Just like you can build a triad by stacking two thirds, you can build quartal chords by stacking two fourths. There are no official names for the different types of quartal chords, so I will refer to them by their interval structure. Perfect quartal chord (4-4) will therefore describe a quartal chord of two stacked perfect fourths, perfect-augmented quartal chord (4-#4) will describe an augmented fourth above a perfect forth, and so on.
To be able to build diatonic quartal chords from all degrees of ionian, melodic minor, harmonic minor and harmonic major, we not only need quartal chords consisting of perfect and augmented fourths, but also those that include diminished fourths (i. e. major thirds). This is why the second inversion of the major triad and the first inversion of the minor triad are included in this chapter as well. Another item you might not readily identify as a quartal chord is the diminished-perfect quartal chord (b4-4), which is actually a dominant seventh chord lacking the fifth. You don’t need to practice these three additional quartal chords in the grouping and circle exercises.
This chapter follows the same outline as the chapter on triads.