The bebop dominant scale is a scale of 8 notes.
In C, the notes are:
C, D, E, F, G, A, Bb, B
That is one reason it works so well in 4/4. If you play regular eighth notes, the scale sits very naturally inside the bar and helps the line keep moving without losing its rhythmic shape.
The key sound is the move from Bb to B to C. The B natural is usually not a resting note. It is a passing note that helps the phrase connect and resolve.
A basic dominant line
Add the passing note
A shorter phrase
Use only part of it:
Over three chords
The classic place for it is Dm7 - G7 - Cmaj7. Keep the bebop sound mainly on G7:
One practical exercise
- Loop Dm7 - G7 - Cmaj7.
- Play simple chord tones on Dm7 and Cmaj7.
- Use the bebop note only on G7.
- Do not stop on B natural.
- Resolve the line clearly into Cmaj7.
One thing to listen for
If the phrase sounds heavy, shorten it. Bebop lines usually work better when the passing note moves quickly and the resolution is clear.