·         We saw in Step 11 that the tritone or sharp fourth is the "fingerprint" of a dominant chord.

·         As a matter of fact, just the tritone on its own can be used very effectively as a form of the dominant seventh, especially in combinations.

·         Example [13.1] is a left-hand blues progression made of nothing but tritones.  Notice the minimal movement required to get from each chord to the next.  Imagine the melodic freedom such sparse harmonies allow the improviser.

·         Adding a further fourth to the tritone gives us the basic quartal dominant shell VIIb III¹ VI¹ (Example [13.2]).

·         As in the case of quartal major chords we can slot in the next fourth in the series by bringing down an octave, giving the structure VIIb II¹ III¹ VI¹ (Example [13.3]).  In conventional form the symbol for this would be 13 and it's a shape that can be employed virtually anywhere a 7 or 9, as well as 13, is encountered.

·         When tertian dominants were considered (Step 4) we saw that such chords could be very effectively reshaped by altering upper intervals and mixing them in different combinations to give harmonic movement and interesting textures.  The same principles apply to forms based on fourths.

·         Thus G7 9b 13 in quartal is F A¹b B¹ E¹ (very nice chord -  a kind of altered Fo, Example [13.4]).  G 7 11# 13 would be F B¹ C¹# E (also nice - Example [13.5]).

·         Notice that dominant 11 (or sus 4) chords in this system look like Δ7s.  So G11 13 is F A¹ C¹ E¹, the same notes as FΔ7.  This just serves to reemphasise the close harmonic relationship between V7, IVΔ and II- chords.

·         As a matter of fact the quartal 13 shapes on V will serve as II- chords in many contexts.  So if you're playing something in D minor, you can often use the G dominant shell, the G9 13 form (Example [13.3]) or even the G11# 13 structure (Example [13.5]) as versions of the tonic minor.