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Chord Shape Improvisation, Part 1
At this point, you should have a nice roadmap for embarking on the journey of minor chord shape improvisation:
1) Learn the minor versions of the three movable chord shapes, the "E Shape", the "A Shape", and the "D Shape".
2) Learn the corresponding minor pentatonic scale for each shape.
3) Associate the appropriate scale degrees with the chord shapes (i.e. root, b3rd, 5th) and learn to identify them quickly. This is the most important step. At this point your ear has a lot to work with, and the other steps are "gravy".
4) Understand and utilize the b7th and 4th scale degrees (also in the pentatonic scale).
5) Learn the full minor scale that corresponds with the chord shape, and begin to identify the scale degrees, starting with those discussed first, and eventually moving on to the 2nd and b6th (the two not included in the minor pentatonic scale).
6) Connect the dots between the shapes. In the actual key of A minor, we know three distinct positions, at the open position ("A Shape"), 5th position ("E Shape"), and 7th position ("D Shape"). Then everything repeats, so we also know the 12th position ("A Shape"), the 17th position ("E Shape"), and the 19th position ("D Shape"). You have the opportunity with these three shapes the cover the entire fretboard.
7) Transpose to a new key. Start with the keys that have a shape that can be used in open position. We've done A minor, so that leaves E minor and D minor. If you can play in A minor, E minor, and D minor, you've got most of the pop music idiom covered. Try some other keys at that point (B minor, F# minor, etc.) and see how the shapes connect when you don't have one in the open position.
Below I have another sequence that "connects the dots" between the shapes in our original tonality of A minor, and also illustrates ideas that can be generated from the shapes themselves, as well as from the transitioning between the shapes.