When learning how to play jazz guitar, one of the most important device to master is to play each tone of a chord in order to outline a specific progression.
Extended diatonic arpeggios are seventh chord arpeggios (R-3-5-7) from the diatonic scale (a.k.a major scale) that contain supplementary notes above the root. These extensions are 9th, 11th and 13th.
Harmonizing The Major Scale
The best way to understand how diatonic arpeggios are built is to harmonize the major scale by stacking thirds in order to get seven distinct chords.
You can see and hear that each tetrad chord (four note chords) can be extended with 9th, 11th and 13th.
It means that 9th chords are built with five notes (1-3-5-7-9), 11th chords are built with six notes (1-3-5-7-9-11) and thirteenth chords with seven notes (1-3-5-7-9-11-13).
These extensions are represented by the red rectangles.
The upper-structure of an arpeggio includes the notes above the seventh (9-11-13).
This upper-structure takes part of the formation of secondary arpeggios.
Degree I (maj7)
For example a Cmaj13 arpeggio is in fact based on a tetrad chord (Cmaj7 : 1-3-5-7) composed of a root (C), major third (E), perfect fifth (G) and major seventh (B).
The extensions (the upper-structure) of Cmaj7 derived from the C major scale (the diatonic scale) are the ninth (D), the eleventh (F) and the thirteenth (A).
These three chord-tones represent the upper-structure of Cmaj13.
From this you can see that a Cmaj13 arpeggio is built with four distinct secondary arpeggios that are Cmaj7, Em7, G7 and a Bm7b5.
This is closely related to another technique very used by improvisers, composers and arrangers called diatonic substitution.
Degree II (min7)
The Dmin13 arpeggio below is a combination of four seventh arpeggios.
Dmin7 (D-F-A-C), Fmaj7 5 (F-A-C-E), Amin7 (A-C-E-G) and Cmaj7 (C-E-G-B).
Degree III (min7)
Em11 (b9,b13) is produced when you harmonize the degree III of the diatonic scale.
It is built with four tetrad arpeggios.
Em7 starting on the root, G7 starting on the third, Bm7b5 starting on the fifth and Dm7 starting on the minor seventh.
Degree IV (maj7)
When stacking thirds on the degree IV of the major scale you get an extended major 7 arpeggio named maj13(#11).
This arpeggio is composed of four secondary arpeggios : two major 7 arpeggios and two min7 arpeggios.
Degree V (7)
The following exercise shows how the V degree (dominant) can be extended with three chords-tones, thus giving four seventh arpeggios. G7, Bm7b5, Dm7 and FMaj7.
Degree VI (min7)
The arpeggio of the VI degree is a minor seventh arpeggio extended with a 9th, 11th and 13th.
You can see the four superimposed arpeggios within this extended arpeggio.
Degree VII (m7b5)
The last arpeggio related to the VII degree of the diatonic scale contains a b5, b9 and b13.
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