Theory of guitar

Chords and chord progressions are derived from various scales and the intervals contained within those scales. In order to understand chords and chord progressions, you must understand how these scales can be broken down into various combinations of intervals.
we explored the relationship between the root note and each of the other intervals contained within both the major scale and the minor scale as they lay out across any two adjacent strings.
Let's put a couple of these intervals to work and make some music.

we learned that the most basic chord is called a TRIAD and that triads are built by combining the R, 3 and 5. These are the most important intervals to memorize. We will be working with the 3rd in this lesson and the 5th in the next lesson. The rest of the intervals will be addressed in later lessons.
Also  we discussed the fact that two or more notes played together creates HARMONY. What we're going to do is HARMONIZE the major and minor scales using 3rds and 5ths from the scale.
Start with the C major scale on the A-string:

To add the 3rd harmony, we need to figure out which note from the scale is two notes above each of our scale tones. This note will give us a 3rd to play along with our original notes. That may sound weird - going up the scale two notes to get the 3rd - but the note you start with is 1, the next note is 2 and the next note is the 3rd.
So, if we start with the first note, C, and number that note 1, then D would be 2 and E would be 3. We've done this enough times already that you should be saying, "Hey... haven't we done this already?" Yes, we have. But this time, we're going to give it a new twist.
Now, let's do the same thing for the second note in the scale. D is 1, E is 2 and F is three. So F is going to be the 3rd of D within the scale.
I keep saying within the scale or from the scale, because the 3rds that we get by using only notes from the C major scale won't necessarily match up with the 3rds that we would normally get by following a different major scale from each note. We'el take a good look at this in a moment, though. For now, just find the notes that are going to act as our harmony.
If we do the same thing that we did with the C and D to each of the remaining notes of our scale, we get: G A B C D as the harmony notes for E F G A B, respectively. Notice that each harmony note is found from within the original major scale.
Let's add this all together on the staff:

Remember that harmony means to play two or more notes at the same time. This is shown on the staff by stacking the notes on top of each other with the note heads attached to the same stem. When you see notes on the staff stacked like this, the notes in each stack are played together.

Now, a moment ago I mentioned that the 3rds derived in this manner don't necessarily match the 3rds that you would get by using a major scale from each note. This is what I mean by that.
Take a look at the D and F harmony on the second beat of the first measure. We know from the D major scale (D E F# G A B C#) that the major 3rd of D is F#. Therefore, F (half-step lower) would be the minor 3rd of D. We can verify this by comparing this interval to the scale that we know that has a minor 3rd, the D natural minor scale (D E F G A Bb C). If you haven't worked out the minor scale in every key, you better do that. You really DO need to know this stuff.
So C to E is a major 3rd and D to F is a minor 3rd. What about E to G?
There are three ways that you can check and verify an interval. The first way is to use the major scale starting from the same note as the lowest note of the interval. If you want to find out what interval E to G is, then you could compare that to the E major scale (E F# G# A B C# D#) and see how things line up. The second way is to compare to the minor scale starting from the same note as the lowest note of the interval. In this case you would use the E minor scale (E F# G A B C D). If you use the minor scale, you have to remember that the 3, 6 and 7 are already flattened (minor) in that scale.  if you are not clear on this point.
In my opinion, it is best to stick with using the major scale to compare and verify intervals so that you avoid the confusion that can occur if you forget to account for the intervals that are already altered within the minor scale.
A third way to compare and verify intervals is to see them on the guitar neck. This method works very well when combined with your knowledge of the major and minor scales.
we went to the trouble of dissecting the scale and learning to see each interval of the scale lying on an adjacent string. The purpose of that exercise is to make you aware of what the intervals look like on the guitar itself.
Let's take a look at the major and minor 3rd:

Major 3rd   Minor 3rd

Now let's look at how our harmonized scale lays out on the A and D-strings:

Seen this way, it is immediately obvious which harmonies are major (C-E, F-A, G-B) and which are minor (D-F, E-G, A-C, B-D).
Let's add this new information onto our staff:

If you look closely, you should see that the major and minor intervals form an easily recognizable pattern:

1st measure: M3 m3 m3 M3
2nd measure: M3 m3 m3 M3

If we look at the whole-steps and half-steps between each harmony, we will see that they are also the same in each measure:

1st measure: M3   m3   m3   M3
    W   W   h  
2nd measure: M3   m3   m3   M3

That leaves only the whole-step between the two measures, so let's put that in:

M3   m3   m3   M3   M3   m3   m3   M3
  W   W   h   W   W   W   h  

Now, we know from working with the major scale in every key, that while each key has a different combination of notes, the intervals are exactly the same, no matter which note you start on. That means that you can use this exact same pattern of major and minor 3rds to harmonize the major scale in any key. All you have to do is play the correct order of the harmonies and follow the whole-step/half-step pattern of the scale.

So, the major scale, no matter what key you play it in, will always yield this exact same pattern of major and minor 3rds, and the harmonies will always follow the same W/h-step pattern. This fact allows us to assign a number to each of the harmonies, so that we can talk about them without regard to which key signature is being used:

I   ii   iii   IV   V   vi   vii   I
M3   m3   m3   M3   M3   m3   m3   M3
  W   W   h   W   W   W   h  

In this case, Roman numerals are used instead of regular (Arabic) numbers. This is to distinguish between intervals (which are designated with Arabic numerals) and harmonies built from each note of the scale (which use Roman numerals). Notice that upper case numerals are used to designate major and lower case numerals are used to designate minor.
These Roman numerals are very important, because they are used to analyze and identify the chords within a chord progression. We'el talk some more about this in the next lesson. For now, just learn to call each harmony by the correct number, and memorize the pattern of major and minor, as well as where each type sits along the W/h-step pattern.

Now, before I set you to work playing this harmonized scale in every key and on every pair of strings (You knew that was coming, didn't you?), let me point out one more thing.
You know that the scale can be played up and down the entire length of the string. Once you reach the octave, you can just keep going higher through the scale until you run out of frets. You also know that you can play any notes from the scale that are below your starting note. This is also true for the harmonized scale. Notice that both the starting harmony and the ending harmony are considered I. This is because they are the same harmony. They're just an octave apart. Any notes that are an octave apart (higher or lower) are considered the same thing. This is because notes that are an octave apart function the same within a song.
So, once you reach I an octave higher, you can keep going into the next octave until you can't play any higher. The same thing is true for any scale tones that are below your root note. They can be harmonized too.
You need to practice the harmonized scale all the way up and down the strings, not just from I to I.
Also, when you are working with the G and B-strings, remember that the note on the B-string will be a fret higher than usual. This is always true when it comes to the B-string.

This is where I get to tell you what you should already know by now. You need to work this harmonized scale out in every key on every pair of strings and all the way up and down the neck.
Go for it!