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The melodic major consists of 1 2 b3 4 5 6 #7 while the harmonic minor consists of 1, 2, b3, 4, 5, b6, #7.

Both appear to be "minor major 7th" chords.

So when someone refers to one of these, how do I know which they're referring to? Or is it simply an ambiguous term?

I often see both written as i maj7.

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    How do both these scales appear to be minor-major 7th chords? Both scales do support i m-m 7 chords, true, but each scale contains far too many notes for any minor-major 7th chord. (I don't think a minor-major 7th chord on the tonic would contain the supertonic, for example, but both scales do.) – Dekkadeci Nov 11 '18 at 7:10
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Both of these scales will produce that 'minor major seventh' chord, by using the notes contained therein, and 'stacking thirds'. That's not a problem. That's exactly what will happen!

In most minor keys, expect any notes from the three minor scales to pop up. That means in Am, for example, A B C D E F F# G G#. So, now, it's possible to also have a more common m7 - A C E G, as opposed to A C E G#. In fact, the classical melodic minor scale notes means both chords can be made using just the notes from that scale.

Think of theory more as guidelines, and explanations of what might happen, rather than any rigid rules. Yes, there's an ambiguity there, if you like, but if that mM7 can be used in a minor piece, bear in mind that that minor piece could be from any of the minors. There's nothing anywhere to say otherwise, or even to say 'thou must keep to one set'.

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