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My teacher taught this lick starting on the root. So it is the root, flat seventh, flat fifth, and third. Are you saying it should be considered as the ninth, root, flat sixth, flat fifth?

So playing in the key of G, would one start on the G or the A? If you consider that it starts on the root, then one can start the lick on the sixth, tritone, or minor third of whatever key you're in.
 

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My teacher taught this lick starting on the root. So it is the root, flat seventh, flat fifth, and third. Are you saying it should be considered as the ninth, root, flat sixth, flat fifth?

So playing in the key of G, would one start on the G or the A? If you consider that it starts on the root, then one can start the lick on the sixth, tritone, or minor third of whatever key you're in.
You could indeed think of it as starting on the root of the dominant chord you're substituting. So you would start on G, not A in your example.

You'd typically use this lick on the V7 chord of, say, a ii-V-I. The diminished chord you would use would be the one whose root is the major 3rd of the dominant chord you're playing over. For example, you see a G7 (key of C). The 3rd of that is B. So play the pattern for B dim which is C#-B, G-F, Bb-Ab, E-D, C#-B, etc. Start on any of those notes, the first of which are indeed the 6th, tritone or minor third of G as you said. But your 4th starting note choice is actually the G, the root itself, which is exactly what your teacher said. You could also think of using the 7th (F dim), b9 (Ab dim) or 5th (D dim) patterns, all equivalent to B dim.

Hope that makes sense.

I love this lick and have had it under my fingers for years. I typically only use it in cadenzas because otherwise the chords usually go by too fast for me to figure out where to put it. But now that you've asked and I've thought through it, I could probably apply it without too many mental gymnastics. Thinking of the starting note as the tritone is probably the quickest, easiest way to use it in practice.
 
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