I’ve learned a lot about improvisation in the past few years.  One of the tricks of Bebop is that it extended the scale from 7 distinct notes to eight.  This is important since there are 8 beats  per measure.  The added note was typically one that made the chord tones fall on the downbeats of a run.  For instance, if the chord is C Major ( C E G B) the bebop scale adds the G#.  The run (from low to high) is C D E F G G# A B C.  For a C dominant 7 ( C E G Bb) the added note was the B natural and the run would be C D E F G A Bb B C.

I decided to take this a step further.  One other rule of Jazz is to avoid playing the root tone, to delay resolving the riff.  So let’s take the root out of the scale, and “define” the ninth as a good tone.

When playing over a major chord, you also want to avoid the fourth, as it clashes, and not in a good way.  A standard replacement is the #4.

Another rule:  Only the downbeats of the run have to be in the scale.  The upbeats can be any passing tone.

Add these together and a fairly simple pattern emerges.  Let’s start the run on the 3rd (since we are avoiding the root).

E

We skip the 4th and go to the #4. Then to then next chord tone.

E F# G

We next want to hit the major 7th.  We can chose either the 6th or the b7th, but it seems to make more sense to stay inside the scale than go outside.

E F# G A B

Skip the root, and try get the next beat on the ninth.  Only note left to chose is the b9.

E F# G A B C# D

Let’s get back to where we started.  Only transition note available is the #9.

E F# G A B C# D D# E.

Play it over a Cmaj7.  Start with any of the downbeat notes.  Doesn’t take too long to get used to the sound.

For a C dominant 7th I’d probably adjust it to this:

E F# G G# Bb C# D D# E.

But there is a lot more leway in a dominant 7th.