The Big Picture

The Vertical Approach

Here is a 2-octave major scale in the key of C. The scale degrees are numbered 1 through 15. Keep in mind that
when you change keys the letter names change but
the numerical relationships stay the same. Chords are built
by stacking 3rds. C to E is a 3rd and E to G is a 3rd.
It would look like this on the staff:

This is known as a triad (3 tones) and is the basic building block of other chords. The 3 notes are the root, 3rd, and the 5th. Any note but the root can be altered to change the type of triad. For instance you could flat the 3rd to make it minor or sharp the 5th to make it augmented...and so on.

Adding another 3rd gives us a 7th chord. Keep in mind that we've just added another note that can be altered so the possible types increase. Add another 3rd and you get a 9th chord. Another 3rd gets an 11th, another 3rd gets a 13th. One more 3rd gets us back to C. So within 2 octaves we've used every note in the scale. C-E-G-B-D-F-A or 1-3-5-7-9-11-13. This explanation is simplistic (multiply the above by 12 different keys) but I hope you can see the concept. The possibilities are massive but it is a closed system. It is theoretically possible to practice every possibility. Every instrument has its own unique limitations and the guitar is no exception. Some theoretically possible chords are not physically possible on the guitar. So you must learn your instrument also.

What about scales? A complete understanding of harmony (chords) will make your soloing much more interesting. I view a typical 7-tone scale as a 7th arpeggio with 3 non-chord tones added. Knowing which notes are chord tones then allows me to apply the principles of my harmonic knowledge to my single note soloing. So even when I'm playing one note at a time my concept is still vertical.

My teacher, John Elliott, called this approach "the Theory of Harmony".

It is this "vertical-ness" that makes western music unique among all the musics of the world.