# Inside Jazz: Linear Transformations, Pt. 2

In last month’s column, we learned how scales and arpeggios can be combined for the construction of line forms (“Linear Transformations,” May 2011 PG). This month, we’ll continue exploring the concept as an ongoing extension of that information.

Similar to chord forms, linear structures are based upon inversions, and those inversions not only have identifiable shapes, but also position themselves in vertical and horizontal positions across the fretboard. The linear arpeggios in our previous study were vertical chord forms that were “flattened” horizontally across the staff with their “skeletons” functioning as the arpeggios of the chord forms themselves—specifically Em7 and Gmaj7 as relative forms.

Often, we use inversions that embody identities that are very recognizable. These shapes are the very skeletons that reside within an improvisation. In Fig. 1 you can see how we move from Ab dim to E7 and then Em7 on the lowest four strings. (Note: In Ab dim, we’re spelling Cb enharmonically as B to make it easier to see the 6th-string common tone shared by all three chords.)

In Fig. 2, we shift this same chordal movement to the 4–3–2–1 string set. The voice leading is exactly the same in both examples, with F moving to E and then Ab (or G#) moving to G. I have placed arrows to indicate these movements.

We can see the result of combining both Em7 (or G6) voicings in Fig. 3. The upper bracket indicates the shape from Fig. 2 and the lower bracket indicates the shape from Fig. 1.

Chord forms and linear patterns are very similar. Both have specific shapes, and once they become familiar, these shapes begin to appear as inversions and transpositions across different areas of the fretboard. You can see Fig. 4 as an example of how to combine two separate linear arpeggios—both of the forms illustrated with vertical brackets in Fig. 1 now appear horizontally. The arpeggios appear in red (vertically beamed lower) while the upper beams hold melodic additions completing the full pattern.