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.
A lot of these answers are only partially correct and some have incorrect information in them. I'll try to clarify.

It's important to understand that chord quality and construction is independent of scales. Yes, both are defined by intervals, but their construction is mutually exclusive.

A scale is a sequence of intervals. In western music, there are Major scales and three types of Minor scales. Each type has a unique sequence of intervals that define it (as many of the posts here discuss). A scale can become a Key when the root note is assigned. For example, the Major scale becomes the key of "C Major" when you define "C" as the tonic of it. But all of this is irrelevant to chord construction.

Chords are also constructed of sets of intervals. Chords are simply 3 or more intervals intended to be played in unison (or rapid sequence as in strumming a guitar). A Major chord is defined as the Unison, a Major 3rd, and the Perfect 5th (technically a Minor 3rd above the first Major 3rd). Technically, these are not intervals of a scale, though a lot of people think of them that way. They are simply the number of semi-tones (or half-steps, if you like) between the notes.

Triads are very specific types of chords using exactly the Unison, a Major or Minor 3rd above it, and a Major or Minor 3rd above that. A Major chord is a type of Triad, but a Seventh chord is not because it has 4 intervals. Some chords have upwards of 7 or more intervals.

Finally, it doesn't matter which scale you are using, the chord constitution will always be the same. When playing a C Major chord on a piano, you will *always* play the same 3 physical keys (the C key, E key, and G key) regardless of which scale / Key you are playing in. The *only* thing that would change based on the key (i.e. scale) would be the note names of those 3 keys, but the physical pitches will always be the same.

If you are looking for which intervals chords are constructed from, this page lists a couple of dozen chord types and their intervals:
<https://www.internetchorddatabase.com/Reference.aspx>