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How can one improvise over a I-III-VI-IV progression (C - E - Am - F) on the piano. using the C major pentatonic/A minor pentatonic (with the occasional E flat) sounds too simple. What other variations can one use, especially on the E and F chords?

Thanks

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The chords C, Am, and F are simply in the key of C, so you would use the C major scale over them. Since the major pentatonic scale is just a subset of the C major scale it is of course also a correct choice. However, you miss out on the notes B and F, which are part of the full scale. Over the E chord you could play the A harmonic minor scale, which you get by simply replacing the note G by G# (the third of the E chord). This will make your melodies reflect more closely the underlying chord progression. Note that E is the dominant chord of A minor, and the A harmonic minor scale will emphasize that chord quality.

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Folks seeking complexity beyond the more mundane harmonies & melodies (like myself) tend to employ diminished or augmented chords, of which there are vastly many. Something that comes to mind is "a scale" I actually encountered in Computer Music class, way back when-- a bit of C code included a "Miles Davis blues scale". Not having it handy, a search has me reading a great blog entry that thoroughly addresses variations of blues forms.. even addressing "blue notes" (microtones breaking through the 12-tone constraint!).

The blues scale is the minor pentatonic with a note added, the sharp fourth/flat fifth.

Diminished chords sound great over blues. C diminished seventh is C, Eb, Gb, A. The combination of the major sixth A with the flat third Eb is especially tasty, since there’s a tritone between them. Check out the turnaround at the end of Miles Davis’ trumpet solo in “All Of You” on Round About Midnight for a great diminished chord blues lick."

It includes guitar illustrations, but the discussion of theory & links to works are great for a player of any instrument.

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    The OP already has the chords in place, and is asking about melody notes, so it's no answer to the question. Being pedantic, Co = C, Eb, Gb, Bbb, - there's no maj 6 in it! Quotations such as this lose credibility for me.
    – Tim
    Dec 2 '16 at 8:50

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