Lesson 3a - Triads

In discussing key signatures, we found that repeated ascending P5 intervals 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 similar to this example, but diatonic harmony as we know did not truly begin until music began regularly featuring a third chordal member. By stacking two intervals of a third, we create a triad, which contains not only the two thirds, but also the interval of a fifth between the outer pitches. 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.

Building diatonic triads

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:

• the lowest pitch is called the root of the chord
• the pitch that is a 3rd above the root is called the chordal third
• the pitch that is a 5th above the root is called the chordal fifth

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.

Triad inversions

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.

A note on terminology

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.

Goals for this topic

Using the examples below:

• determine what role each chord member – root, third, and fifth – plays in determining the quality of a triad
• find all three intervals contained in a root-position triad for each chord quality
• find the rest of the interval sizes between chord members of a triad (Hint: This may involve moving some chord members up or down an octave)
  • thirds (2)
  • fourth (1)
  • fifth (1)
  • sixths (2)
• relate these interval sizes to our system for labeling triad inversions
  • provide inversion figures for root position, first-inversion, and second-inversion triads
• be able to explain how to turn any inverted and/or open-voiced triad into a root-position triad in a closed voicing

Triad qualities

Triad inversions

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

Triad voicings

Conclusions

Your first goal should be to come up with a way to define each triad’s 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:

• If the chordal fifth is either a diminished or augmented fifth, then the triad is labeled as diminished or augmented respectively.
  • Diminished triads always have a minor 3rd between the root and chordal third.
  • Augmented triads always have a major 3rd between the root and chordal third.
• If the chordal fifth is a perfect fifth, the chordal third determines whether a triad is major or minor.
  • Major triads have a M3 above the root.
  • Minor triads have a m3 above the root.

From this, we can create a couple of simple groupings based on the chord members:

• Between root and chordal 3rd
  • Augmented and major triads always have a M3 (or inversion)
  • Minor and diminished triads always have a m3 (or inversion)
• Between root and chordal fifth
  • Major and minor triads always have P5 (or inversion)
  • Diminished triads always have a d5 (or inversion)
  • Augmented triads always have an A5 (or inversion)

Therefore, if a triad is in root position, you can determine triad qualities by the measuring the intervals of the stacked thirds.

• Major: M3 + m3
• Minor: m3 + M3
• Diminished: m3 + m3
• Augmented: M3 + M3

Inversions and their labels

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 inversions
• 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 have realized that you cannot identify the inversion of the chord until you know the root. The simplest method for finding the root for any triad is to re-arrange the pitches until you have a triad that is stacked using only thirds. To be clear, this means no fourths, no sixths, and everything within a octave. You can even eliminate any duplicate pitches. Once you have this simplified arrangement of pitches, you can easily determine the root and quality of the chord using the method above.

For inversions, it is not necessary to know each interval within a triad, but instead, you only need to identify the chordal member in the bass.

• Root position: 5/3
  • the root of the chord is in the bass
  • The 5 and 3 refer to the simple intervals above the bass
• First inversion: 6/3 (shortened to 6)
  • the 3rd of the chord is in the bass
  • The 6 and 3 refer to the simple intervals above the bass
• Second inversion: 6/4
  • the 5th of the chord is in the bass- The 6 and 4 refer to the simple intervals above the bass

Of 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.

• The thirds exist between the root/third and third/fifth
• The sixths come when you invert these either of the thirds, so between the third/root and fifth/third
• The fifth always exists between root/fifth
• The fourth is the inversion of the fifth, so between fifth/root

Chordal voicings

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 a process that includes the following ideas:

• Attempt #1: Open voicing is spread out.
  • True, but this is a subjective measure. What constitutes “spread out”?
• Attempt #2: Closed voicings use only simple intervals and open positions have compound intervals.
  • This is interesting in that it works if the chord only has no repeated pitches, but does not hold up if a chord has repeated notes or more than four distinct pitches.
• Attempt #3: - Closed voicings contain all chord members within one octave.
  • This is almost there , but does not explain how a chord with more than four pitches can be in closed position.
• Attempt #4: Open voicing skips one of the voices.
  • This definition is almost there, but the term “voices” is problematic because “voices” does not relate directly to a chord.

A complete definition combines these ideas.

• Closed voicing stacks all pitches of a chord in an ascending order that does not skip a chordal member.
• Open voicings can have chord members stacked in any order and skip chord members.
  • All open voicings will cover more than one octave because of this.

Root versus bass

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.

Finding a chord quality while inverted

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.