Again, let's take a glance at these important scale structures. One-string scales is the way I'll describe them now because that's how you can perfectly see the inner structure of each basic scale.
In the Basic scales - F.A.Q section you will find further explanations on this subject.
It once occurred that one of my students showed interest in learning the inner structures in an inverse way, which I then considered a very unique however not so important idea. The Ancient Greek musicians also employed the idea of inversed structures, i.e. they defined each scales and the corresponding notes pitch wise not upwards but downwards (more on this see section The origin of basic scales). Hence reversed basic scales prove to be useful after all. You will find helpful information on this in section Basic scales on one string. OSIRE will also be useful for modeling these scales.
The inverse of Major scale is Phrygian scale.