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gogins / csound-extended

Extensions for Csound including algorithmic composition, Android app, and WebAssembly.
GNU Lesser General Public License v2.1
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Which set-class types are invariant under the K operation of the Generalized Contextual Group? #192

Closed gogins closed 2 years ago

gogins commented 2 years ago

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.

gogins commented 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?

gogins commented 2 years ago

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.

gogins commented 2 years ago

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.

gogins commented 2 years ago

k_dualities.txt

gogins commented 2 years ago

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.