·         Perhaps the most famous and influential example of the fourths system applied to minor chords is Miles Davis's "So what".  The tune (head) takes the form of call-and response, a traditional pattern going back to early blues, field songs and the African roots of jazz.  The bass calls with a modal line.  The band responds with two minor chords.

·         Modes are scales formed by starting on any of the white notes on the piano keyboard except C (which, of course, gives the major scale).  We have already become familiar with one mode, the lydian, represented by the scale running from F to F¹.  "So what" uses the dorian mode, which runs from D to D¹.

·         The two chords with which the horns reply to the bass's dorian call are basically E-7 followed by D-7.  But their special quality comes from their voicings (and many an aspiring jazz musician has experienced the pleasure of discovering the simple secret).

·         The conventional shell representation of the -7 is enhanced by introducing the fourth in the left hand, making a I IV VII structure.  Example [12.1] gives the bass motif and the answering quartal E- and D- chords.

·         The complete head comprises two statements of the section given in the example, then two rounds of the same thing but a semitone higher, followed by two back in the original key.  Play it, and work out the quartal Eb- and Db- chords that occur in the middle section.

·         You may be thinking that there's an inconsistency between the format given here for the quartal minor (I IV VII X XII) and the previous assertion (Step 11) that I IV at the root of a chord appears ambiguous to the ear.

·         "So what" and all the other pieces spawned by the modal revolution in jazz exploit these ambiguities.  The ear is offered several alternative ways of making harmonic sense of the piece.

·         D dorian is built from notes of the C major scale, so C is an implied tonal centre for the piece.  But F lydian is also a strong tonal influence, as well as D minor.  Moreover, the IV note in each chord makes a claim to be the defining tonal element, so both the A from the E- quartal chord and G from the D- are prominent, and their corresponding modes (the aeolian and myxolydian respectively) are implied.

·         As a consequence of these ambiguities, modal pieces using quartal minor chords have the quality of extended unresolved suspensions, and their lack of harmonic commitment allows the improviser a lot of freedom.

·         It also means that almost any combination of fourths within the relevant modes will serve as permissible chords.  You can lock your fingers into the I IV VII X XII shape and move them all over the white keys in the D dorian section of "So what" and the resulting chords will work.  Try it for D dorian and for the same mode in other keys.