Harmony encompasses the study of chords and how they relate to each other. Here, we focus on diatonic harmony, that is, the study of chords of a given scale.
If you need to refresh your memory about all this, now would be a good idea to go back to chords, intervals and scales.
A scale contains seven chords that use the notes of a given scale. Just like diatonic notes, these seven chords are diatonic because they are said to belong to the scale.
In the following, we are gonna build those seven chords considering the C major scale:
1 2 3^4 5 6 7^8
C D E F G A B C
The first chord consists of the root, the 3rd and 5th degrees of the scale, that is, C-E-G, which we recognize as being the C major triad, or C. It is named the I chord. The roman numeral 'I' stands for one here. It is capitalized to indicate that this is a major chord.
The second chord is built with degrees 2, 4 and 6, that is, D-F-A, which we know is the D minor triad, or Dm. It is named the ii chord. The roman numeral is this time not capitalized to indicate that it is a minor chord.
The third chord in the progression is built with degrees 3, 5 and 7, that is, E-G-B. This is the E minor triad, or Em. It is the iii chord.
We do the same thing for the next degrees and get:
F for the IV chord,
G for the V chord,
Am for the vi chord,
B° (Bdim) for the vii° chord.
We have the following progression for the C major scale:
C Dm Em F G Am B°
This is the general sequence of chords for major scales (in terms of quality):
I ii iii IV V vi vii°
It indicates that the chord qualities go in the following order:
major minor minor major major minor diminished
We could write the chord progressions for all major scales (12 of them) and we would get the same exact progression in terms of quality. This is why these chords get their own roman numeral numbering, which indicates the position in the progression but also the quality.
We can do the exact same thing we did for major scales to the minor scales. We would obtain the following progression:
i ii° III iv v VI VII
Just like with scales, the diatonic chords of a minor scale follow the same progression as those of a major scale, but starting from the 6th.
Major harmony with seventh chords
Why not do with four what we can do with just three? Seventh chords go to the next level by adding a fourth note to the triads.
To build a seventh chord, we consider the triad and add a seventh degree pitch. We also add a '7' at the end of the corresponding triad's name (if the chord is major, we also add 'maj' before the '7'). For example, the first chord of the C major scale is Cmaj7 made up of the 1st, 3rd, 5th and 7th degree pitches.
The chord progression becomes:
Imaj7 iim7 iiim7 IVmaj7 V7 vim7 viiØ7
In the C major scale (key of C), the corresponding chords are:
Cmaj7 Dm7 Em7 Fmaj7 G7 Am7 Bm7♭5
The V chord is a dominant seventh chord. The vii chord is called a minor seventh flat five chord also known as half-diminished (hence the Ø symbol).
This pretty much ends our delving into music theory. If you want to know more about it, you may want to read some music theory books, for example, Music Theory: a practical guide to all musicians by Barrett Tagliarino.