MAKE IT MELODIC
Although the example in this tutorial makes use of runs up and down the corresponding scale for each chord, this is mainly to illustrate that all of the notes in the scale will actually work over that chord. When applying this technique in the real world, it often works better if you try to avoid just running up and down the scales if possible, and instead concentrate on forming proper melodies from the notes available in the scale.
The raised fourth in the Lydian dominant scale makes it a great scale to use over standard dominant 7th chords. A 7#11 chord is another cool-sounding jazz chord, made by adding a sharpened 11th degree to a dominant 7th chord. The sharpened 11th is actually the same note as the scale’s raised fourth, just an octave higher up the keyboard – so fits nicely. An example is C7#11, made up of C, E, G, Bb, and F#.