The triad can be used to create a matrix of possibilities for routing courses through progressions. In
Diagram No. 1, all of the possible major and minor triads that can work as arpeggiated melodic material
over the chords of a ii–V7(alt)–I–vi7(alt) progression are catalogued. These choices were based on chord
tones and acceptable tensions. On the V7(alt) chords, only altered tensions are used.
Diagram No. 1—Triad Matrix for a ii–V7(alt)–I–VI7(alt) Progression
Major and Minor Triad Matrix of Possibilities - Specific Routes Taken
The routes taken in example 1 are all stepwise, which has the tendency to produce a smooth fl ow. Notice
how each arpeggiated triad acts as a springboard into each phrase. By all means, feel free to experiment
with different routes once the matrix has been established.
Triad Matrix Application—ii–V7(alt) –I–VI7(alt) Progression
Now let’s apply the triad matrix to a more complicated progression. This progression, which is in the style
of the first three bars of Coltrane’s “Giant Steps,” has been used to demonstrate how this complex cycle
can be simplified.
Diagram No. 2 illustrates all of the major and minor triads that are available over the chords. The
choices are based on chord tones and acceptable tensions (on the dominant chords, only non-altered
tensions are used). Again, the routes used are stepwise to accommodate the diffi cult changes, but try
experimenting with others.
Diagram No. 2—Triad Matrix for Changes in the Style of the First Three Bars of “Giant Steps”
Major and Minor Triad Matrix of Possibilities - Specific Routes Taken
The improvisations in example 2 range from the most to the least amount of stepwise traveling. The application
of this matrix, in combination with the rapid, modulating changes, produces a sound that’s very
reflective of Coltrane’s composition.
Triad Matrix Application—Changes in the Style of the First Three Bars of “Giant Steps”
Obviously, there are many matrix variations available to explore. The whole point is to establish an improvisation
matrix using just a couple of variables (such as major and minor triads or minor pentatonic scales).
Remember, using too many devices can make things sound undefined and vague.