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What are the precise harmonic functions of the Minor sixth chord? I remember that I read somewhere that they play often the role of the I degree in a chord progression (like the often used 6/9 chord) but why this? If this is correct when I find that D-6 in picture I should say that I'm in the tonality of D minor and not F major.. basically that one cannot be a sixth of F cause on the sixth degree of a major scale I should find a min7 chord right? Thank you and sorry for the dumb question, I'm studying jazz and still have so much to learn!

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Dm6, as you have written, comprises D F A B. The fact that there's a B♮ in there isn't that important. That note features in the scale of D melodic minor (D E F G A B C♯), so it could be expected in Dm - or the relative F major too.

As far as its function is concerned, it gets used as V/V, containing notes similar to G9(no root). It's also closely related to vi in key F, no surprise there!

F69 contains F A C D G, so isn't really a comparable chord.

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