »characteristic« fullbar prolongation. The finer local right hand structure seems to be governed by the truth values and .

A closer look at the entire bass progression shows that Skriabin avoids exactly two tones throughout the bass: and . In other words, there is an analogy between the common local avoid-tones (but each time relative to the local bass) and the global avoid-tones in the bass. If we again interpret these global avoid tones in terms of >lowest< truth values, we would have to infer them from the chords and . The bass tones of the opening four bars are , i.e., one might argue that the global avoid tones in the bass line are logically derivable from the opening of the piece.

It is a nice coincidence that intuitionistic logics seems to be applicable to the music of a composer, who rather intuitively searched for new pathways into a musical world beyond -- but still in contact with -- the tonal tradition.

Acknowledgements: I’m grateful to Andreas Nestke und Aline Honingh for critical reading of the manuscript and valuable comments.

References