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As mentioned, chords have three or more tones. First we will look to chords with three notes only: the triads.
There are two different approaches to building chords. The first approach is by using different intervals. The other approach is by using only the third as interval. We'll first take a quick look at the first approach, then we'll dive a little deeper into the second approach, which is more practical.
Triads are built using an unison, a third and a fifth, starting at the root tone.
When we look at the C major chord (a triad), which is C-E-G in root position, then:
If you change the type of intervals (major/minor, augmented, diminished), you change the type of chord. This is how it works:
The unison is alway perfect. When building a C chord, the first tone is always the C.
The third can be major or minor.
The fifth can be perfect, augmented or diminished.
With a little math you could find that there are six possible combination. However, only four of them are usefull (examples in C):
C major, C minor, C augmented (+) and C diminished.
Note that the chord symbol for diminished is a little circle.