Construction of the Minor Scale

All scales come from a very precise sequence of steps and half-steps. Stating simply, we can say that all you need to know is a sequence of a certain type or mode of scale to be able to build all the scales. From a practical point of view, its more complicated because there are many different types of scales (and the relative modes), and accordingly the memorization and its musical use are also more complex.
We have already analyzed the construction of the Major Diatonic Scale, and have seen that using a logical construction system, we can build a MDS from one note.
Remember the sequence of steps (t) and half-steps (st) of a MDS:

In a Minor Scale the sequence of half-steps changes because the succession of the intervals changes with the type of minor scale that we want to build. They are three types of minor scales that we will analyze, each with their own interval sequence.

The first model that we will analyze is the Natural Minor Scale (NMS). As for every scale, it is best to compare the succession of the steps and half-steps with the major scale of that same note.
The MDS of C, as we know, is built like this:

At this point, observing the interval sequence of the NMS seen above, we can apply the variations of the interested notes, which are the III°, the VI° and the VII°. These will be lowered to 1st: the flat symbol refers to the fact that 1st are removed from the note. In practice the III° (E note) is lowered to Eb, the VI° from A decreases to Ab and the VII° goes from B to Bb. Here is the Natural Minor Scale of C:

Lets now try to build a new minor scale, in the scale of A for example. We first look at the Major Diatonic Scale of A.

To build the NMS of A, lower to 1st the III° (from C# to C), the VI° (from F# to F) and the VII° (from G# to G). This is the scale:

You can refer to the table of the natural minor scale for all the scales, but try to build them using this technique.

We can now clarify a characteristic that connects a MDS to a NMS. A MDS has its relative minor that comes from the VI° of the same MDS.
For example: on the VI° of the MDS of C we find the A note. Starting the succession of notes with the A, then with the notes of the C scale, we get a sequence of notes that is the same as the natural minor scale of A. In the following example we see the MDS of C in the first bar and its relative minor, which is the NMS of A in the second bar.

There is a rule that says a NMS can also be defined as a relative minor. To use some examples, the MDS of G has its relative minor in the NMS of E, or the MDS of D has its relative minor in the NMS of B.
The rule can also be inverted. The relative major of a NMS comes from the III° of that same NMS. If we use the NMS of C as an example, its relative major is found on the III°, which is Eb (in fact, on the major scale of Eb we find the C note in the VI°, which is its relative minor). In the example below, we see the MDS of Eb and its relative minor Cm.

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