Chords and how they function in a key are refered to by an identification system called roman numeral analysis. Each chord in a key is assigned a roman numeral so that their root relationships can be studied. The root of the chord and its scale position in the key determine the roman numeral assigned. Upper case roman numerals signify major triads in root position while lower case roman numerals signify minor triads in root position. A "o" is used after a roman numeral to indicate that a triad is diminished and a "+" for augmented. In all major keys the tonic triad (I) is major, the supertonic and mediant triads (ii and iii) are minor, the subdominant and dominant triads (IV and V) are major, the submediant triad (vi) is minor, and the leading-tone triad (viio) is diminished.
The following example shows how triads in the key of C major are identified with roman numerals. Notice that I, IV, and V are major; ii, iii, and vi are minor; and viio is diminished.
Diatonic Triads in Major
The quality of the triads in a minor key are different from major. They also differ depending on which form of the minor scale is being used. Scale degrees 6 and 7 are variable and give rise to six additional triads. Compare the triad qualities of each of the following minor key examples. Notice that all the triads except tonic can be of more than one quality.
Of the thirteen possible triad qualities in minor some are used more often than the others. Those shown below are the most frequently used triad qualities in minor. Notice that the roots belong to the harmonic minor scale and the notes of each triad comes from the natural minor scale except for V and viio which come from the harmonic minor scale.
Diatonic Triads in Natural Minor
Diatonic Triads in Harmonic Minor
Diatonic Triads in Melodic Minor
Common Triads in Minor
Roman numerals are used to indicate the sequence of chords in a music example. Look at the Schubert example below. The key of the example is indicated by writing the key name below the key signature followed by a colon. Underneath each chord change is placed a roman numeral. This example is in A-flat major and the chord progression is I - IV - V - I or Ab major - Db major - Eb major - Ab major. The chord progression I - IV - V - I is very common in tonal music.
from Impromptu, op. 90, no.4 by Schubert
This example by Brahms is in Bb major. It consists of a sequence of triads in root position.
from Ich Schell mein Horn ins Jammertal, Op. 43, No.3 by Brahms
Notice the sequence of chords in this example. In the progression vi - ii - V - I each of the roots are related by ascending fourths or descending fifths. This type of chord progression is very common in tonal music.
from Rondo a capriccio, Op. 129 by Beethoven