[These are my own concepts taken from Dave Liebmans Brilliant Book A chromatic approach to jazz]
This first idea is a simple way of weaving in and out of unrelated harmony.
Here the C natural slides into the C# and then into an F# arpeggio which then revolves by letting the C# fall back into the C natural of the F major arpeggio with a flat 5 resolving to the fourth.
The next example is an extended line with a substitution of a substitution creating chromatic interest.
Below we see a concept of weaving through two different key centres. Thinking F for D minor and then through F# and sidestepping back to resolve the line.
Flat 5 substitution. D minor and A flat major.
Dave Liebmans book is an excellent and inspiring means of absorbing chromatic improvisational knowledge and ideas for your own playing.
I am not promoting this book. But I am very grateful for its existence and for its powerful inspiration to me on a daily basis. Anyway, below is a brief overview.
This book should be seen as a method to help the artist to develop his or her own way when trying to improvise chromatically. Through the concepts and examples offered, the improvisor should be able to use this material alongside already familiar tonal ideas. Specifically, the book serves as a guide for organizing chromaticism into a coherent musical statement meant to satisfy both the intellectual and emotional needs of artistic creation.
The reader will be introduced to more than one way of conceiving chromatic lines and harmonies. There is nothing theoretically complex or new in the text, it is the organization of the material as well as many musical examples and transcriptions (Bach, Scriabin, Coltrane, Shorter, Hancock, Beirach, Liebman a.o.) which should serve to inspire musicians to expand their usual diatonic vocabulary.
This book also provides insight into the style of playing that David Liebman is known for. In addition the book contains 100 assorted solo lines and 100 chord voicings.