Since a minor 6 chord is 1 b3 5 6 that is the chord has a major 6 th note, what chord has 1 b3 5 b6 (wrt major scale) or (1 3 5 6) wrt minor scale?
In its literal sense you would (or could) call it a mb6 chord. This particular chord however is an inversion of major 7 in a different key. Amb6 for instance is an inversion of Fmaj7 and that is what most people would call it.
Take a look at the notes.
Amb6: A, C, E, F (1,b3,5,b6)
FM7: F A C E (1,3,5,7)
Musicians can get into lengthy discussions and arguments about what chords should be named. Personally I don’t worry about it, I just try to think about things in context.
There are other chords that can be inversions, but mb6 seems to cause more arguments than others. Two of these common inversions are Sus chords and major 6 chords.
Sus chords
Sus2 chords are inversions of Sus4 chords at the 4th degree.
For example Csus4..
Scale formula: 1 4 5
Notes: C F G
The 4th degree of C is F, therefore an Fsus2 will have the same notes as Csus4…
Fsus2 formula 1 2 5
Fsus2 notes F G C
Major 6 chords
The same thing with M6. Major 6 chords have the same notes as minor7 chords built around the relative minor. For example, A minor is the relative minor of C major. Therefore C6 = Am7.
M6 formula: 1 3 5 6
C6 notes: C E G A
m7 formula: 1 b3 5 b7
Am7 notes: A C E G
There are others but these are the ones I try mostly not to forget about.
Hope that helps.
