This mode is the same as the Lydian mode, but because it has a minor 7th in it, it makes this mode very useful when soloing over dominant chords, especially those with a b5 or #11. The character pitches in this mode are the 3, #4 and b7.
By stacking 3rds above the root, we get a list of dominant chords that are formed:
1-3-5= Major triad
1-3-5-b7= Dominant 7
1-3-5-b7-9= Dominant 9
1-3-5-b7-9-#11= Dominant 9#11
1-3-5-b7-9-#11-13= Dominant 13#11
Respelling the #4 as a b5 will produce other types of altered dominant chords:
1-3-b5= Major triad w/b5
1-3-b5-b7= Dominant 7b5
1-3-b5-b7-9= Dominant 9b5
1-3-b5-b7-9-13= Dominant 13b5
Lydian-Dominant Vamp- When soloing over this vamp, The 3rd, b7th and #4 are the tones to focus on.
Vamp #1: (C7b5/C9b5) (Use C Lydian-Dominant. All black dots on C notes)