Here is a two-octave major scale in the key of C:
The Big Picture
This is known as a triad (3 tones) and is the basic building block of other more complex chords. The 3 notes are the root, the 3rd, and the 5th. Any note but the root can be altered to create a different type of triad. For instance, you could flat (lower) the 3rd and that would make it a minor triad. Or you could sharp (raise) the 5th - that would make it an augmented triad. There are several types of triads and they are all created by altering the 3rd &/or the 5th of the chord.
Adding another 3rd gives us a 7th chord: C-E-G-B or 1-3-5-7. We've now added another alterable note so the possible types increase. Adding another 3rd gives us a 9th, another 3rd an 11th chord; another 3rd yields a 13th. One more 3rd gets us back to C. So in 2 octaves we've stacked up every note in the scale:
C-E-G-B-D-F-A or 1-3-5-7-9-11-13.
This explanation is simplistic - for instance, the notes of a triad (or any chord) don't have to be in numerical order. They could be stacked 3-5-1 or 5-1-3 (these are called inversions). The notes of a triad (or any chord) don't have to be stacked in numerical order (close voicing) but can be spread out in wider intervals, i.e. 1-5-3 (open voicing). Also, you need to multiply the above by 12 keys (all the letter names change although the numerical relationships stay the same within each key) - but I hope you can see the concept. The possibilities are massive but it is a closed system. It is theoretically possible to define and practice every possibility. Every instrument has its own unique limitations and the guitar is no exception; some theoretically possible chords &/or voicings are not physically possible on the guitar. After all, you only have 6 strings and 4 fingers (5 if you count your thumb!). So as we go through the theoretical possibilities you gain the knowledge of the instrument, i.e. what is possible and what is not possible on the guitar.
I guarantee you more is possible than you've ever realized!
The scale degrees are numbered 1 through 15.
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:
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