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This Jazz Piano Tutorial is about Superimposition.
When improvising you can play a melody that outlines or suggests a chord progression different to the one being played by the rhythm section (or your left hand). The easiest way to do this is by using arpeggios (because it spells out the chords), but you can also use the relevant chord-scales.
Anticipate a chord - play a melody (arpeggio, chord-scale, guide tones, etc.) that implies a chord a few beats too early
Delay a chord - play a melody that implies a chord a few beats too late
Omit a chord - play a melody that ignores a chord (play through a chord)
Add a chord - play a melody that implies a new chord not actually played by the rhythm section
Substitute a chord - play a melody that implies a substitute chord a few beats early
Superimpose new chords - play a melody that implies a completely different and unrelated chord progression not being played by the rhythm section.
Anticipating and Delaying a chord during your improvisation is called 'Bar-line Shift'. This technique has been used since the early days of Jazz, especially by people like:
Lester Young
Coleman Hawkins
Charlie Parker
Superimposing a completely new chord progression over an existing one is called 'Superimposition'. This is a more modern technique and has been used by people like:
John Coltrane
Lennie Tristano
David Liebman
Superimposed chord progression sound better if they are structurally strong, functional/cadential or otherwise well-known (cliché). That way, even though the notes you are playing clashes with the underlying harmony, the strong structure gives your solo form and logic and ensures that it still sounds good.
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