My NYU pop theory class is going from non-functional harmony to the most functional harmony there is, the ii-V-I cadence. It's subdominant to dominant to tonic, Western tonal harmony the way God and Beethoven intended.
The ii-V-I comes in two flavors, major and minor. The major version is simple. Take some major scale, for example, C major.
To make the ii chord, start on scale degree two and add every alternate scale tone. In C, start on D and add F and A, which produces a Dm chord.
To make the V chord, start on scale degree five and add every alternate scale tone. In C, start on G and add B and D, which produces a G chord.
To make the I chord, start on scale degree one and add every alternate scale tone. In C, start on C and add E and G, which produces a C chord.
Add more alternating scale tones onto each chord to get sevenths, ninths and higher chord extensions.
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