When our discussion of key signatures, we explored how the interval of the perfect 5th was the impetus for dividing the octave into twelve parts. By inserting a non-perfect 5th into the string of perfect 5ths once we have moved through the first seven letter names, we found the critical change from which diatonic functions arise.
The effect of this change can be seen easily when looking at the diatonic 5ths stacked on a major scale.
If you study the evolution of music, you will find that early harmony focused on perfect intervals, but diatonic harmony as we know it did not truly begin until composers began dividing the perfect 5th by adding a third chord member. This chordal third created two stacked intervals of a 3rd called a triad. Any harmonic system which relies on stacking thirds is called tertian harmony.
Triads are important to almost all of Western music and form the basic unit in diatonic (key-based) harmony. While many theoretical systems have evolved to describe how triads function harmonically, it is important that we are able to identify the structure of triads themselves independent of their key-based functions, so we will begin by studying their intervallic structure.
As dyads have two pitches, all triads have exactly three pitches, although certain chord members can occasionally be omitted (and therefore implied) depending on the context. We name the chord members by the distance above the bottom pitch when the chord is stacked in thirds:
This can be confusing to beginning theory students, because we refer to intervals, scale degrees, and chordal members using the same ordinal numbers – thirds, fifths, etc. – and most often do not use the word “chordal”. As you become more experienced in describing these things, you will be able to discern the meaning from context, but if you would like to avoid confusion for now, you can preface the ordinal number with the word “chordal” until you are comfortable.
Because triads have three pitches, there are three possible configurations that depend on which note of the triad is in the lowest voice. We will call these inversions, but they are sometimes referred to as positions. The system that we use to label inversions relies on the intervals within the triad.