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Watch the Theory online guitar lesson by Brad Carlton from Guitar Lab: The Golden Arp

The Add 9 arpeggio consists of four notes: the root, third, fifth and ninth steps of the major scale. The ninth is the octave of the second scale degree so we will think in terms of a condensed arpeggio, ie 1 2 3 5. This places all four notes within one octave.

Consult example one to see which scales the Add 9 arpeggio is a subset of. As you can see, 1 2 3 5 is a subset of four different scales. The Ionian 1 2 3 4 5 6 7 , the Lydian 1 2 3 #4 5 6 7, the mixolydian 1 2 3 4 5 6 b7. What this means is that everything you learn in this group of lessons can be used when dealing with these four scales. You may add other notes from the prevailing tonality to color the Add 9 arpeggio to convey the harmonic color of your choice.

By thinking in terms of note subsets, you can then thoroughly research all applications of note groups. Be sure to apply this principle to everything you learn.