This post in our Jazz Workouts series is our Major 7 (b5) Workout. This will help you practice your Maj7(b5) chords in all 12 keys. The exercise goes through the Circle of 4ths (C-F-Bb-Eb-Ab-Db-Gb-B-E-A-D-G) and each chord is played for 8 bars before switching to the next. These chords can be tricky to improvise over so it is incredibly helpful to practice these chords isolated to get the sounds in your ears and onto your instrument. There are a lot of ways to think about approaching Maj7(b5) chords, but two great theoretical ways are the Lydian mode and Minor Pentatonic a half step down.
For example, if we are playing a Cmaj7(b5), you could play C Lydian which would be related to the G major scale.
If we use the Minor Pentatonic scale over this chord we would play an B minor pentatonic in this case (half step down from tonic).
Use the chord charts below as a guide, and use the play-along to practice!