some points about triads

Triads are 3 note chords built out of 3rds. Here are the 4 basic types:

These are in root position and close voicing, but triads can be spaced out more, inverted (i.e. the root needn't be the lowest note) and can have more than 3 notes so long as there aren't more than 3 different notes. The following are all A major chords:

I tend to regard the Augmented and Major triads as related (both contain major 3rds) and the Minor and Diminished as related (both having minor 3rds). But actually the Major and Minor are related as they both contain a Perfect 5th. The Augmented and Diminished triads have no commonality at all -- in fact they're kind of "opposites":



Traditionally triads ended up having harmonic functions as they conveyed a sense of key. They acquired names based upon their root as it related to its parent scale:

I tonic
II supertonic
III mediant
IV subdominant
V dominant
VI submediant
VII leading tone

(The 'sub' label does mean under: a subdominant chord is a fifth below just as the dominant is a fifth above the tonic. The submediant is a third below the tonic, just as the mediant is a third above.)

Keys were established by a strong V - I relationship, usually by a
II - V - I
(root movement of a fifth being felt strongest). In the 20th century triads were used by composers much, much more freely as keys were less important than modality or color. You'll find Ponce using progressions like D min to Eb min, F min to B maj, C maj to Gb maj to C maj (all in his fabulous piece Variations sur "Folia de Espana" and Fugue -- vid. variations vii and viii). Of course the voicing is important, but more on that later.

See also Sixth Chord.