Let's study the sexuality of the scales !

A major chord is defined by the following succession of semitones :  4 / 3 / 5.

Exemple. From C, we'll get : C / E / G / C

If we reverse this succession of semitones 5 / 3 / 4, we'll get  C  / F / Ab / C which is  an inversion of a minor chord.

These two chords form a couple (major / minor). Each one being the mirror of the other one.

Let's now take a major scale. Its succession of semitones is : 2 / 2 / 1 / 2 / 2 / 2 / 1.

If we reverse it : 1 / 2 / 2 / 2 / 1 / 2 / 2 .

Starting from C it gives : C  Db  Eb  F  G  Ab  Bb  C which is a Ab major scale started from the C.

The major scale is its own mirror.

The conclusion is that some musical structures (chords or scales) are forming couples with their mirror, whereas some other are similar to their mirror and could be qualified as "hermaphrodites".