Chords are built in a triad structure (simply meaning there are three essential intervals or notes, necessary to form a chord – without these three requisite intervals, no chord truly exists). As explained below, the combination of the 1st, 3rd, and 5th intervals (the major chord formula) is essentially adding thirds to the root – commonly referred to as “stacking thirds” – producing what is known as tertian chords.
To illustrate this, take the Key of D Major from the Circle of Fifths, and count out the 1st, 3rd, and 5th degrees by stacking thirds. The scale of D Major is comprised of D, E, F♯, G, A, B, C♯ – since D is the first interval, count up three steps to F♯ (D-1, E-2, F♯-3), then complete the formula by counting up to the next third, beginning on F♯ (F♯-1, G-2, A-3). This yields the major chord formula of 1st, 3rd and 5th, so a D Major is comprised of D-F♯-A.
Furthermore, stacking thirds will produce the 1st, 3rd, 5th, 7th, 9th, 11th and 13th – take careful notice that the 15th interval is omitted because it is the second perfect octave of the root this is why you will never see an extension past the thirteenth interval. In order to end on the first perfect octave (8th) or an even numbered extension such as the fourteenth, you would have to stack seconds or fourths (constructing what are known as secundal and quartral chords).
The following sections contain formulas of common tertian chords within their respective families. You will notice that even though some of the intervals change from natural to sharp, flat or double flat, the triad structure of the tertian remains the same.