Jazz Piano Improvisation
When it comes to coming to be an excellent jazz improviser, it's all about learning jazz language. So unlike the 'half-step below method' (which can be outside the range), when coming close to from over it seems far better when you maintain your notes within the scale that you remain in. That's why it's called the 'chord scale above' technique - it stays in the range.
So instead of playing two eight notes in a row, Bookmarks which would last one quarter note ('one' - 'and'), you can divide that quarter note right into 3 'eighth note triplet' notes - where each note of the triplet coincides length. The first improvisation method is 'chord tone soloing', which means to compose melodies making use of the four chord tones of the chord (1 3 5 7).
I typically play natural 9ths over many chords - including all 3 chords of the major ii-V-I. This 'chordal appearance' seems best if you play your right hand loudly, and left hand (chord) a little bit more quiet - to make sure that the audience hears the melody note ahead.
It's fine for these enclosures ahead out of range, as long as they end up resolving to the 'target note' - which will usually be one of the chord tones. The 'chord scale above' technique - precede any kind of chord tone (1 3 5 7) with the note above. In music, a 'triplet' is when you play 3 equally spaced notes in the area of two.
Now you can play this 5 note scale (the incorrect notes) over the exact same C minor 7 chord in your left hand. With this strategy you simply play the same notes that you're currently playing in the chord. Chord scale over - half-step listed below - target note (e.g. E - C# - D).
A lot of jazz piano solos include an area where the melody stops, and the pianist plays a collection of chord enunciations, to an intriguing rhythm. These include chord tone soloing, strategy patterns, triplet rhythms, 'chordal appearances', 'playing out' and a lot more.