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Symmetrical arpeggios are regular arpeggios with all of their 'data' condensed onto two strings. This allows the same shape to be played in each octave or two-string grouping. Instead of playing an arpeggio through a particular position or chord shape, we now have the ability to perform this arpeggio in a linearly fashion up the fretboard, at speed, without learning new shapes.
Refreshing the Basics
Take this regular Gmaj7 arp (R, 3, 5, 7) playing through Shape 1 of G Major.
*blue denotes chord tones
Condensing the Data
All of the intervals in the above arpeggio are contained in the first four notes that you play (R, 3, 5, 7), before repeating up an octave. If we relocate the 7th interval so that we now start with this note, we can condense the information of this arpeggio onto only two two strings:
Now move this shape up an octave onto strings 4 and 3:
And finally onto strings 2 and 1:
By having the same fingerings in each octave, you should now be able to play through this arpeggio faster than the traditional shape. You can execute this arpeggio by using a consistent alternate picking technique, or by picking each new string in turn and using hammer ons and pull offs for the other notes. Please transpose into any key.
Changing the Tonality
We can adopt the same principles for other tonalities, such as dominant and minor 7th arpeggios, as well as m7b5. Below are examples of each:
Extending the Usage
As a teaser, try this sneaky trick for size. If an Am7 is being played, you don't need to use the same arpeggio during improvisation to make things interesting. Over this chord, I often play a Gmaj7 arpeggio (in symmetrical form if I want to burn across the fretboard).
Gmaj7 contains the notes G, B, D, F# - yielding the intervals b7, 9, 11, 13 over the Am7 chord. Instantly this implies a Dorian tonality. This superimposition of arpeggios over chords is a lesson in itself and indeed a vast topic.