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Please note that chords like G7b5 (G-B-Db-F) are used on a regular basis in jazz and there is nothing "wrong" with them. You may want to explore incomplete chords. E.g. G-B-F-Ab suggests the sound of G7b9, and avoids a bit awkward (though also "legal") sound of G7b9b5. B-F-Ab is another way to suggest the sound of Bo7, even if it doesn'...


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Building tertian triads and seventh chords on each scale degree is an idea you are borrowing from diatonic harmony. But, while the diatonic scale will give you chords I ii iii IV V vi viio I the harmony used to make clear tonality is essential V I with a subdominant like ii6 or IV. You can use that as a point of departure for harmonizing the double harmonic ...


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