How to extend Jazz Modes and Scales:
Going back to our negative harmony web page CLICK we had a scale extension of Ionian and Phrygian.
Employing our old friends “Tetrachords” we can build complete 2 octave scales when the octave [or repeated starting note] is missed. In this case the whole tone scale and its transposition builds the scale extension.
We can also build 2 octave scales by joining together two “One octave” scales.
Many composer like Tcherepnin, Messiaen, Boulez along with more modern improviser/composers like Keith Emerson and Allan Holdsworth have applied this for its rich polytonality, modal expansion and textural counterpoint.
This idea along with negative harmony is really well suited to the piano both in terms of improvisation and composition. If you are looking for originality then there is a whole new world waiting here to be discovered and applied.