The lydian flat 7 mode comes from the 4th note of the melodic minor scale and can be used for dominant chords and dominant chords with a ♭5 or ♯11th(same note)
The Melodic minor scale is the major scale with a lowered 3rd in it. I found this is the easiest way to remember these scales.
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Here is a link to the melodic minor modes page in case you want to check out the other modes from this scale.
Melodic Minor Modes
This mode I’ll play against an F7 chord.
The F Lydian flat 7 played against an F7 chord
This mode is good because it contains a ♭5 a natural 5 and a ♭7. This mode is good for 9th, ♯11th and 13th chords too. Flatted 5th’s are ok but not ♯5’s
The flatted fifth is a “blue” note. One of the notes that give the blues scale its character
The Lydian Flat 7 Mode List
The Lydian Flat 7 Formula
The Formula is 1-2-3-♯4-5-6-♭7
This is how you make it from a major scale. Raise the 4 and lower the 7
I hope you found this page useful.