Perhaps one of the most important things to learn about chords in improvised music is the idea of chord synonyms. For instance, a C major 6th chord, written C6, is equivalent to an A minor 7th (they both contain the notes C, E, G and A). Note that voicings played by a chordal instrument often omit the root and sometimes the fifth. The 3rd + 7th (or 6th) are almost always present.
Important synonyms are listed below:
I6 = vi min7 ex C6 = Amin7th
Imaj7= vi min9th (no root) ex Cmaj7 = Amin9th
im6 = IV9 (no root) = VIIb9b13 (no root) = vi -7b5 ex Cmin6 = F9 = B7b9b13
= Amin7b5
iii min7th = Imaj9 (no root) ex Emin7 = Cmaj9th (no root)
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More Advanced:
Any fully diminished chord is actually 4 different Dom7b9 chords:
Ab dim7 is spelled Ab , B, D, F = G7b9, Bb7b9, C#7b9 and E7b9 (all without
root)
Note that symmetrical scales (diminished, whole tone,
augmented etc.) display qualities similar to the synonym above due to their
symmetry.
Esusb9 (phyrgian or 2nd mode of D melodic minor)
C#7b13#9
Fmaj7+11
Bmin7b5/11 (no third which is unusual but this sound works)
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There are more synonyms but these are the important ones.
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