If you ever notice that six steps up the scale this is a major sixth but if we invert it this becomes part of a minor chord. Minor third, major sixth. Pretty much all the intervals will behave that way.
A major third will become a minor sixth. A minor third becomes a major sixth. Even a minor seven becomes a major second.
And a minor second becomes a major seventh. Because you’re moving around the octave you’re basically subtracting eight notes so whatever you get is going to end up being nine. A third, a sixth.
Three and six equals nine but interestingly the perfect intervals the fifth and the fourth do not switch major and minor qualities.
