Roman Numeral notation / analysis of chord progressions

Let us take a standard seven-note scale. A chord that is formed by using the 1st, 3rd and 5th note of a scale is called a basic triad / chord. This chord formed using original scale is the I chord of the scale (root note is the 1st note of the scale). Now, let us move to the next scale degree – starting the scale from what would have been the second note of the original; the 1st-3rd-5th chord of this degree is the II chord (root note of this chord is the 2nd note of the scale).

Similarly for III, IV, V, VI and VII. The VIII chord means that the root note of the chord is back to the original. So it is the I chord again, and it is written as I and not VIII. When we get a major or an augmented chord in such a process, the chord is written out in capital letters (e.g. I, IV, V) and when it is a minor or a diminished chord, it is written in small letters (e.g. ii, vi). Augmented chords are written with a "+" sign, diminished are written with a "o" sign above the number.

Let us take the example of C major: CDEFGABC

The basic triads obtained by taking the first three notes from each scale degree are:

CEG – C major (I)
DFA – D minor (ii)
EGB – E minor (iii)
FAC – F major (IV)
GBD – G major (V)
ACE – A minor (vi)
BDF – B diminished (viio)

Again, the G major scale is: G A B C D E F# G, and the chords are:
I = G major, ii = A minor, iii = B minor, IV = C major, V = D major, vi = E minor and viio = F# diminished.

Again, F major scale is: F G A Bb C D E F, and the chords are:
I= F major, ii= G minor, iii = A minor, IV = Bb major, V = C major, vi = D minor, viio = E diminished

Thus we find that any major scale gives three major triads that together can harmonize (sound good with), every note of that scale. They are the I, IV and V chords. It also provides three relative minor chords, one related to each of the three major chords, viz. the ii, iii and vi chords. Apart from these there is a diminished chord at viio. Thus the basic chords of a major scale are:

I – ii – iii – IV – V – vi - vii^o

continued....
http://basicmusictheory.blogspot.com/2009/10/roman-numeral-notation-analysis-of.html

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