Diatonic harmony- the building block of composition

Note: Before you read this post it would help you if you read my post on notes, the major scale, and building chords.
As discussed previously a diatonic scale is a scale consisting only of the 7 notes which fit within a givins scale's formula. The most famous and useful (at least in western music) is the major scale (i.e. The major scale is diatonic b/c is consists of all 7 notes derived from the W-W-H-W-W-W-H formula). If you recall, major chords are built from the major scale by taking the 1,3, and 5 notes of the scale and the minor chord is made by taking the 1, 3b, and 5 notes of the major scale. These notes are chosen because chords are made by stacking either major or minor 3rd intervals (See my post on intervals if you don’t know what major and minor 3rds are)

Now lets get into the diatonic harmony. Basically diatonic harmony is using the 7 notes of a scale to make 7 different chords that are all in the key of the root note. So all the notes and chords in diatonic harmony will only use scale tones. No outside tones are used.
We will use the key if C major as an example. As discussed before the C major scale is C – D – E – F – G – A – B – C. This is in the key of C because the 1st note of the scale is C. So if you start from the C note and “stack 3rds” (note, an easier way to look at stacking thirds is that we are using every other note) we get C, E, G—or the 1, 3, 5. Those are the notes of the C major chord. But how do we derive other chords from the C major scale? Simple. We just start stacking thirds from another note and then compare the results to that notes major scale. Here is what I mean:

If we start on the second note, D, and stack 3rds we get the notes D, F, and A. Lets compare those notes to the D major scale so we can see what chord that is. Let’s apply our major scale formula of W-W-H-W-W-W-H to the D note. The result is D-E-F#-G-A-B-C#-D. So the notes D, F, and A would be the 1, 3b, 5 of that scale. (because the F# note is flatted to an F). So 1, 3b, 5 is the formula for a minor chord. So the notes D, F, A are a D minor chord. So the second chord in the C major diatonic harmony is D minor!
Lets look at the rest of the notes. (blue represents the 1st note) 
So we have
E, G, B or the 1, 3b, 5 compared to the E major scale of E-F#-G#-A-B-C#-D#-E. that gives us an E minor.
F, A, C or the 1, 3, 5 compared to the F major scale of F-G-A-Bb-C-D-E-F. That gives is F major.
G, B, D or the 1, 3, 5 compared to the G major scale of G-A-B-C-D-E-F#-G That gives is G major.
A, C, E or the 1, 3b, 5 compared to the A major scale of A-B-C#-D-E-F#-G#-A. that gives us an A minor
B, D, F or the 1,3b, 5b compared to the B major scale of B-C#-D#-E-F#-G#-A#-B. That gives us B diminished.
So the diatonic chords of C major are:

Note the roman numerals below each chord. These refer to the degree of the scale each chord is build on. And the case of the numeral indicates if that chord is major or minor. The little “zero” by the vii indicates that chord is diminished. So if someone says they are playing a ii-V-I ( 2-5-1) in the key of C they want you to play the chords Dm, G, C.
It’s also important to note that each one of these scale degrees as a different name: