Question: My question relates to the chord pattern formulas.

For this Example we are commonly given these two formula patterns as one of the steps to construct chords in a key. I have been self teaching/learning and can't seem to find any information on the web to explain how these patterns are derived?

For the Major scale = {Maj, Min, Min, Maj, Maj, Min, Dim} is used to build the chords in a key

For the Minor scale = {Min, Dim, Maj, Min, Min, Maj, Maj} is used to build the chords in a key

Anyone who can shed light on this part I would really appreciate.
Thanks

Answer: 
The minor scale is just the major scale displaced by a 6th. It becomes clearer if we label the elements of the major scale below and then list the associated components of the minor scale.

Major scale = 1-Maj, 2-Min, 3-Min, 4-Maj, 5-Maj, 6-Min, 7-Dim

Minor scale = 6-Min, 7-Dim, 1-Maj, 2-Min, 3-Min, 4-Maj, 5-Maj
I tend to organize this using modes.

A diatonic scale has good distribution across the octave and (in some sense, both in terms of spacing and with respect to the overtone series highlighting thirds and fifths) naturally supports the notion of choosing every other note (thirds) to build a diatonic chord. These notes are then placed in parallel to finish the construction. I squint my eyes and see this as building harmonic elements by parallelizing melodic ones.

With that idea, we try taking a scale (melodic element) and putting it in parallel with other scales. We'll choose modes (relative to the root degree) for the scales and use the reasoning above to choose every other mode. Hence, we add modes in parallel according to some cyclic order of (1,3,5,7,2,4,6) to build progressions of diatonic triads, sevenths, etc... A triad example in C-major:

```
 I    ii   iii  IV   V    vi   viid I
-G----A----B----C----D----E----F----G- Mode=Mixolydian (5)
-E----F----G----A----B----C----D----E- Mode=Phrygian (3)
-C----D----E----F----G----A----B----C- Mode=Ionian (1)

```

From the intervals, we get an ordering of **MmmMMmd** chords being produced that repeat (i.e. it's **cyclic**). So, we can see for example that the natural minor case is already written in the example, we just start at the A on the bottom row (which represents aeolian and a parallel order of 6-1-3), making **mdMmmMM**.