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: 
For the purposes of this question, chords are most usefully defined as every other note from the root of the chord, with chords having their roots on each note of the corresponding scale.

### Triads (3-note chords)

Given a major or minor scale, the chords, given by the scale degrees comprising each chord are

| scale degrees | major scale example (C) | chord quality | minor scale example (A) | chord quality |
| --- | --- | --- | --- | --- |
| 1 3 5 | C E G | major | A C E | minor |
| 2 4 6 | D F A | minor | B D F | diminished |
| 3 5 7 | E G B | minor | C E G | major |
| 4 6 1 | F A C | major | D F A | minor |
| 5 7 2 | G B D | major | E G1 B | minor1 |
| 6 1 3 | A C E | minor | F A C | major |
| 7 2 4 | B D F | diminished | G2 B D | major2 |

### Seventh chords (4-note chords)

| scale degrees | major scale example (C) | chord quality | minor scale example (A) | chord quality |
| --- | --- | --- | --- | --- |
| 1 3 5 7 | C E G B | major | A C E G | minor |
| 2 4 6 1 | D F A C | minor | B D F A | half-diminished |
| 3 5 7 2 | E G B D | minor | C E G B | major |
| 4 6 1 3 | F A C E | major | D F A C | minor |
| 5 7 2 4 | G B D F | dominant | E G3 B D | minor3 |
| 6 1 3 5 | A C E G | minor | F A C E | major |
| 7 2 4 6 | B D F A | half-diminished | G4 B D F | major4 |

---

1 It is conventional in a minor key to raise the 7th scale degree by a half step to create a leading tone. Thus the chord rooted on the 5th scale degree becomes major.

2 It is conventional in a minor key to raise the 7th scale degree by a half step to create a leading tone. Thus the chord rooted on the 7th scale degree becomes diminished.

3 It is conventional in a minor key to raise the 7th scale degree by a half step to create a leading tone. Thus the chord rooted on the 5th scale degree becomes a dominant seventh chord.

4 It is conventional in a minor key to raise the 7th scale degree by a half step to create a leading tone. Thus the chord rooted on the 7th scale degree becomes a fully diminished seventh chord.
The patterns derive from the three note triads built on each tone of the gamut of letters `A B C D E F G`. You call these the *diatonic* triads...

[![enter image description here](https://i.stack.imgur.com/J17pu.png)](https://i.stack.imgur.com/J17pu.png)

...notice that the pattern is really *one pattern of seven chords* where major and minor are just segments within that seven chord pattern.

The seven chord pattern can theoretically ascend or descend infinitely which is represented visually more easily as a circle...

[![enter image description here](https://i.stack.imgur.com/bcaOI.png)](https://i.stack.imgur.com/bcaOI.png)