Lydian Dominant : The Simpson Scale

 The Simpson Theme created by Danny Elfman is based on C lydian dominat scale(That tune has hung in my head for long time)

Let us see at Lydian Dominat Scale:

Spelling :R 2 3 #4 5 6 b7
Aka: Lydain b7 Scale,Acoustic Scale, Overtone Scale

It is seven note scale.This scale is a cross between a Lydian and a Mixolydian scale as it has #4 as in Lydian and b7 as in mixolydian. It is a very jazzy sounding scale.

This scale can be looked at in various ways but the most efficeint way is to look at it is as fourth mode of melodic minor(for C lydian dominant it is 4th mode of G melodic minor )

However, we will see lydian dominat  from Ionian perspective. In Ionian mode (major scale) when you first sharpen the fourth and then flatten the seventh, lydian dominat scale is obtained.
Ionian mode                   Lydian Mode                    Lydian Dominat
1 2 3 4 5 6 7------->    1 2 3 #4 5 6 7  --------->     1 2 3 #4 5 6 b7

Chords to use over : 7, 9,13, 7#11, 9#11,13#11.

If this looks complex find Frank Gambale = )