Intervals, Scales, Chords, and the "CAGED" System:
The major scale is a familiar succession of notes that sounds the same no matter which fret it starts on ("Do Re Mi Fa So La Ti (Do) ..."). It can be used as a basis for defining all of the sounds in our musical system.
If you assign a number to every note of the major scale, you get the "interval" pattern used to define other sounds:
Do Re Mi Fa So La Ti (Do)
1 2 3 4 5 6 7 (1)
That number pattern always forms the same fingering pattern (shape) on the guitar fretboard, and it can be MOVED up and down the neck to start on any note (fret).
The fingering pattern used to play a major scale on the guitar is as follows:
(diagram and tab)
The CAGED Diagrams - the basis of all music theory on guitar:
The entire fretboard chart above can be broken up into smaller, more managable sections, labeled by the letters C A G E and D. The "caged" system is a common way of organizing fingering patterns up and down the guitar neck. These shapes form the basis of every applied concept in music theory on the guitar - all of the scales, chords, and progressions playable on the guitar are created using the interval numbers in these diagrams:
(diagram and tab)
You can put each of those patterns on any fret on the guitar - start on any "1" and count up to "7" - and they will create the same characteristic sound: "Do Re Mi Fa So La Ti (Do) . . . "
It is important to understand that the diagrams can be slid to any fret on the neck. They are "movable" patterns - the number 1 can be put on any fret on the guitar, and all of the other notes are found by relative position (1 fret up, 1 fret down, etc... If you start the pattern on the letter A (i.e., put the number 1 on the 5th fret of the sixth string - a letter A), then you are playing an "A major scale". The number 1 is usually called the "root" note. In an A major scale, the root note is A. In a C major scale, the root note is C, etc... Please reread this section and pick out the numbers in these diagrams until they are thoroughly understood.
The major scale is very important because all of the other scales can be derived from it by changing and/or adding notes to the 1, 2, 3, 4, 5, 6, 7 interval pattern. Chords are created by combining three or more notes of a scale, and playing them together on the fretboard.
Scales are important because they provide the basis for melodies. Scale notes played out of order, and with rhythmic variety, create melodies. Chords are important because they define which notes can be combined together to form the characteristic sounds heard in our musical system. The notes of chords - played individually and combined with scales - also create melodies.
Learning how chords and scales work to create "harmonious" sounds is the basis of understanding how sound works in our musical system. Understanding how those number patterns and shapes work on the guitar, to create harmonious sound, is the purpose of understanding music theory.