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: 
Trying to encapsulate an answer that's concise and short!

Triads are basically '*stacked thirds*'. That is, notes 1,3,5, and 2,4,6, and 3,5,7 etc.It is a fact that each root is from a diatonic note in that key. Thus 1,3,5 in key C is CEG; 2,4,6 is DFA, 3,5,7 is EGB etc.Some of those 'thirds' intervals are major (M), others minor (m). One has both intervals minor, (d) - diminished.

That gives a sequence of M m m M M m d, as others say.

Start the sequence on the last m - m d M m m M M - same order, different start point. So, really, one pattern!
With the help of all the above contributors and especially @piiperi I would like to answer my own question as a way to demonstrate newly learned knowledge that you have all taught me and hopefully make it easier for others trying to learn this as well.

As peri stated the process can be confusing to a newcomer counting intervals and then relating them to thirds. The aha moment was when I studied peri's statement that major or minor is defined by deciding whether the 1st third in the triad is 4 semitones (A major) or 3 semitones (Minor) or 3ST on both sides of the middle third (Diminished).

I was still very perplexed and kept going in circles with my reasoning as I tried to understand how one would come up with the cord pattern from scratch.

```
                        {Maj, Min, Min, Maj, Maj, Min, Dim} 

```

I wanted to be able to take any note (Key) and then use it to build a family of Chords.

First I had to understand the pattern \_W\_W\_H\_W\_W\_W\_H (Whole and half steps) and then realize this is the main chord building template. I knew the pattern as fixed on the keyboard, however I failed to understand the pattern must start in the key you are working with i.e. your whole step must start from the first to second degree in the scale you are working.

For Example:

To build chords in D Major, start with D in the first blank of the template then complete the scale. It is quickly apparent by looking at the whole and half steps there are errors needing to be fixed, therefore you proceed to make the required changes to match the pattern by raising a semitone where needed.

D W E W F H G W A W B W C H

Step 2: Correct them to match the whole and half step intervals

D W E W F# H G W A W B W C# H

Again Without Intervals Shown:

D,E,F#,G,A,B,C#

Step 3: Build Chords for all notes in the scale

DF#A,
EGB,
F#AC#,
GBD,
AC#E,
BDF#,
C#EG,

Step 4: Apply Major or Minor designations by looking at the intervals in the triad

Major
Minor
Minor
Major
Major
Minor
Diminished

For Minor scale you convert the major scale by lowering the 3rd 6th and 7th degrees by one 1/2 step. For a new student perspective it should also be noted that a degree should not be confused with intervals. A degree is simply a position in the sequence 1,2,3,4,5,6,7 for the scale. So in our D major scale 3,6,7 would be F#,B and C# therefore the D minor scale would be

D,E,F,G,A,Bflat,C

Chords can then be built and we can discover the Pattern:

```
                      {Min, Dim, Maj, Min, Min, Maj, Maj}

```

By evaluating the intervals in the triad as we did for the major scale above.