In discussing key signatures, we found that repeatedly ascending intervals of a perfect 5th cycles through all twelve pitch classes before repeating. And if we alter a particular one of those perfect 5ths by a half step–creating a diminished 5th after moving through the first seven letter names–the cycle repeats back on itself and creates the diatonic collection of seven pitches that we associate with Western diatonic tonality.
This effect can be further demonstrated by stacking intervals of a diatonic 5th on the major scale.
If the study of 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 adding a third chordal 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 our ultimate goal is to describe how triads function harmonically, it is important that we are able to identify the structure of triads themselves independent of their diatonic functions, so we will begin by studying their intervallic structure.
All diatonic triads have exactly three pitches, although chordal members may be doubled and 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.
As dyads have two pitches, the word “triad” implies any collection of three pitches. In diatonic music, however, we use this word to refer to a certain intervallic structure, so until we reach the unit on post-tonal harmony, you may assume that the word “triad” refers to the stacked thirds of diatonic harmony.
Using the examples below:
Because ABC notation is not capable of using superscript, the inversion figures in the next example are notated as fractions. If you were to write these by hand or use custom notation software, you would notate all inversion figures using superscript. For example, a major chord in first inversion would be written as M6
Your first goal should be to come up with a way to define each triad quality. To begin, you may classify triadic qualities by dividing them into two groups based on the defining chord members of the triads.
When looking at a diatonic triad in root position:
From this, we can create a couple of simple groupings based on the chord members:
Therefore, if a triad is in root position, you can determine triad qualities by the measuring the intervals of the stacked thirds.
Having identified the intervallic structures of each triad, we can look at the various inversions of these triad. This entails knowing the naming conventions of inversions, the shorthand method for labeling them, and a method for determining the chord quality of a triad that is not presented in root position (stacked as two thirds on top of each other.) From the simple presentation of the above example, you should be able to identify that it is not necessary to know each interval within a triad to determine the inversion, but instead, you only need to identify the chordal member in the bass.
5
and 3
refer to the simple intervals above the bass6
and 3
refer to the simple intervals above the bass6
and 4
refer to the simple intervals above the bassOf note, there are six different possible intervals in a triad, depending on the inversion: two 3rds, two sixths, one fourth, and one fifth. These intervals always exist between the same two chord members.
This information is all important, but it assumes that you already know which chordal member of an inverted triad is the root. To develop a method for finding the root of an unnamed chord, we must first understand how the inversion interacts with the chord’s voicing.
Using the examples of open and closed voicings, students often work through the following process:
The final definition combined these three ideas.
Understanding the difference between the terms root and bass is the last piece of information necessary to find the quality of any chord; students often confuse the two. The term bass always refers to the lowest voice of any chord. The root is the lowest member of the chord if the chord is in root position, meaning that the triad is stacked as two thirds. If a chord is in root position, the root and bass will be the same pitch, however if a triad is in first or second inversion, the root and bass will be different pitches.
Combining a knowledge of inversions and voicings is critical in correctly identifying chord qualities. Teachers often suggest to students that they can find chord qualities by putting a chord in root position, but a chord in root position can be spread across multiple staves and still difficult to parse. We really mean that they should put the chord in root position and closed voicing. This allows the student to look at the interval qualities and determine the quality of the triad based on their knowledge of triadic interval structures.
I also suggest that you look at the method for identifying triads from the Open Music Theory. You can find this listed under the Further Reading for this topic.