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Hello, I'm not quite sure what mirror symmetry is actually supposed to mean in this context. Is it meant that you play a piece backwards?

This is an interesting observation, because it makes sense to think in terms of vertical or horizontal mirror symmetry. If you think of a musical score, a vertical axis can be understood as a kind of bar line on which the notes of the left side are mirrored on the right side, so that the music then runs backwards, so to speak. A horizontal axis can be thought of as a horizontal line between the treble clef and the bass clef, on which the music of one side is mirrored. The latter concerns the mirror symmetry of the keyboard, with the mirror axis d. The whole thing is explained well comprehensibly and understandably on the already above mentioned Kickstarter project or by Marc-André Hamelin on Youtube:

https://www.kickstarter.com/project...tions-16-mirror-symmetrical-piano-pieces



I hope i could help you!

In the meantime i learned on Youtube about another jazz pianist, Vardan Ovsepian, practising with mirror symmetrical inversion. He published some exercises and seems to use them as a tool for improvisation. I am not an improvisor, are all pieces mentioned in the other posts fully written out? I am more interested in compositions that don't focus mainly on the technical aspect.

The proportion of improvisation is certainly high among jazz pianists like Chick Corea, Jesus Molina, Jeremy Siskind and Dan Tepfer. Not all of them seem to have published sheet music editions, while Vardan Ovsepian, whom you mentioned, as well as Victor Alcántara, who also wrote a theory book on the subject, have published fully written-out pieces that focus on the mirror symmetry of the keyboard. Pieces by Bela Bártók, Vincent Persichetti, Rodion Shchedrin are probably also available in libraries.