Closed gogins closed 2 years ago
I believe 3 and 4 voice chords are invariant in this way, but 5 voices are not. What about 6 and 7 voice chords?
To identify an invariant:
chord_k = chord.K() is chord_k.eOPT() == chord.eOPT()?
This should be applied to all iterates in chord spaces of from 3 to 7 dimensions.
Chord spaces of arity higher than 5 are problematic due to inefficiency. I will also test scale degrees for the major and minor scales at different arities.
I wonder if there are problems on the boundaries. In any event, most of these can certainly be used to construct chord progressions with some sort of analogy to the major/minor duality.
There are lot of these dualities, and I wonder if some of them are musically interesting and/or fruitful.
Investigate this up to 7 voices and document in Doxygen comments.
This question is quite important for the algorithmic composition of tonal and quasi-tonal music, as it abstracts the major/minor duality.